Hierarchical DEMATEL-DTP Method for Identifying Key Factors Affecting Plateau-Characteristic Agroecological Security

Abstract

The development of agriculture with special characteristics has become a global trend, especially in highland areas with unique local advantages. Plateau-characteristic agriculture plays an important role in ensuring food security, maintaining ecological balance, and promoting sustainable development in plateau areas. However, because many plateau areas are ecologically fragile and have limited environmental recovery capacity, failure to manage them properly can lead to irreversible environmental degradation and affect socioeconomic stability. Therefore, ensuring plateau-characteristic agroecological security (PCAES) is particularly important and warrants in-depth investigation. However, existing research has yet to systematically identify the key factors affecting PCAES. To fill this gap, this study analyzes 41 factors affecting PCAES at the macro, meso, and micro levels. Then, a DTP (driver–pressure–state–impact–response–management (DPSIRM), technology–environment–resources–economy (TERE), and production–operation–service (POS), collectively referred to as DTP) hierarchy is established to analyze the factors from different perspectives. On this basis, we use a hierarchical decision-making trial and evaluation laboratory (DEMATEL) method to identify nine key factors that influence PCAES, including biodiversity indices, intensity of investment in pollution control, a comprehensive mechanization rate of major crops, and intensity of agricultural R&D investment, among others. Finally, based on the interrelationships among these key factors, we put forward recommendations for PCAES management, taking into account domestic and international experience and the actual situation of the plateau region. Clarifying the factors affecting PCAES will help local governments undertake targeted risk management and scientific decision-making and promote the sustainable development of local economies.

1. Introduction

A strong agricultural foundation contributes to national stability. “Characteristic agriculture“ is a new development in contemporary agriculture. It is a modern form of agriculture that transforms the unique agricultural resources of a region into characteristic agricultural products. It is considered representative of new, high-quality productive forces. Today, there is a global trend toward improving the quality and added value of agricultural products and developing specialized, large-scale, intelligent characteristic agriculture [1]. Japan, for example, has promoted the “one village, one product“ initiative to maximize productivity despite limited arable land [2]. South Korea’s “Saemaul Movement” exemplifies how local government support can drive the development of characteristic agriculture [3]. Western Europe has developed mixed agriculture that combines planting and animal husbandry in alignment with local realities [4]. The US and Germany, meanwhile, are pioneering the use of artificial intelligence in agriculture, highlighting a key future direction for characteristic farming [5,6]. Based on its unique agricultural context of ”big country, small farmers,” China has set goals focused on becoming a modern agricultural powerhouse. While characteristic agriculture has improved the quality and efficiency of agricultural production, the overexploitation of resources has degraded agroecosystems, posing challenges to the long-term sustainability of agriculture [7]. This conflict between agriculture and environmental protection can undermine sustainable development, thus warranting urgent attention [8].

Various plateau areas around the world (e.g., the Deccan Plateau in India, the Colorado Plateau in the US, and the Yunnan–Gui Plateau in China) have taken advantage of their unique natural and geographical features to develop diverse, adaptable, and resilient forms of characteristic agriculture. However, a tendency to emphasize economic development while ignoring environmental protection persists in some plateau regions [9]. Therefore, when promoting the development of plateau-characteristic agriculture (PCA), it is necessary to adopt a systematic approach consistent with the principles of ecological development, focusing not only on economic growth and increasing the agricultural product supply but also on improving environmental sustainability [10,11]. The UN’s Sustainable Development Goals specify that agricultural production needs to adopt practices that boost yields while safeguarding ecosystems [12]. Agricultural research has accordingly shifted its focus from enhancing production efficiency [13] and fostering technological innovation [14] to prioritizing rational resource utilization [15], ensuring food security, maintaining agroecological safety [16], and achieving sustainable agricultural development [17]. Related studies have focused on areas such as agroecological security (AES) and characteristic agriculture.

Agricultural sustainability is directly tied to food security [18]. Studies of AES mainly focus on its problems and current state. First, the problem of AES arises from imbalances and contradictions in the relationship between elements within the agricultural system, especially between inputs and outputs. Studying the evolution of Spanish agriculture from 1992 to 2017, Guzmán et al. [19] noted that conflicts between economic pursuits, resource management, and environmental protection generate irrational behaviors that degrade agroecosystems. Relatedly, Grinberga-Zalite and Zvirbule [20] noted that while the increased use of pesticides and fertilizers can increase short-term agricultural output, over time they will erode the ecosystem. Regarding the current state of AES, most studies have used multiattribute, multiobjective, or multicriteria decision-making methods in conjunction with specific data for evaluation [21]. Antle et al. [22] proposed a user-driven approach to developing new agricultural system models and constructed an evaluation framework for agricultural systems. Du and Fan [23] used an analytical network process approach to assess the spatiotemporal dynamics of agricultural sustainability in 30 Chinese provinces. Chen et al. [24] explored the agricultural total-factor productivity of 30 Chinese provinces from 2000 to 2017 using three-stage data envelopment analysis. Sun et al. [25] measured the green efficiency of Chinese agriculture using data envelopment analysis based on the super-efficiency slacks-based measure. Buitenhuis et al. [26] introduced a resilience assessment tool to measure the effect of the EU’s Common Agricultural Policy on the resilience of the Dutch agricultural system.

Recent studies have focused on the benefits and ecological implications of characteristic agriculture. Regarding its benefits, Adenle et al. [27] noted that the economic advantages of characteristic agriculture can help alleviate local poverty. Similarly, Pawlak and Kołodziejczak [28] pointed out that characteristic agriculture can boost the food supply and contribute to global food security. Long [29] added that the production and foreign trade of regionally distinctive agricultural products can improve a country’s export competitiveness. Yang and Solangi [30] found that agriculture with unique characteristics can redirect managerial focus from short-term economic gain to long-term sustainability. Regarding ecological implications, studies have proposed management strategies to address the ecological security challenges that accompany the growth of characteristic agriculture. Xiong et al. [31] suggested that environmental regulation should be moderate, noting that excessive regulation can be counterproductive. Thompson et al. [32] used structural equation modeling to examine the factors influencing European farmers’ adoption of sustainable approaches to agricultural production. Du and Li [33] used the hierarchical decision-making trial and evaluation laboratory (DEMATEL) method to identify the factors affecting the ecological security of marine ranching (which can be considered a form of characteristic agriculture). Feng et al. [34] used an improved nondominated sequential genetic algorithm to explore the optimization of water, energy, land, and CO₂ in agricultural systems.

While AES and the development of characteristic agriculture have received considerable academic attention, studies focusing specifically on plateau-characteristic agroecological security (PCAES) remain limited. Based on a review and synthesis of the existing literature, we find that current research in this area still needs improvement in the following aspects: (1) The factors are not specific to PCAES. Although studies have established AES indicator systems (factors), they are oriented toward the overall perspective of macro-level AES. Since PCA development can be affected by factors such as the abundance of biological resources, fragility of the ecosystem, limitations of land use, frequency of natural disasters, and slowness of economic development, it is debatable whether existing factors are suitable for evaluating PCAES. (2) The factors influencing PCAES have not been systematized. While studies have examined factors based on local ecological conditions and agricultural enterprises’ production and operational behaviors, these factors are still fragmented when viewed in different frameworks. The development process, changes in influences in the system, and interrelationships among factors have not been thoroughly addressed. (3) The key factors affecting PCAES have not been identified. The Pareto principle [35] in management suggests that a limited number of key factors (20%) commonly have the most influence (80%) on the system. In other words, key factors should be controlled to seek Pareto optimization and safeguard PCAES. However, existing studies largely analyze a wide range of factors without clearly identifying the key factors. This is not conducive to solving PCAES problems since it fails to prioritize major contradictions over minor ones.

The goal of this study is to develop a hierarchical DEMATEL-DTP method for identifying the key factors affecting PCAES, followed by practical recommendations to address these issues. First, combining existing research results with the uniqueness of PCA, we sort out the factors affecting PCAES at the macro, meso, and micro levels. Then, we compose a DTP framework based on three models (DPSIRM, TERE, and POS) that are closely related to AES and analyze these factors from different perspectives. On this basis, we construct a hierarchical DEMATEL-DTP method to identify the key factors affecting PCAES and make management recommendations based on the interrelationships among these key factors.

The rest of this paper is organized as follows. Section 2 analyzes the factors affecting PCAES, and Section 3 presents the hierarchical DEMATEL-DTP method. Section 4 describes our results regarding the identification of key factors. Section 5 discusses the interrelationships among the key factors and makes management recommendations. Section 6 concludes the paper.

2. Analysis of Factors Affecting PCAES

PCA is a modern agricultural model that relies on the unique natural conditions and resource advantages of plateau regions, with green development, efficient production, and technological innovation as its core concepts. Its resource endowment is characterized by high-intensity light, thick soil, and high-quality water. Its production methods focus on ecological sustainability, and its development path emphasizes technology-driven industrial upgrading. Such features indicate that PCA is different from ecological agriculture, intensive agriculture, and urban agriculture in developed regions. Thus, the analysis of factors must be based on the actual situation [36,37], fully accounting for the geographic, ecological, and economic peculiarities of PCA.

Therefore, we made extensive references to journal papers, policy reports, and other literature on AES and specialty agriculture to compile a total of 41 PCAES factors including macro, meso, and micro levels. Most of these factors were taken directly from established assessment frameworks [33,38,39,40,41,42,43,44,45], while others were indirectly inferred by analyzing discussions and descriptive content in the literature [36,37,46,47,48,49,50,51].

At the macro level, the factors affecting PCAES mainly concern data on long-term trends and changes in the overall state of the plateau region, typically provided by local or national government departments. These factors encompass aspects such as the ecological quality index, biodiversity indices, per capita water resources, and soil erosion rate. Plateau areas are uniquely endowed with resources, but their ecosystems are more fragile and less resilient to environmental change. The abovementioned macro-level indicators can, to a certain extent, reflect PCA characteristics as well as the current status of PCAES, providing a basis for relevant departments to regulate and protect these areas.

At the meso level (between the macro and micro levels), the factors reflect the characteristics and development dynamics of specific sectors and industries. Examples include PCA profitability, the production of major agricultural commodities, the utilization of agricultural solid waste, and wastewater treatment rates. The PCA production approach emphasizes greenness and sustainability. Indicators at the meso level highlight the importance of integrating ecological sustainability with economic development as PCA clusters adapt to environmental and operational constraints while adopting modern technologies to optimize productivity.

At the micro level, the factors pertain to individual production and operational behaviors (e.g., those of specific enterprises) and their interrelationships. These include indicators such as the number of locally certified agricultural products, the proportion of scientific and technological researchers engaged in agriculture-related activities, and the intensity of investment in agricultural R&D. The micro-level indicators emphasize the role of modern science and technology in enhancing production capacity, aligning with PCA’s focus on improving productivity through technological innovation.

PCA is a system that requires management approaches tailored to its geographic, ecological, and economic realities.

Table 1. The factors of PCAES at macro level.

Factors	Interpretation	Selection Basis	Reference
Natural population growth rate	Birth rate minus death rate.	Continued population growth has indeed boosted agricultural production.	[38]
Urbanization rate	Urban population divided by total population.	The process of urbanization can result in population loss, a decrease in arable land, and the wastage of land resources.	[46]
Per capita agricultural GDP	Agricultural GDP divided by the total population at year-end.	Per capita agricultural GDP represents the overall state of agricultural development.	[39]
Per capita arable land area	The ratio of total arable land area to population.	This indicator reflects the pressure on arable land resources, and a decrease in per capita arable land area will jeopardize agricultural security.	[38]
Per capita water resources	The ratio of total water resources to population.	This indicator reflects the pressure on water resources, and water scarcity has become one of the important factors constraining the sustainable development of the economy and society.	[40]
Ecological quality index	This index typically includes multiple ecological parameters and sub-indicators to comprehensively assess the quality of the ecosystem.	Quantify ecological quality with a numerical range typically from 0 to 100. Higher indices indicate better ecosystem quality, which is more conducive to agricultural production.	[41]
Biodiversity indices	The specific situation of the biodiversity index in agricultural production areas.	Protecting and enhancing biodiversity are crucial for achieving sustainable agricultural development.	[33]
Water pollution concentration	The concentration of pollutants in a unit volume of water.	This indicator reflects the current level of pollution in water resources. The concentration of water pollution directly affects water quality, which has a significant impact on agricultural production.	[47]
Overall compliance rate of routine monitoring	The compliance rate of agricultural products during routine national monitoring for agricultural product quality and safety.	Regular inspections of agricultural product quality and safety enable comprehensive, timely, and accurate understanding and monitoring of the status of agricultural product quality and safety.	[37]
The growth amount of agricultural product exports	The increase in the value of agricultural products exported from the domestic market to foreign countries compared to the previous year.	It reflects the development trends of domestic agriculture and the growth of international market demand, making it a positive economic indicator.
Value added of agriculture and related industries	The proportion of value added created by agricultural and related industrial production activities to GDP in the current year.	It reflects the influence of plateau-characteristic agricultural development on social and economic development.	[42]
Soil erosion situation	The soil erosion rate in agricultural production areas for the current year.	Soil erosion is a form of land degradation that has serious impacts on agricultural production, ecological environment, and human well-being.	[43]
Vegetation degradation situation	The change in vegetation coverage rate in agricultural production areas compared to the previous year.	Plants serve as a crucial safeguard for agricultural ecological security, and a reduction in vegetation is unfavorable for agricultural development.
Losses from anthropogenic or natural disasters	Losses incurred by natural disasters or man-made disasters at a certain stage.	Natural disasters or man-made disasters can cause significant losses to agricultural production and the agricultural ecological environment.	[33]
Policies related to environment and ecology	The proportion of policies related to agricultural environment and ecological safety to the total policies in the current year.	Environmental protection policies play a protective role in ensuring the ecological security of plateau-characteristic agriculture.	[44]
Degraded farmland management area	The area of degraded farmland effectively remediated.	Fertile soil is the most crucial resource in ecosystems; yet these resources are being lost at an alarming rate.	[36]
The intensity of investment in pollution control	The level of financial expenditure and resource allocation by governments and businesses in controlling and reducing environmental pollution.	This reflects the level of importance the government places on local pollution control, which is beneficial for the development of local agricultural ecological security.	[41]
The degree of high-quality farmland construction	The level at which local farmland construction meets high-standard requirements.	High-standard farmland represents the essence of agricultural arable land, serving as a core element in ensuring national food security and a crucial guarantee for promoting high-quality agricultural development.	[37]
Financial investment in agricultural special funds	Special funds invested by national and local governments in projects for the ecological protection of plateau-characteristic agriculture.	By increasing financial support for agriculture, we can ensure the sustainable and stable development of agricultural ecosystems.	[48]
Government subsidy	The amount of fiscal subsidies, tax incentives, and financial support provided by the government in the current year for agricultural ecological security and agricultural development.

,

Table 2. The factors of PCAES at meso level.

Factors	Interpretation	Selection Basis	Reference
Demand for characteristic agricultural products	The demand situation for characteristic agricultural products in the current year.	The demand for characteristic agricultural products can be transformed into the drivers behind the production of these unique agricultural goods.	[41]
Profit margin	The ratio of profit to investment cost in industries related to plateau-characteristic agriculture.	To measure the profitability of enterprises related to plateau-characteristic agriculture. When these enterprises have higher economic benefits, they are motivated to continue developing.	[33]
Effective irrigation area index	The arable land area with adequate water sources, relatively flat terrain, and supporting irrigation infrastructure or equipment, capable of normal irrigation activities in the current year.	This indicator reflects the level of construction of local farmland water conservancy projects and other infrastructure.	[38]
Coverage rate of high-quality seeds for major crops	The proportion of cultivated crops using selectively bred high-quality varieties.	High-quality seeds typically possess characteristics such as high yield, good quality, and strong resistance, which are significant for increasing crop productivity and quality and ensuring food security.	[37]
Land reclamation rate	The proportion of arable land area at the end of the year to the total land area.	Arable land is a crucial foundation for agricultural production, and changes in arable land area directly affect national agricultural security.	[38]
Cultivated land quality class	The suitability of agricultural crops for arable land is categorized into 15 grades by the Ministry of Natural Resources based on their suitability and adaptability.	The grading of arable land quality is crucial for guiding agricultural production layout, alleviating resource and environmental pressures, and improving the quality and safety level of agricultural products.	[45]
Output of major agricultural products	The annual production volume of major agricultural products such as grains, meat, eggs, milk, vegetables, and fruits.	One of the key points of ecological security is to ensure that target crops achieve sufficient output. While emphasizing ecological environment, agricultural development should not be overlooked, and a balance between the two must be maintained.	[37]
Employment and resettlement situation of farmers	The employment and training of local farmers by enterprises related to plateau-characteristic agriculture.	The development of enterprises and industries related to plateau-characteristic agriculture can create numerous job opportunities, thereby increasing farmers’ income and enhancing their enthusiasm for production.	[49]
Comprehensive utilization rate of agricultural solid waste	The proportion of effective treatment and utilization of agricultural solid waste (such as livestock and poultry manure).	Improving the comprehensive utilization rate of agricultural solid waste is of great significance for promoting sustainable agricultural development, improving rural ecological environment, and increasing farmers’ income.	[50]
Wastewater treatment rate	The proportion of treated wastewater to the total volume of wastewater discharged.	Increasing the wastewater treatment rate not only helps to protect and improve agricultural ecological environments but also promotes sustainable agricultural development and enhances the well-being of farmers.	[51]
Leading agricultural industrialization enterprises	The proportion of leading enterprises identified as agricultural industrialization in the total number of agricultural enterprises.	Leading enterprises in agricultural industrialization are at the leading level in the same industry, and the more the number of leading enterprises in agricultural industrialization is identified, the better the agricultural development in the region.	[37]
Comprehensive mechanization rate of major crops	The proportion of mechanized operations in each stage of crop production, from cultivation to harvesting.	This indicator is typically used to measure the level of agricultural mechanization in a region or country, serving as one of the important indicators of agricultural modernization.	[40]

and

Table 3. The factors of PCAES at micro level.

Factors	Interpretation	Selection Basis	Reference
Per capita labor input	Average annual labor hours per square kilometer of cultivated land.	It is an important indicator of the level of intensification in agricultural production, with higher inputs indicating lower levels of agricultural mechanization.	[38]
Consumption of agricultural plastic film per unit of arable land	The ratio of agricultural plastic film usage to arable land area.	Plastic mulch, being non-biodegradable and erosion-resistant polymer compounds, leaves significant residues that not only affect soil quality but also have adverse effects on agricultural ecological environments.	[40]
Utilization rate of fertilizers for major crops	The extent to which fertilizers are absorbed and utilized by crops during the production process.	This reflects the utilization rate of fertilizers. Increasing fertilizer utilization can reduce excessive use, lower agricultural production costs, and minimize environmental pollution.	[37]
Pesticide utilization rate of main crops	The degree to which pesticides applied during crop production are absorbed and utilized by the crops.	Long-term extensive use of pesticides can lead to pesticide residues in the soil, groundwater contamination, reduced crop quality, and adverse effects on arable land and agricultural ecological security.
“Three products and one standard” agricultural products	Refers to the number of agricultural products certified as pollution-free, green, organic, or geographical indication during the year.	It reflects the ecological level of agricultural production and brand value and is an important indicator of the effectiveness of green development.
Utilization of clean technology	Proportion of agricultural enterprises using clean technology in agricultural production.	The widespread use of clean technology can significantly reduce pollution during the production process.	[34]
Comprehensive utilization rate of crop straw	The proportion of crop straw that is reasonably utilized through various means after harvest.	This indicator reflects the level of resource utilization of agricultural waste and is an important measure for promoting sustainable agricultural development and a circular economy.	[37]
Agricultural science and technology personnel	Ratio of the number of agricultural science and technology personnel to the total number of agricultural workers.	The new technologies and varieties developed by scientific and technological personnel are crucial for agricultural development.	[42]
Intensity of agricultural R&D investment	Proportion of agricultural research and development investment funds to GDP.	This indicator is crucial for measuring the importance that a country or region places on agricultural science and technology innovation. It reflects the strategic position of agricultural science and technology in economic development.

detail the macro-, meso-, and micro-level factors.

3. Hierarchical DEMATEL-DTP Method

Here, we present our hierarchical DEMATEL-DTP method. Three models—DPSIRM, TERE, and POS—are integrated to identify the key factors affecting PCAES, which is a complex system. First, we introduce hierarchical DEMATEL and the three models. Then, we give the reasons for their use in terms of their relevance to PCAES. Finally, the steps of the hierarchical DEMATEL-DTP method are presented.

3.1. Hierarchical DEMATEL

DEMATEL [52] is widely used to identify key factors in simple systems across various fields. It faces certain limitations as socioeconomic challenges become increasingly complex. Thus, as problems evolve and intertwine with numerous factors, more sophisticated approaches are needed. Du and Li [53] introduced a hierarchical DEMATEL method tailored to complex systems, which are characterized by an array of factors, diverse types of influences, and layered relationships. Since PCAES has similarly intricate features, we use hierarchical DEMATEL to discern the important elements in the complex PCAES system. Figure 1 presents the detailed framework (see Section 4.1 for explanation of symbols $F_{1:1}$, $F_{1:1\supset 1}$, etc. in the figure, and the same for the rest of Section 3).

Hierarchical DEMATEL allows for investigating relationships in a complex system from different perspectives, which are represented by different rules. In Figure 1, Rule 1 outlines the DPSIRM model, which is used to dissect the mechanisms of six categories of subsystems—driver, pressure, state, influence, response, and management—with regard to sustainable development, and presents the causal relationships and interactions of the factors affecting PCAES. Rule 2 introduces the TERE model, which scrutinizes the mechanism of the four subsystems of technology, resources, economy, and environment in terms of ecosystem carrying capacity, demonstrating the dynamic optimization process of PCAES. Rule 3 concerns the POS model, which focuses on the mechanism of three types of subsystems—agricultural production, operation, and service—in terms of agricultural modernization efficiency and shows the changes in the efficiency of each dimension in PCAES. Thus, hierarchical DEMATEL-DTP can enable a comprehensive and nuanced analysis of relationships in the complex PCAES system and reveal the relationships at different levels of PCAES subsystems. This approach helps ensure the systematic identification of key factors. The factors in Table 1, Table 2 and Table 3 can be sorted into various categories of factor sets under different rules.

3.2. DPSIRM Model

Its predecessors, including pressure–state–response [54], driver–state–response [55], and driver–pressure–state–impact–response (DPSIR) [33], while influential, have certain limitations, failing to offer a comprehensive assessment of complex systems such as PCAES. The inclusion of the management (M) subsystem transforms the unidirectional nature of classical DPSIR into a dynamic causal feedback loop [56]. It is important to note that while R entails remedial measures after ecological damage, M emphasizes preemptive, source-oriented interventions [57].

Each subsystem in DPSIRM is intertwined with PCAES. First, the D subsystem acts as the main catalyst, driving changes in PCAES and mainly encompassing social and economic drivers. Second, the P subsystem, influenced by the D and M subsystems, mainly concerns resource and environmental pressures stemming from PCA production. Following this, the S subsystem encapsulates the evolving environmental, resource, and production state of PCA under the influence of P and M. Then, the I subsystem delineates the socioeconomic and environmental effects of the S and M subsystems in PCA production. The R subsystem pertains to pollution control and environmental protection measures implemented by governments or enterprises following damage to the PCAES system. Finally, the M subsystem signifies proactive, source-oriented human responses intended to safeguard PCAES and promote sustainable agricultural development.

In line with the meanings of these six subsystems, we analyze the relationships between various types of factors, categorize and number all factors listed in Table 1, Table 2 and Table 3, and obtain the structural model under Rule 1. This is depicted in Figure 2, which shows the direct influence relationships between all factors. Note that after numbering all factors according to the meaning of the subsystems in the DPSIRM model, the subsequent TERE and POS structural models only categorize the factors without renumbering them to ensure that the numbering is not confusing.

Table 4. Numbering of each factor.

ID	Factor	ID	Factor
f1	Natural population growth rate	f22	The growth amount of agricultural product exports
f2	Urbanization rate	f23	Value added of agriculture and related industries
f3	Per capita agricultural GDP	f24	Employment and resettlement situation of farmers
f4	Demand for characteristic agricultural products	f25	Soil erosion situation
f5	Profit margin	f26	Vegetation degradation situation
f6	Per capita labor input	f27	losses from anthropogenic or natural disasters
f7	Per capita arable land area	f28	Policies related to environment and ecology
f8	Per capita water resources	f29	Utilization of clean technology
f9	Consumption of agricultural plastic film per unit of arable land	f30	Comprehensive utilization rate of crop straw
f10	Utilization rate of fertilizers for major crops	f31	Degraded farmland management area
f11	Pesticide utilization rate of main crops	f32	Comprehensive utilization rate of agricultural solid waste
f12	Ecological quality index	f33	Wastewater treatment rate
f13	Effective irrigation area index	f34	The intensity of investment in pollution control
f14	Coverage rate of high-quality seeds for major crops	f35	Leading agricultural industrialization enterprises
f15	land reclamation rate	f36	The degree of high-quality farmland construction
f16	Cultivated land quality class	f37	Financial investment in agricultural special funds
f17	Biodiversity indices	f38	Government subsidy
f18	Water pollution concentration	f39	Comprehensive mechanization rate of major crops
f19	Overall compliance rate of routine monitoring	f40	Agricultural science and technology personnel
f20	“Three products and one standard” agricultural products	f41	Intensity of agricultural R&D investment
f21	Output of major agricultural products	-	-

shows the numbering of the factors.

Figure 2 shows how we partitioned the complex system into distinct subsystems (D, P, S, I, R, and M), each of which is further decomposed into various sub-subsystems, which in turn are further decomposed into different factors. This hierarchical decomposition reveals the direct influence relationships among each subsystem, sub-subsystem, and individual factors. Note that the arrow lines in Figure 2 indicate that the factors (subsystems) at the start of the arrow have a direct influence on the factors (subsystems) at the end of the arrow. For example, $D\to P,D\to D$ in level 1 indicates that D not only has a direct influence on P but also has a direct influence on itself. Similarly, “social drivers $\to$ economic drivers, social drivers $\to$ social drivers” in level 2 indicates that the sub-subsystem “social drivers” has a direct influence not only on the sub-subsystem “economic drivers” but also on itself. Since the factors in the lowest level cannot influence themselves, f₁ $\to$ f₂ in level 3 indicates that factors f₁ and f₂ can have a direct influence on each other but cannot influence themselves. The meanings of the arrows in Figure 3 and Figure 4 are the same as here and will not be repeated.

3.3. TERE Model

The TERE model was proposed by Wang et al. [58] to measure ocean carrying capacity. Du and Li [33] refined the model, positing that the environment is both the source and direct influencer of resources, applying it to evaluate marine ecological ranching. Building on this, we suggest that economic development and financial inputs also exert a direct influence on the environment to some extent, further improving the model and using it to analyze PCAES.

First, advancements in technologies (T), such as energy-saving, emission-reduction, and production technologies, driven by enterprise development or industrial cluster effects, enhance the sustainability and environmental friendliness of agricultural production. Second, socioeconomic progress, government financial support, and R&D investment by agricultural enterprises yield substantial economic (Ec) benefits. Furthermore, resources (R) encapsulate the resources consumed and conserved during production, measured in terms of the current pressure and state of these resources. Finally, environment (En) encompasses the ecological changes and effects resulting from human production activities and environmental policies.

By dissecting these four dimensions, we analyze the direct influence relationships between the various types of factors, categorize all factors listed in Table 1, Table 2 and Table 3, and obtain the structural model under Rule 2, as shown in Figure 3.

3.4. POS Model

Modern agriculture has evolved beyond merely enhancing production efficiency. There is a pressing need to pursue environmentally friendly production methods, innovative market-oriented agricultural business models, and modern, scientific agricultural services. Based on this, Shi et al. [40] examined agricultural modernization through these three interacting subsystems, exploring methods and pathways for improving the efficiency of agricultural modernization.

The three links of P, O, and S run throughout the entire PCAES system. First, agricultural production (P) should emphasize the sustainability of factors such as a favorable environment, healthy agricultural products, clean production methods, and biodiversity. Second, agricultural production affects ecological security (e.g., the non-food production of arable land [59] and the destruction of water and soil resources), making it necessary to optimize and adjust the structure of the agricultural industry to ensure the sustainability of agricultural operations (O). Finally, agriculture-related services involving environmental protection, pollution control, infrastructure development, financial support, and agricultural science and technology inputs can significantly enhance ecological resilience and the prosperity of the agricultural economy.

Based on the meanings of these three dimensions, we analyze the direct influence relationships between the various types of factors, categorize all factors listed in Table 1, Table 2 and Table 3, and obtain the structural model under Rule 3, as shown in Figure 4.

3.5. Steps in the Hierarchical DEMATEL-DTP Method

Here, we introduce the specific steps of the method. For more specific details, see [53].

Step 1: Hierarchical decomposition

Initially, we decompose the PCAES system horizontally based on three rules. Subsequently, vertical decomposition is performed within these specific rules, breaking down PCAES into different subsystems; Figure 1 shows the decomposition process. Next, each subsystem is further divided into sub-subsystems—namely, the process from level 1 to level 2 in Figure 2, Figure 3 and Figure 4. These sub-subsystems are then broken down into individual factors—that is, the process from level 2 to level 3 in Figure 2, Figure 3 and Figure 4. By embedding Figure 2, Figure 3 and Figure 4 into Figure 1, we can present a structure with multiple levels of nesting. Each rule plays a distinct role in identifying the critical factors. Therefore, we use multicriteria decision-making methods, such as analytic hierarchy process (AHP), to determine the weights of these three rules based on their importance.

Step 2: Direct influence analysis

In the multilevel hierarchical structure established in step 1, a 0–4 scale (0 for “no influence,” 1 for “low influence,” 2 for “medium influence,” 3 for “high influence,” and 4 for “relatively high influence”) is used to assess the degree of direct influence of each pair of factors in each subsystem. This process produces an initial direct-relation (IDR) matrix. Next, we briefly describe this process, which is depicted in Figure 5.

Suppose the PCAES system is $F=\left\{f_n|n=1,\cdots ,N\right\}$, where f_n denotes the nth factor in Table 1, Table 2 and Table 3, and N = 41. Next, to simplify problems, we suppose system F is divided into only two levels under the rth rule, and the subsystem at level 1 is denoted as $F_{r:q_r}$, $r=1,2,3$, and $q_r=1,\cdots ,Q_r$, where $Q_r$ denotes the number of subsystems in F. Then, suppose the subsystem at level 1 is $F=\left\{f_n|n=1,\cdots ,N\right\}$, where $f_i^{r:q_r}$ is a factor at level 2, and $N_{r:q_r}$ is the number of factors in the subsystem. Furthermore, suppose $x_{r:q_r{q}_r^{\prime }}\in \left\{0,1,2,3,4\right\}$ denotes the direct influence degree of $F_{r:q_r}$ on $F_{r:q_r^{\prime }}$ $(F_{r:q_r}\to F_{r:q_r^{\prime }})$. Then, the IDR matrix in system $F$ at level 1 under the rth rule can be constructed as $X_r={[x_{r:q_r{q}_r^{\prime }}]}_{Q_r\times Q_r}$, where $r=1,2,3$, $q_r=1,\cdots ,Q_r$. In hierarchical DEMATEL, it is also necessary to judge the direct influence degree between the factors in each subsystem. Similarly, suppose $x_{ij}^{r:q_r{q}_r^{\prime }}\in \left\{0,1,2,3,4\right\}$ denotes the direct influence degree of $f_i^{r:q_r}$ on $f_j^{r:q_r^{\prime }}$ $(f_i^{r:q_r}\to f_j^{r:q_r^{\prime }})$. In this case, the IDR matrix in subsystem $F_{r:q_r}$ at level 2 can be constructed as $X_{r:q_r}={[x_{ij}^{r:q_r}]}_{N_{r:q_r}\times N_{r:q_r}}$, where $r=1,2,3$, $q_r=1,\cdots ,Q_r$.

We can see in Figure 5 that $f_1^{r:q_r}$ in level 2 is the first factor of subsystem $F_{r:q_r}$ in level 1. Thus, $f_1^{r:q_r}$ can be represented by a nested structure, such as $F_{r:q_r\supset 1}$. Similarly, $f_i^{r:q_r}$ can be represented by $F_{r:q_r\supset i}$, and $f_{N_{r:q_r}}^{r:q_r}$ can be represented by $F_{r:q_r\supset N_{r:q_r}}$. This nested structure is used throughout this paper, except in Section 3.5, to represent the sub-subsystems and factors.

Step 3: Construction of the super-IDR matrix

In this step, we construct a matrix that delineates the direct influence degree between any two factors in system $F$ under the rth rule, termed the super-IDR matrix ${\overline{X}}_r$.

As defined previously, suppose any two subsystems at level 1 under the rth rule are $F_{r:q_r}=\left\{f_i^{r:q_r}\right|i=1,\cdots ,N_{r:q_r}\}$ and $F_{r:q_r^{\prime }}=\left\{f_j^{r:q_r^{\prime }}\right|j=1,\cdots ,N_{r:q_r^{\prime }}\}$. Next, assume $z_i^{r:q_r}$ and $z_j^{r:q_r^{\prime }}$ represent the centrality degrees of factors $f_i^{r:q_r}$ and $f_j^{r:q_r^{\prime }}$ of level 2 in subsystems $F_{r:q_r}$ and $F_{r:q_r^{\prime }}$, respectively, which are computed using the classical DEMATEL method, as in [60]. Now, the modified IDR matrix of $F_{r:q_r}\to F_{r:q_r^{\prime }}$ can be constructed as ${\overline{X}}_{r:q_r{q}_r^{\prime }}={[{\overline{x}}_{ij}^{r:q_r{q}_r^{\prime }}]}_{N_{r:q_r}\times N_{r:q_r}}$, where ${\overline{x}}_{ij}^{r:q_r{q}_r^{\prime }}$ is the modified direct influence degree for $f_i^{r:q_r}\to f_j^{r:q_r^{\prime }}$, and it can be computed using Equation (1), $i=1,\cdots ,N_{r:q_r}$, $j=1,\cdots ,N_{r:q_r^{\prime }}$. Then, the super-IDR matrix at level 1 under the rth rule is defined as ${\overline{X}}_r={[{\overline{x}}_{ij}^r]}_{N_r\times N_r}$, where $N_r=N_{r:1}+\cdots +N_{r:Q_r}$. ${\overline{X}}_r$ can be constructed by integrating all modified matrices ${\overline{X}}_{r:q_r{q}_r^{\prime }}$ using Equation (2).

$${\overline{x}}_{ij}^{r:q_r{q}_r^{\prime }}=\left\{\begin{array}{l}{\displaystyle \frac{x_{r:q_r{q}_r^{\prime }}}{{\displaystyle \sum _{i=1}^{N_{r:q_r}}{\displaystyle \sum _{j=1}^{N_{r:q_r^{\prime }}}{x}_{ij}^{r:q_r{q}_r^{\prime }}}}}}\times x_{ij}^{r:q_r{q}_r^{\prime }},q_r=q_r^{\prime }\\ {\displaystyle \frac{x_{r:q_r{q}_r^{\prime }}}{{\displaystyle \sum _{i=1}^{N_{r:q_r}}{\displaystyle \sum _{j=1}^{N_{r:q_r^{\prime }}}{z}_i^{r:q_r}{z}_i^{r:q_r^{\prime }}}}}}\times z_i^{r:q_r}{z}_i^{r:q_r^{\prime }},q_r\ne q_r^{\prime }\end{array}\right.,$$

(1)

$${\overline{X}}_r={[{\overline{x}}_{ij}^r]}_{N_r\times N_r}=\left[\begin{array}{ccc}{\overline{X}}_{r:11}& \cdots & {\overline{X}}_{r:1Q_r}\\ ⋮& \ddots & ⋮\\ {\overline{X}}_{r:Q_{r}1}& \cdots & {\overline{X}}_{r:Q_r{Q}_r}\end{array}\right].$$

(2)

If the system exhibits a multitiered structure (more than two levels), it is sufficient to repeat the above operation step by step from the bottom (low level) to the top (high level).

Step 4: Identification of key factors

Following the classical DEMATEL method, the ordered total relation matrix for system F under the rth rule can be determined by $T_r={[t_{ij}^r]}_{N\times N}=M_r{(I-M_r)}^{-1},$ where $M_r$ is the normalized matrix for the super-IDR matrix ${\overline{X}}_r$, I is the N $\times$ N identity matrix, and $r=1,2,3$. $M_r$ can be calculated using Equation (3):

$$M_r={[m_{ij}^r]}_{N\times N}={\overline{X}}_r/\theta ,$$

(3)

where $\theta =ma{x}_{1\le j\le N}{\displaystyle \sum _{i=1}^N{\overline{x}}_{ij}^r}$ is the normalization factor of the super-IDR matrix ${\overline{X}}_r$; that is, the maximum value of the row sums of the matrix is taken.

Then, suppose the weight of the rth rule is defined as $w_r$, ${\displaystyle {\sum }_{r=1}^3{w}_r=1,w_r\ge 0},r=1,2,3$. At this point, the final total relation matrix $\overline{T}={[{\overline{t}}_{ij}]}_{N\times N}$ for system F can be determined using Equation (4), where ${\overline{t}}_{ij}$ denotes the final influence degree of $f_i$ on $f_j$$(f_i\to f_j)$:

$$\overline{T}=w_r{T}_h={[w_r{t}_{ij}^r]}_{N\times N}.$$

(4)

Next, the centrality degree $(d_i+c_i)$ and cause degree $(d_i-c_i)$ of each factor ($f_i$) in $\overline{T}$ can be calculated using the classical DEMATEL method. Finally, the key factors affecting PCAES are identified based on the centrality degree; cause factors and result factors are identified based on the cause degree.

It is important to note that in hierarchical DEMATEL, there are four main indicators for judging the degree of influence of factors: centrality degree ($d_i+c_i$), cause degree ($d_i-c_i$), influence degree ($d_i$), and influenced degree ($c_i$). Here, $d_i$ represents the influence degree of $f_i$ on other factors, while $c_i$ denotes the influence of $f_i$ from other factors (i.e., the degree of being influenced). Centrality degree ($d_i+c_i$), also known as prominence or importance, indicates the overall significance of factor $f_i$ in the system. Cause degree ($d_i-c_i$), also known as the relation, is used to categorize factor $f_i$ into causal groups based on its positive or negative value. These metrics are indispensable for discerning the key elements of the PCAES system.

4. Analysis Process and Results

Here, we use the hierarchical DEMATEL-DTP method introduced in Section 3.5 to provide an example of how to identify the key factors, cause factors, and result factors of the PCAES system.

4.1. Hierarchical Decomposition

A hierarchical decomposition of the PCAES system is required. Under Rule 1, all elements in the PCAES system are divided into three levels. Level 1 comprises six subsystems (D, P, S, I, R, and M), denoted as $F=F_{1:1}=\left\{F_{1:1\supset 1},\cdots ,F_{1:1\supset 6}\right\}$. Based on level 1, these six subsystems are further divided into 13 sub-subsystems in level 2, denoted as $F_{1:1\supset 1}=\left\{F_{1:1\supset 1\supset 1},F_{1:1\supset 1\supset 2}\right\}$,…, $F_{1:1\supset 6}=\left\{F_{1:1\supset 6\supset 1},F_{1:1\supset 6\supset 2}\right\}$. Continuing the decomposition process, these 13 sub-subsystems are divided into 41 factors in level 3, denoted as $F_{1:1\supset 1\supset 1}=\left\{F_{1:1\supset 1\supset 1\supset 1},F_{1:1\supset 1\supset 1\supset 2}\right\}$,…, $F_{1:1\supset 6\supset 2}=\left\{F_{1:1\supset 6\supset 2\supset 1},F_{1:1\supset 6\supset 2\supset 2},F_{1:1\supset 6\supset 2\supset 3}\right\}$. Next, we can represent the subsystems, sub-subsystems, and factors in the same way under the other two rules; these are illustrated in Figure 1, Figure 2, Figure 3 and Figure 4. Finally, we use AHP [61] to determine the weights of these rules and obtain w₁ = 0.5, w₂ = 0.3, and w₃ = 0.2.

4.2. Direct Influence Analysis

To ensure the reliability and validity of the scoring process, experts were invited to score the degree of direct influence between any two subsystems, sub-subsystems, and factors in Figure 2, Figure 3 and Figure 4. All experts received a brief description of the hierarchical DEMATEL-DTP method and the definitions of each indicator prior to scoring. Scoring was conducted independently in the form of a questionnaire, and the average of all experts’ scores was used to construct the IDR matrix.

Taking the two subsystems “social drivers” and “economic drivers” under the driver subsystem (D) as an example, the IDR matrix can be constructed according to the following process. After counting the average of all expert ratings, we find that the social drivers $(F_{1:1\supset 1\supset 1})$ have a relatively moderate effect on the economic drivers $(F_{1:1\supset 1\supset 2})$; that is, $F_{1:1\supset 1\supset 1}\to F_{1:1\supset 1\supset 2}=2$. Similarly, the direct influence of social drivers on themselves is 2 $(F_{1:1\supset 1\supset 1}\to F_{1:1\supset 1\supset 1}=2)$, that of economic drivers on social drivers is 3 $(F_{1:1\supset 1\supset 2}\to F_{1:1\supset 1\supset 1}=3)$, and that of economic drivers on themselves is 3. Thus, the influence of social drivers and economic drivers on each other and on themselves can be expressed as a 2 × 2 IDR matrix: $X_{1:1\supset 1}={[{\overline{x}}_{ij}^{1:1\supset 1}]}_{2\times 2}=\left(\begin{array}{cc}2& 2\\ 3& 3\end{array}\right)$. By analogy, we end up with a 6 × 6 IDR matrix at level 1 under R₁: $X_{1:1}={[{\overline{x}}_{ij}^{1:1}]}_{6\times 6}=\left(\begin{array}{cccccc}2& 3& 0& 0& 0& 0\\ 0& 2& 3& 0& 0& 0\\ 0& 0& 3& 3& 0& 0\\ 3& 0& 0& 0& 3& 4\\ 2& 2& 2& 2& 0& 3\end{array}\right)$.

At level 2, there are six IDR matrices, as follows: $X_{1:1\supset 1}={[{\overline{x}}_{ij}^{1:1\supset 1}]}_{2\times 2}=\left(\begin{array}{cc}2& 2\\ 3& 3\end{array}\right)$, …, $X_{1:1\supset 6}={[{\overline{x}}_{ij}^{1:1\supset 6}]}_{2\times 2}=\left(\begin{array}{cc}3& 3\\ 4& 3\end{array}\right)$. At level 3, there are 13 IDR matrices, as follows: $X_{1:1\supset 1\supset 1}={[{\overline{x}}_{ij}^{1:1\supset 1\supset 1}]}_{2\times 2}=\left(\begin{array}{cc}0& 3\\ 2& 0\end{array}\right)$, …, $X_{1:1\supset 6\supset 2}={[{\overline{x}}_{ij}^{1:1\supset 6\supset 2}]}_{3\times 3}=\left(\begin{array}{ccc}0& 2& 2\\ 2& 0& 2\\ 4& 3& 0\end{array}\right)$.

All IDR matrices of the PCAES system are detailed in Figure A1.

4.3. Construction of the Super-IDR Matrix

Before identifying the key factors, we need to consider the direct relationships between all factors. The IDR matrices obtained in Section 4.2 are not sufficient because the relationships between the factors in the different subsystems and in the sub-subsystems are still unknown. Here, then, we construct a super-IDR matrix that can show the degree of direct influence between all factors in the system. Taking the driver subsystem (D) under R₁, the super-IDR matrix can be constructed as in the following steps.

First, the centrality degree of each factor in the subsystem is calculated. The D subsystem contains two subsystems: social drivers ($F_{1:1\supset 1\supset 1}$) and economic drivers ($F_{1:1\supset 1\supset 2}$). Using the classical DEMATEL method to calculate the IDR matrices of these two subsystems, we can obtain the total relation matrix ($T_{1:1\supset 1\supset 1}$) and centrality degree ($z_i^{1:1\supset 1\supset 1}$) of the social drivers and the total relation matrix ($T_{1:1\supset 1\supset 2}$) and centrality degree ($z_j^{1:1\supset 1\supset 2}$) of the economic drivers.

Table 5. The centrality degree of factors with total relation matrices for $F_{1:1\supset 1\supset 1}$ and $F_{1:1\supset 1\supset 2}$.

Subsystem	Factor	${\mathit{f}}_1^{1:1\supset 1\supset \mathit{s}}$	${\mathit{f}}_2^{1:1\supset 1\supset \mathit{s}}$	${\mathit{f}}_3^{1:1\supset 1\supset \mathit{s}}$	di	ci	${\mathit{z}}_{\mathit{i}}^{1:1\supset 1\supset \mathit{s}}$
$F_{1:1\supset 1\supset 1}$	$f_1^{1:1\supset 1\supset 1}$	2.0000	3.0000	-	5.0000	4.0000	9.0000
	$f_2^{1:1\supset 1\supset 1}$	2.0000	2.0000	-	4.0000	5.0000	9.0000
$F_{1:1\supset 1\supset 2}$	$f_1^{1:1\supset 1\supset 2}$	0.3125	0.4375	0.4375	1.1875	1.6542	2.8417
	$f_2^{1:1\supset 1\supset 2}$	0.8458	0.3708	0.9042	2.1208	1.1292	3.2500
	$f_3^{1:1\supset 1\supset 2}$	0.4958	0.3208	0.2542	1.0708	1.5958	2.6667

shows the results, where values in italics indicate the influence degree between factors; s denotes the sequence of subsystems in $F_{1:1\supset 1}$, with s = 1 for the first two rows and s = 2 for the others.

Second, we calculate the direct influence between all factors. For the modified direct influence degree among the factors in one subsystem, we use the modified IDR matrix ${\overline{X}}_{1:1\supset 1\supset 11}$ for economic drivers as an example to demonstrate the calculation process. The direct influence of political drivers on themselves ($F_{1:1\supset 1\supset 1}\to F_{1:1\supset 1\supset 1}$) is known to be 2 $(x_{11}^{1:1\supset 1}=2)$ from Figure A1, and the direct influence among the factors ($f_i^{1:1\supset 1\supset 1}\to f_j^{1:1\supset 1\supset 1}$) in political drivers can also be determined from the IDR matrix ($X_{1:1\supset 1\supset 1}$) in Figure A1. By substituting these values into Equation (1), we can obtain ${\overline{X}}_{1:1\supset 1\supset 11}={\left[{\overline{x}}_{ij}^{1:1\supset 1\supset 11}\right]}_{2\times 2}$. The calculation process is shown in the following equation:

$${\overline{X}}_{1:1\supset 1\supset 11}={\displaystyle \frac{x_{11}^{1:1\supset 1}}{{\displaystyle {\sum }_{i=1}^2{\displaystyle {\sum }_{j=1}^2{x}_{ij}^{1:1\supset 1\supset 1}}}}}{X}_{1:1\supset 1\supset 1}={\displaystyle \frac{2}{5}}\times \left(\begin{array}{cc}0& 3\\ 2& 0\end{array}\right)=\left(\begin{array}{cc}0.0000& 1.2000\\ 0.8000& 0.0000\end{array}\right).$$

(5)

Meanwhile, for the modified direct influence degree among factors from different subsystems, we use the modified IDR matrix ${\overline{X}}_{1:1\supset 1\supset 12}$ for policy drivers as an example to demonstrate the calculation process. From Table 5, we know that the centrality degree of each factor in policy drivers and economic drivers is $(z_i^{1:1\supset 1\supset 1},z_j^{1:1\supset 1\supset 2})$; from Figure A1, we know that the direct influence of policy drivers on economic drivers $(F_{1:1\supset 1\supset 1}\to F_{1:1\supset 1\supset 2})$ is 2 $(x_{12}^{1:1\supset 1}=2)$. By substituting these values into Equation (1), we can obtain ${\overline{X}}_{1:1\supset 1\supset 12}={\left[{\overline{x}}_{ij}^{1:1\supset 1\supset 12}\right]}_{2\times 3}$. The calculation process is shown in the following equation:

$${\overline{X}}_{1:1\supset 1\supset 12}={\displaystyle \frac{x_{12}^{1:1\supset 1}}{{\displaystyle {\sum }_{i=1}^2{\displaystyle {\sum }_{j=1}^3{z}_i^{1:1\supset 1\supset 1}{z}_j^{1:1\supset 1\supset 2}}}}}{z}_i^{1:1\supset 1\supset 1}{z}_j^{1:1\supset 1\supset 2}={\displaystyle \frac{2}{157.65}}\times \left(\begin{array}{ccc}\begin{array}{l}25.575\\ 25.575\end{array}& \begin{array}{l}29.25\\ 29.25\end{array}& \begin{array}{l}24\\ 24\end{array}\end{array}\right)=\left(\begin{array}{ccc}\begin{array}{l}0.3245\\ 0.3245\end{array}& \begin{array}{l}0.3711\\ 0.3711\end{array}& \begin{array}{l}0.3045\\ 0.3045\end{array}\end{array}\right).$$

(6)

Similarly, we can obtain the other modified IDR matrices ${\overline{X}}_{1:1\supset 1\supset 21}$ and ${\overline{X}}_{1:1\supset 1\supset 22}$ associated with the drivers $F_{1:1\supset 1}$. Finally, all of the modified IDR matrices ${\overline{X}}_{1:1\supset 1\supset 11}$, ${\overline{X}}_{1:1\supset 1\supset 12}$, ${\overline{X}}_{1:1\supset 1\supset 21}$, and ${\overline{X}}_{1:1\supset 1\supset 22}$ are combined according to Equation (2) to obtain the super-IDR matrix ${\overline{X}}_{1:1\supset 1}$ of the driver subsystem (D) within level 2, as shown in the following equation:

$${\overline{X}}_{1:1\supset 1}=\left(\begin{array}{cc}{\overline{X}}_{1:1\supset 1\supset 11}& {\overline{X}}_{1:1\supset 1\supset 12}\\ {\overline{X}}_{1:1\supset 1\supset 21}& {\overline{X}}_{1:1\supset 1\supset 22}\end{array}\right)=\left(\begin{array}{ccccc}0.0000& 1.2000& 0.3245& 0.3711& 0.3045\\ 0.8000& 0.0000& 0.3245& 0.3711& 0.3045\\ 0.4867& 0.4867& 0.0000& 0.4615& 0.2308\\ 0.5566& 0.5566& 0.6923& 0.0000& 0.9231\\ 0.4567& 0.4567& 0.4615& 0.2308& 0.0000\end{array}\right).$$

(7)

Subsequently, by repeating the above three steps, the super-IDR matrix of the other subsystems (P, S, I, R, and M) in level 2 can be obtained. The construction of the super-IDR matrix for level 1 is also the same. Finally, we obtain the super-IDR matrix ${\overline{X}}_{1:1}={[{\overline{x}}_{ij}^{1:1}]}_{41\times 41}$ of PCAES under R₁. Similarly, under R₂ and R₃, we also repeat the above three steps to obtain the super-IDR matrices ${\overline{X}}_{2:1}={[{\overline{x}}_{ij}^{2:1}]}_{41\times 41}$, ${\overline{X}}_{3:1}={[{\overline{x}}_{ij}^{3:1}]}_{41\times 41}$ for PCAES. For details, see

Table A1. The super-IDR matrix ${\overline{X}}_{1:1}$ under rule $R_1$ in PCAES system.

Factor	f1	f2	f3	f4	f5	f6	f7	f8	f9	f10	f11	f12	f13	f14	f15	f16	f17	f18	f19	f20	f21	f22	f23	f24	f25	f26	f27	f28	f29	f30	f31	f32	f33	f34	f35	f36	f37	f38	f39	f40	f41
f1	0.0000	0.2400	0.0649	0.0742	0.0609	0.1039	0.1294	0.1039	0.1160	0.1065	0.1151	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000
f2	0.1600	0.0000	0.0649	0.0742	0.0609	0.1051	0.1309	0.1051	0.1173	0.1077	0.1165	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000
f3	0.0973	0.0973	0.0000	0.0923	0.0462	0.0813	0.1012	0.0813	0.0907	0.0833	0.0901	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000
f4	0.1113	0.1113	0.1385	0.0000	0.1846	0.0945	0.1177	0.0945	0.1055	0.0969	0.1047	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000
f5	0.0913	0.0913	0.0923	0.0462	0.0000	0.0771	0.0961	0.0771	0.0861	0.0791	0.0855	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000
f6	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0741	0.0370	0.0465	0.0429	0.0465	0.0334	0.0328	0.0346	0.0553	0.0491	0.0568	0.0564	0.0448	0.0489	0.0497	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000
f7	0.0000	0.0000	0.0000	0.0000	0.0000	0.1111	0.0000	0.1111	0.0591	0.0546	0.0591	0.0416	0.0409	0.0431	0.0689	0.0612	0.0707	0.0702	0.0558	0.0610	0.0619	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000
f8	0.0000	0.0000	0.0000	0.0000	0.0000	0.0370	0.0741	0.0000	0.0465	0.0429	0.0465	0.0334	0.0328	0.0346	0.0553	0.0491	0.0568	0.0564	0.0448	0.0489	0.0497	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000
f9	0.0000	0.0000	0.0000	0.0000	0.0000	0.0697	0.0887	0.0697	0.0000	0.0684	0.1026	0.0373	0.0367	0.0387	0.0618	0.0548	0.0634	0.0629	0.0501	0.0547	0.0555	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000
f10	0.0000	0.0000	0.0000	0.0000	0.0000	0.0643	0.0819	0.0643	0.0684	0.0000	0.0684	0.0342	0.0337	0.0355	0.0567	0.0503	0.0582	0.0578	0.0460	0.0502	0.0509	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000
f11	0.0000	0.0000	0.0000	0.0000	0.0000	0.0697	0.0887	0.0697	0.0684	0.0684	0.0000	0.0370	0.0364	0.0384	0.0613	0.0544	0.0629	0.0625	0.0497	0.0542	0.0550	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000
f12	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0229	0.0343	0.0343	0.0137	0.0158	0.0157	0.0218	0.0240	0.0243	0.0361	0.0393	0.0329	0.0354	0.0354	0.0376	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000
f13	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0114	0.0000	0.0229	0.0114	0.0137	0.0158	0.0157	0.0218	0.0240	0.0243	0.0356	0.0387	0.0324	0.0349	0.0349	0.0370	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000
f14	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0114	0.0343	0.0000	0.0229	0.0143	0.0164	0.0163	0.0226	0.0250	0.0252	0.0375	0.0408	0.0341	0.0368	0.0368	0.0390	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000
f15	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0229	0.0343	0.0229	0.0000	0.0886	0.1018	0.1011	0.0226	0.0250	0.0252	0.0599	0.0652	0.0545	0.0587	0.0587	0.0623	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000
f16	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0319	0.0319	0.0332	0.0332	0.0000	0.0336	0.0336	0.0405	0.0447	0.0451	0.0532	0.0579	0.0484	0.0521	0.0521	0.0554	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000
f17	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0367	0.0367	0.0381	0.0381	0.0504	0.0000	0.0672	0.0465	0.0513	0.0518	0.0614	0.0669	0.0559	0.0602	0.0602	0.0640	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000
f18	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0365	0.0365	0.0379	0.0379	0.0504	0.0504	0.0000	0.0462	0.0510	0.0515	0.0610	0.0664	0.0556	0.0598	0.0598	0.0635	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000
f19	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0218	0.0218	0.0226	0.0226	0.0270	0.0310	0.0308	0.0000	0.0220	0.0440	0.0485	0.0528	0.0442	0.0476	0.0476	0.0505	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000
f20	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0240	0.0240	0.0250	0.0250	0.0298	0.0342	0.0340	0.0659	0.0000	0.0659	0.0530	0.0577	0.0482	0.0519	0.0519	0.0552	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000
f21	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0243	0.0243	0.0252	0.0252	0.0301	0.0346	0.0343	0.0440	0.0440	0.0000	0.0538	0.0585	0.0489	0.0527	0.0527	0.0560	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000
f22	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.1667	0.1111	0.0730	0.0730	0.0782	0.0706	0.0570	0.0627	0.0662	0.0791	0.0802	0.0841	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000
f23	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.1111	0.0000	0.1111	0.0786	0.0786	0.0843	0.0768	0.0620	0.0683	0.0720	0.0861	0.0873	0.0915	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000
f24	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0556	0.1111	0.0000	0.0654	0.0654	0.0702	0.0643	0.0519	0.0571	0.0603	0.0721	0.0731	0.0766	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000
f25	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.1094	0.1179	0.0981	0.0000	0.0952	0.1429	0.0692	0.0559	0.0615	0.0649	0.0776	0.0787	0.0824	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000
f26	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.1094	0.1179	0.0981	0.0952	0.0000	0.1429	0.0692	0.0559	0.0615	0.0649	0.0776	0.0787	0.0824	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000
f27	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.1174	0.1264	0.1053	0.0952	0.0952	0.0000	0.0735	0.0593	0.0653	0.0689	0.0824	0.0835	0.0875	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000
f28	0.0953	0.0964	0.0745	0.0867	0.0707	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0606	0.0606	0.0808	0.0968	0.0981	0.1043	0.0721	0.0637	0.0706	0.0785	0.0930	0.0863	0.1006
f29	0.0769	0.0778	0.0602	0.0700	0.0571	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0202	0.0000	0.0404	0.0606	0.0780	0.0790	0.0840	0.0582	0.0514	0.0570	0.0634	0.0751	0.0697	0.0812
f30	0.0847	0.0857	0.0662	0.0770	0.0629	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0404	0.0404	0.0000	0.0404	0.0867	0.0878	0.0933	0.0641	0.0566	0.0627	0.0698	0.0827	0.0767	0.0894
f31	0.0893	0.0904	0.0699	0.0813	0.0663	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0404	0.0202	0.0404	0.0000	0.0916	0.0928	0.0986	0.0676	0.0597	0.0662	0.0736	0.0872	0.0810	0.0943
f32	0.1068	0.1080	0.0835	0.0971	0.0793	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0726	0.0585	0.0650	0.0687	0.0000	0.0963	0.0642	0.0808	0.0714	0.0791	0.0880	0.1043	0.0968	0.1128
f33	0.1083	0.1095	0.0847	0.0985	0.0804	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0736	0.0592	0.0658	0.0696	0.0642	0.0000	0.0642	0.0819	0.0723	0.0802	0.0892	0.1057	0.0981	0.1143
f34	0.1135	0.1148	0.0888	0.1032	0.0843	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0782	0.0630	0.0700	0.0740	0.1283	0.1283	0.0000	0.0858	0.0758	0.0841	0.0935	0.1108	0.1028	0.1198
f35	0.0574	0.0581	0.0449	0.0522	0.0426	0.0393	0.0489	0.0393	0.0439	0.0403	0.0435	0.0184	0.0182	0.0191	0.0306	0.0271	0.0314	0.0312	0.0248	0.0270	0.0274	0.0425	0.0463	0.0387	0.0417	0.0417	0.0443	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0462	0.0692	0.0923	0.0587	0.0546	0.0629
f36	0.0507	0.0513	0.0397	0.0461	0.0376	0.0347	0.0432	0.0347	0.0387	0.0356	0.0385	0.0163	0.0160	0.0169	0.0270	0.0240	0.0277	0.0275	0.0219	0.0239	0.0242	0.0376	0.0409	0.0342	0.0368	0.0368	0.0391	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0231	0.0000	0.0462	0.0462	0.0515	0.0478	0.0552
f37	0.0562	0.0569	0.0440	0.0511	0.0417	0.0385	0.0479	0.0385	0.0430	0.0395	0.0427	0.0181	0.0178	0.0187	0.0299	0.0266	0.0307	0.0305	0.0243	0.0265	0.0269	0.0417	0.0453	0.0379	0.0408	0.0408	0.0434	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0462	0.0692	0.0000	0.0692	0.0572	0.0531	0.0613
f38	0.0625	0.0633	0.0489	0.0569	0.0464	0.0428	0.0533	0.0428	0.0478	0.0439	0.0474	0.0201	0.0198	0.0208	0.0333	0.0296	0.0342	0.0339	0.0270	0.0295	0.0299	0.0463	0.0504	0.0422	0.0454	0.0454	0.0482	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0692	0.0692	0.0462	0.0000	0.0633	0.0588	0.0678
f39	0.0741	0.0750	0.0580	0.0674	0.0550	0.0507	0.0632	0.0507	0.0566	0.0520	0.0562	0.0238	0.0234	0.0247	0.0395	0.0350	0.0405	0.0402	0.0320	0.0349	0.0354	0.0549	0.0597	0.0500	0.0538	0.0538	0.0572	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0783	0.0687	0.0762	0.0844	0.0000	0.0923	0.0923
f40	0.0688	0.0696	0.0538	0.0625	0.0511	0.0471	0.0586	0.0471	0.0526	0.0482	0.0522	0.0221	0.0217	0.0229	0.0366	0.0325	0.0376	0.0373	0.0297	0.0324	0.0329	0.0509	0.0554	0.0464	0.0500	0.0500	0.0530	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0727	0.0638	0.0708	0.0784	0.0923	0.0000	0.0923
f41	0.0801	0.0811	0.0627	0.0729	0.0595	0.0548	0.0683	0.0548	0.0612	0.0562	0.0608	0.0257	0.0253	0.0267	0.0427	0.0379	0.0438	0.0435	0.0346	0.0378	0.0383	0.0594	0.0646	0.0541	0.0582	0.0582	0.0618	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0839	0.0736	0.0817	0.0905	0.1846	0.1385	0.0000

,

Table A2. The super-IDR matrix ${\overline{X}}_{2:1}$ under rule $R_2$ in PCAES system.

Factor	f19	f20	f21	f35	f29	f32	f33	f30	f39	f40	f41	f1	f2	f3	f4	f5	f22	f23	f24	f28	f34	f37	f38	f6	f7	f8	f16	f17	f18	f31	f36	f9	f10	f11	f12	f13	f14	f15	f25	f26	f41
f19	0.0000	0.0094	0.0188	0.0188	0.0169	0.0169	0.0153	0.0131	0.0138	0.0128	0.0148	0.0299	0.0304	0.0231	0.0262	0.0220	0.0206	0.0222	0.0185	0.0179	0.0179	0.0170	0.0168	0.0249	0.0308	0.0249	0.0203	0.0200	0.0190	0.0171	0.0178	0.0102	0.0094	0.0103	0.0071	0.0071	0.0074	0.0074	0.0093	0.0093	0.0099
f20	0.0282	0.0000	0.0282	0.0188	0.0179	0.0178	0.0162	0.0138	0.0146	0.0135	0.0156	0.0315	0.0321	0.0243	0.0276	0.0232	0.0217	0.0234	0.0195	0.0189	0.0189	0.0179	0.0177	0.0263	0.0325	0.0263	0.0214	0.0211	0.0200	0.0180	0.0188	0.0108	0.0099	0.0108	0.0075	0.0075	0.0078	0.0078	0.0098	0.0098	0.0104
f21	0.0188	0.0188	0.0000	0.0282	0.0193	0.0192	0.0174	0.0149	0.0157	0.0146	0.0168	0.0339	0.0345	0.0262	0.0297	0.0249	0.0233	0.0251	0.0209	0.0203	0.0203	0.0193	0.0190	0.0283	0.0349	0.0283	0.0231	0.0227	0.0215	0.0194	0.0202	0.0116	0.0107	0.0116	0.0080	0.0081	0.0084	0.0084	0.0106	0.0106	0.0112
f35	0.0282	0.0282	0.0282	0.0000	0.0202	0.0201	0.0183	0.0156	0.0165	0.0153	0.0177	0.0355	0.0361	0.0274	0.0311	0.0261	0.0244	0.0263	0.0219	0.0213	0.0213	0.0202	0.0199	0.0296	0.0366	0.0296	0.0242	0.0238	0.0226	0.0203	0.0212	0.0121	0.0112	0.0122	0.0084	0.0085	0.0088	0.0088	0.0111	0.0111	0.0117
f29	0.0113	0.0119	0.0129	0.0135	0.0000	0.0218	0.0218	0.0145	0.0083	0.0077	0.0089	0.0250	0.0254	0.0193	0.0219	0.0184	0.0172	0.0185	0.0154	0.0150	0.0150	0.0142	0.0140	0.0208	0.0258	0.0208	0.0170	0.0167	0.0159	0.0143	0.0149	0.0085	0.0079	0.0086	0.0059	0.0060	0.0062	0.0062	0.0078	0.0078	0.0083
f32	0.0112	0.0119	0.0128	0.0134	0.0145	0.0000	0.0218	0.0145	0.0082	0.0076	0.0088	0.0250	0.0254	0.0193	0.0219	0.0184	0.0172	0.0185	0.0154	0.0150	0.0150	0.0142	0.0140	0.0208	0.0258	0.0208	0.0170	0.0167	0.0159	0.0143	0.0149	0.0085	0.0079	0.0086	0.0059	0.0060	0.0062	0.0062	0.0078	0.0078	0.0083
f33	0.0102	0.0108	0.0116	0.0122	0.0145	0.0145	0.0000	0.0073	0.0075	0.0069	0.0080	0.0227	0.0231	0.0175	0.0199	0.0167	0.0156	0.0168	0.0140	0.0136	0.0136	0.0129	0.0127	0.0189	0.0234	0.0189	0.0154	0.0152	0.0144	0.0130	0.0135	0.0077	0.0071	0.0078	0.0054	0.0054	0.0056	0.0056	0.0071	0.0071	0.0075
f30	0.0087	0.0092	0.0099	0.0104	0.0145	0.0145	0.0073	0.0000	0.0064	0.0059	0.0068	0.0192	0.0195	0.0148	0.0168	0.0141	0.0132	0.0142	0.0118	0.0115	0.0115	0.0109	0.0108	0.0160	0.0198	0.0160	0.0130	0.0128	0.0122	0.0110	0.0114	0.0065	0.0060	0.0066	0.0045	0.0046	0.0048	0.0048	0.0060	0.0060	0.0063
f39	0.0276	0.0292	0.0314	0.0330	0.0165	0.0164	0.0149	0.0127	0.0000	0.0364	0.0364	0.0393	0.0400	0.0304	0.0345	0.0289	0.0271	0.0292	0.0243	0.0236	0.0236	0.0223	0.0221	0.0328	0.0405	0.0328	0.0267	0.0263	0.0250	0.0225	0.0235	0.0134	0.0124	0.0135	0.0093	0.0094	0.0098	0.0097	0.0123	0.0123	0.0130
f40	0.0257	0.0271	0.0292	0.0306	0.0153	0.0153	0.0139	0.0118	0.0364	0.0000	0.0364	0.0366	0.0372	0.0283	0.0321	0.0269	0.0252	0.0271	0.0226	0.0219	0.0219	0.0208	0.0205	0.0305	0.0377	0.0305	0.0249	0.0245	0.0232	0.0209	0.0218	0.0125	0.0115	0.0126	0.0087	0.0087	0.0091	0.0091	0.0114	0.0114	0.0121
f41	0.0296	0.0313	0.0337	0.0353	0.0177	0.0176	0.0160	0.0136	0.0727	0.0545	0.0000	0.0432	0.0440	0.0334	0.0379	0.0318	0.0297	0.0320	0.0267	0.0259	0.0259	0.0245	0.0243	0.0360	0.0445	0.0360	0.0294	0.0289	0.0275	0.0247	0.0258	0.0148	0.0136	0.0148	0.0102	0.0103	0.0107	0.0107	0.0135	0.0135	0.0143
f1	0.0299	0.0315	0.0339	0.0355	0.0250	0.0250	0.0227	0.0192	0.0393	0.0366	0.0432	0.0000	0.0923	0.0250	0.0285	0.0234	0.0259	0.0279	0.0232	0.0098	0.0099	0.0094	0.0094	0.0162	0.0201	0.0162	0.0132	0.0130	0.0124	0.0111	0.0116	0.0133	0.0123	0.0134	0.0092	0.0093	0.0097	0.0097	0.0121	0.0121	0.0129
f2	0.0304	0.0321	0.0345	0.0361	0.0254	0.0254	0.0231	0.0195	0.0400	0.0372	0.0440	0.0615	0.0000	0.0250	0.0285	0.0234	0.0259	0.0279	0.0232	0.0098	0.0099	0.0094	0.0094	0.0165	0.0204	0.0165	0.0135	0.0133	0.0126	0.0113	0.0118	0.0135	0.0125	0.0136	0.0094	0.0094	0.0098	0.0098	0.0123	0.0123	0.0131
f3	0.0231	0.0243	0.0262	0.0274	0.0193	0.0193	0.0175	0.0148	0.0304	0.0283	0.0334	0.0374	0.0374	0.0000	0.0355	0.0178	0.0168	0.0181	0.0151	0.0127	0.0128	0.0122	0.0122	0.0125	0.0155	0.0125	0.0102	0.0101	0.0096	0.0086	0.0090	0.0103	0.0095	0.0103	0.0071	0.0072	0.0075	0.0075	0.0094	0.0094	0.0100
f4	0.0262	0.0276	0.0297	0.0311	0.0219	0.0219	0.0199	0.0168	0.0345	0.0321	0.0379	0.0428	0.0428	0.0533	0.0000	0.0710	0.0192	0.0207	0.0172	0.0146	0.0147	0.0139	0.0139	0.0142	0.0176	0.0142	0.0116	0.0114	0.0108	0.0098	0.0102	0.0117	0.0108	0.0117	0.0081	0.0081	0.0085	0.0085	0.0106	0.0106	0.0113
f5	0.0220	0.0232	0.0249	0.0261	0.0184	0.0184	0.0167	0.0141	0.0289	0.0269	0.0318	0.0351	0.0351	0.0355	0.0178	0.0000	0.0157	0.0170	0.0141	0.0120	0.0120	0.0114	0.0114	0.0119	0.0147	0.0119	0.0097	0.0096	0.0091	0.0082	0.0085	0.0098	0.0090	0.0098	0.0068	0.0068	0.0071	0.0071	0.0089	0.0089	0.0095
f22	0.0206	0.0217	0.0233	0.0244	0.0172	0.0172	0.0156	0.0132	0.0271	0.0252	0.0297	0.0259	0.0259	0.0252	0.0288	0.0236	0.0000	0.0385	0.0256	0.0132	0.0133	0.0126	0.0126	0.0112	0.0138	0.0112	0.0091	0.0090	0.0085	0.0077	0.0080	0.0091	0.0085	0.0092	0.0063	0.0064	0.0067	0.0066	0.0083	0.0083	0.0089
f23	0.0222	0.0234	0.0251	0.0263	0.0185	0.0185	0.0168	0.0142	0.0292	0.0271	0.0320	0.0279	0.0279	0.0271	0.0310	0.0255	0.0256	0.0000	0.0256	0.0142	0.0143	0.0136	0.0136	0.0120	0.0149	0.0120	0.0098	0.0097	0.0092	0.0083	0.0086	0.0099	0.0091	0.0099	0.0068	0.0069	0.0072	0.0072	0.0090	0.0090	0.0095
f24	0.0185	0.0195	0.0209	0.0219	0.0154	0.0154	0.0140	0.0118	0.0243	0.0226	0.0267	0.0232	0.0232	0.0226	0.0258	0.0212	0.0128	0.0256	0.0000	0.0118	0.0119	0.0113	0.0113	0.0100	0.0124	0.0100	0.0082	0.0080	0.0076	0.0069	0.0072	0.0082	0.0076	0.0083	0.0057	0.0057	0.0060	0.0060	0.0075	0.0075	0.0080
f28	0.0179	0.0189	0.0203	0.0213	0.0150	0.0150	0.0136	0.0115	0.0236	0.0219	0.0259	0.0393	0.0393	0.0191	0.0219	0.0179	0.0198	0.0213	0.0178	0.0000	0.0210	0.0210	0.0280	0.0097	0.0120	0.0097	0.0079	0.0078	0.0074	0.0067	0.0070	0.0080	0.0074	0.0080	0.0055	0.0056	0.0058	0.0058	0.0073	0.0073	0.0077
f34	0.0179	0.0189	0.0203	0.0213	0.0150	0.0150	0.0136	0.0115	0.0236	0.0219	0.0259	0.0396	0.0396	0.0193	0.0220	0.0181	0.0200	0.0215	0.0179	0.0210	0.0000	0.0210	0.0210	0.0097	0.0120	0.0097	0.0079	0.0078	0.0074	0.0067	0.0070	0.0080	0.0074	0.0080	0.0055	0.0056	0.0058	0.0058	0.0073	0.0073	0.0077
f37	0.0170	0.0179	0.0193	0.0202	0.0142	0.0142	0.0129	0.0109	0.0223	0.0208	0.0245	0.0375	0.0375	0.0183	0.0209	0.0171	0.0189	0.0204	0.0170	0.0140	0.0210	0.0000	0.0210	0.0092	0.0114	0.0092	0.0075	0.0074	0.0070	0.0063	0.0066	0.0076	0.0070	0.0076	0.0052	0.0053	0.0055	0.0055	0.0069	0.0069	0.0073
f38	0.0168	0.0177	0.0190	0.0199	0.0140	0.0140	0.0127	0.0108	0.0221	0.0205	0.0243	0.0375	0.0375	0.0182	0.0209	0.0171	0.0189	0.0204	0.0170	0.0140	0.0140	0.0140	0.0000	0.0091	0.0113	0.0091	0.0074	0.0073	0.0069	0.0063	0.0065	0.0075	0.0069	0.0075	0.0052	0.0052	0.0054	0.0054	0.0068	0.0068	0.0072
f6	0.0125	0.0131	0.0141	0.0148	0.0104	0.0104	0.0094	0.0080	0.0164	0.0152	0.0180	0.0325	0.0330	0.0251	0.0285	0.0238	0.0223	0.0241	0.0200	0.0195	0.0195	0.0184	0.0182	0.0000	0.0976	0.0488	0.0354	0.0345	0.0326	0.0301	0.0314	0.0499	0.0461	0.0501	0.0346	0.0348	0.0363	0.0362	0.0455	0.0455	0.0483
f7	0.0154	0.0162	0.0175	0.0183	0.0129	0.0129	0.0117	0.0099	0.0203	0.0188	0.0223	0.0401	0.0408	0.0310	0.0352	0.0295	0.0276	0.0298	0.0248	0.0241	0.0241	0.0228	0.0225	0.1463	0.0000	0.1463	0.0450	0.0439	0.0415	0.0383	0.0400	0.0617	0.0570	0.0620	0.0427	0.0431	0.0448	0.0448	0.0563	0.0563	0.0597
f8	0.0125	0.0131	0.0141	0.0148	0.0104	0.0104	0.0094	0.0080	0.0164	0.0152	0.0180	0.0325	0.0330	0.0251	0.0285	0.0238	0.0223	0.0241	0.0200	0.0195	0.0195	0.0184	0.0182	0.0488	0.0976	0.0000	0.0354	0.0345	0.0326	0.0301	0.0314	0.0499	0.0461	0.0501	0.0346	0.0348	0.0363	0.0362	0.0455	0.0455	0.0483
f16	0.0102	0.0107	0.0115	0.0121	0.0085	0.0085	0.0077	0.0065	0.0134	0.0124	0.0147	0.0265	0.0269	0.0205	0.0232	0.0195	0.0182	0.0196	0.0164	0.0159	0.0159	0.0150	0.0149	0.0707	0.0900	0.0707	0.0000	0.0322	0.0322	0.0483	0.0644	0.0407	0.0376	0.0409	0.0282	0.0284	0.0296	0.0295	0.0372	0.0372	0.0394
f17	0.0100	0.0105	0.0113	0.0119	0.0084	0.0084	0.0076	0.0064	0.0132	0.0122	0.0145	0.0261	0.0265	0.0201	0.0228	0.0191	0.0179	0.0193	0.0161	0.0156	0.0156	0.0148	0.0146	0.0689	0.0877	0.0689	0.0483	0.0000	0.0644	0.0483	0.0483	0.0400	0.0370	0.0403	0.0278	0.0280	0.0291	0.0291	0.0366	0.0366	0.0388
f18	0.0095	0.0100	0.0108	0.0113	0.0079	0.0079	0.0072	0.0061	0.0125	0.0116	0.0137	0.0248	0.0252	0.0191	0.0217	0.0182	0.0170	0.0183	0.0153	0.0148	0.0148	0.0140	0.0139	0.0652	0.0830	0.0652	0.0483	0.0483	0.0000	0.0483	0.0483	0.0380	0.0351	0.0382	0.0264	0.0265	0.0277	0.0276	0.0347	0.0347	0.0368
f31	0.0086	0.0090	0.0097	0.0102	0.0072	0.0072	0.0065	0.0055	0.0113	0.0105	0.0124	0.0223	0.0227	0.0172	0.0195	0.0164	0.0153	0.0165	0.0138	0.0134	0.0134	0.0127	0.0125	0.0602	0.0766	0.0602	0.0322	0.0322	0.0161	0.0000	0.0322	0.0342	0.0316	0.0344	0.0237	0.0239	0.0249	0.0249	0.0313	0.0313	0.0332
f36	0.0089	0.0094	0.0101	0.0106	0.0075	0.0075	0.0068	0.0057	0.0117	0.0109	0.0129	0.0233	0.0237	0.0180	0.0204	0.0171	0.0160	0.0172	0.0144	0.0139	0.0139	0.0132	0.0131	0.0628	0.0800	0.0628	0.0483	0.0161	0.0161	0.0322	0.0000	0.0357	0.0330	0.0359	0.0248	0.0249	0.0260	0.0259	0.0326	0.0326	0.0346
f9	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0399	0.0406	0.0308	0.0350	0.0293	0.0274	0.0296	0.0246	0.0239	0.0239	0.0227	0.0224	0.0499	0.0617	0.0499	0.0407	0.0400	0.0380	0.0342	0.0357	0.0000	0.0401	0.0602	0.0328	0.0328	0.0341	0.0341	0.0290	0.0290	0.0312
f10	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0369	0.0375	0.0285	0.0323	0.0271	0.0254	0.0273	0.0228	0.0221	0.0221	0.0209	0.0207	0.0461	0.0570	0.0461	0.0376	0.0370	0.0351	0.0316	0.0330	0.0401	0.0000	0.0401	0.0303	0.0303	0.0315	0.0315	0.0268	0.0268	0.0288
f11	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0401	0.0408	0.0310	0.0352	0.0295	0.0276	0.0297	0.0248	0.0240	0.0241	0.0228	0.0225	0.0501	0.0620	0.0501	0.0409	0.0403	0.0382	0.0344	0.0359	0.0401	0.0401	0.0000	0.0328	0.0328	0.0341	0.0341	0.0290	0.0290	0.0312
f12	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0277	0.0281	0.0214	0.0242	0.0203	0.0190	0.0205	0.0171	0.0166	0.0166	0.0157	0.0155	0.0346	0.0427	0.0346	0.0282	0.0278	0.0264	0.0237	0.0248	0.0328	0.0303	0.0328	0.0000	0.0209	0.0313	0.0313	0.0208	0.0208	0.0223
f13	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0279	0.0283	0.0215	0.0244	0.0205	0.0192	0.0207	0.0172	0.0167	0.0167	0.0158	0.0156	0.0348	0.0431	0.0348	0.0284	0.0280	0.0265	0.0239	0.0249	0.0328	0.0303	0.0328	0.0104	0.0000	0.0209	0.0104	0.0208	0.0208	0.0223
f14	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0290	0.0295	0.0224	0.0254	0.0213	0.0200	0.0215	0.0179	0.0174	0.0174	0.0165	0.0163	0.0363	0.0448	0.0363	0.0296	0.0291	0.0277	0.0249	0.0260	0.0341	0.0315	0.0341	0.0104	0.0313	0.0000	0.0209	0.0216	0.0216	0.0232
f15	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0290	0.0295	0.0224	0.0254	0.0213	0.0199	0.0215	0.0179	0.0174	0.0174	0.0164	0.0163	0.0362	0.0448	0.0362	0.0295	0.0291	0.0276	0.0249	0.0259	0.0341	0.0315	0.0341	0.0209	0.0313	0.0209	0.0000	0.0216	0.0216	0.0232
f25	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0364	0.0370	0.0281	0.0319	0.0268	0.0250	0.0270	0.0225	0.0218	0.0218	0.0207	0.0204	0.0455	0.0563	0.0455	0.0372	0.0366	0.0347	0.0313	0.0326	0.0581	0.0536	0.0581	0.0312	0.0312	0.0325	0.0325	0.0000	0.0373	0.0559
f26	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0364	0.0370	0.0281	0.0319	0.0268	0.0250	0.0270	0.0225	0.0218	0.0218	0.0207	0.0204	0.0455	0.0563	0.0455	0.0372	0.0366	0.0347	0.0313	0.0326	0.0581	0.0536	0.0581	0.0312	0.0312	0.0325	0.0325	0.0373	0.0000	0.0559
f41	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0386	0.0393	0.0299	0.0339	0.0284	0.0266	0.0286	0.0239	0.0232	0.0232	0.0219	0.0217	0.0483	0.0597	0.0483	0.0394	0.0388	0.0368	0.0332	0.0346	0.0623	0.0575	0.0623	0.0335	0.0335	0.0348	0.0348	0.0373	0.0373	0.0000

and

Table A3. The super-IDR matrix ${\overline{X}}_{3:1}$ under rule $R_3$ in PCAES system.

Factor	f6	f7	f8	f9	f12	f13	f14	f15	f16	f17	f18	f1	f2	f3	f4	f5	f19	f20	f21	f22	f23	f24	f25	f26	f27	f10	f11	f28	f29	f30	f31	f32	f33	f34	f35	f36	f37	f38	f39	f40	f41
f6	0.0000	0.0217	0.0109	0.0217	0.0225	0.0225	0.0234	0.0234	0.0186	0.0213	0.0212	0.0158	0.0174	0.0180	0.0190	0.0145	0.0117	0.0130	0.0151	0.0141	0.0142	0.0106	0.0267	0.0267	0.0284	0.0061	0.0055	0.0069	0.0058	0.0058	0.0064	0.0132	0.0134	0.0142	0.0117	0.0103	0.0114	0.0127	0.0134	0.0124	0.0143
f7	0.0326	0.0000	0.0326	0.0217	0.0266	0.0266	0.0277	0.0277	0.0220	0.0253	0.0251	0.0187	0.0205	0.0213	0.0225	0.0171	0.0139	0.0153	0.0179	0.0166	0.0168	0.0125	0.0316	0.0316	0.0336	0.0072	0.0065	0.0082	0.0068	0.0069	0.0075	0.0157	0.0158	0.0168	0.0138	0.0121	0.0135	0.0150	0.0159	0.0147	0.0169
f8	0.0109	0.0217	0.0000	0.0109	0.0207	0.0207	0.0215	0.0215	0.0171	0.0196	0.0195	0.0146	0.0160	0.0166	0.0175	0.0133	0.0108	0.0119	0.0139	0.0130	0.0131	0.0097	0.0246	0.0246	0.0262	0.0056	0.0051	0.0064	0.0053	0.0054	0.0059	0.0122	0.0123	0.0131	0.0108	0.0094	0.0105	0.0117	0.0124	0.0115	0.0132
f9	0.0217	0.0217	0.0217	0.0000	0.0222	0.0222	0.0230	0.0230	0.0183	0.0210	0.0209	0.0156	0.0171	0.0177	0.0187	0.0142	0.0115	0.0127	0.0149	0.0138	0.0140	0.0104	0.0263	0.0263	0.0280	0.0060	0.0054	0.0068	0.0057	0.0057	0.0063	0.0130	0.0131	0.0140	0.0115	0.0101	0.0112	0.0124	0.0132	0.0122	0.0141
f12	0.0225	0.0266	0.0207	0.0222	0.0000	0.0200	0.0300	0.0300	0.0279	0.0321	0.0319	0.0149	0.0164	0.0170	0.0179	0.0136	0.0111	0.0122	0.0142	0.0133	0.0134	0.0100	0.0252	0.0252	0.0268	0.0058	0.0052	0.0065	0.0054	0.0055	0.0060	0.0125	0.0126	0.0134	0.0110	0.0097	0.0108	0.0119	0.0127	0.0117	0.0135
f13	0.0225	0.0266	0.0207	0.0222	0.0100	0.0000	0.0200	0.0100	0.0279	0.0321	0.0319	0.0148	0.0163	0.0168	0.0178	0.0135	0.0110	0.0121	0.0141	0.0132	0.0133	0.0099	0.0250	0.0250	0.0266	0.0057	0.0051	0.0065	0.0054	0.0055	0.0059	0.0124	0.0125	0.0133	0.0110	0.0096	0.0107	0.0118	0.0126	0.0116	0.0134
f14	0.0234	0.0277	0.0215	0.0230	0.0100	0.0300	0.0000	0.0200	0.0290	0.0334	0.0332	0.0155	0.0170	0.0176	0.0186	0.0142	0.0115	0.0127	0.0148	0.0138	0.0140	0.0104	0.0262	0.0262	0.0279	0.0060	0.0054	0.0068	0.0056	0.0057	0.0062	0.0130	0.0131	0.0139	0.0115	0.0101	0.0112	0.0124	0.0132	0.0122	0.0140
f15	0.0234	0.0277	0.0215	0.0230	0.0200	0.0300	0.0200	0.0000	0.0290	0.0334	0.0332	0.0156	0.0171	0.0177	0.0187	0.0142	0.0115	0.0127	0.0148	0.0138	0.0140	0.0104	0.0263	0.0263	0.0279	0.0060	0.0054	0.0068	0.0057	0.0057	0.0062	0.0130	0.0131	0.0140	0.0115	0.0101	0.0112	0.0124	0.0132	0.0122	0.0141
f16	0.0371	0.0440	0.0341	0.0366	0.0186	0.0186	0.0194	0.0194	0.0000	0.0441	0.0441	0.0206	0.0226	0.0234	0.0247	0.0188	0.0153	0.0169	0.0197	0.0183	0.0185	0.0138	0.0348	0.0348	0.0370	0.0080	0.0071	0.0090	0.0075	0.0076	0.0083	0.0172	0.0174	0.0185	0.0152	0.0133	0.0149	0.0165	0.0175	0.0162	0.0186
f17	0.0427	0.0506	0.0392	0.0421	0.0214	0.0214	0.0222	0.0222	0.0662	0.0000	0.0882	0.0239	0.0261	0.0271	0.0286	0.0218	0.0177	0.0195	0.0227	0.0212	0.0214	0.0159	0.0403	0.0403	0.0428	0.0092	0.0083	0.0104	0.0087	0.0088	0.0096	0.0199	0.0201	0.0214	0.0176	0.0154	0.0172	0.0190	0.0202	0.0187	0.0215
f18	0.0424	0.0503	0.0390	0.0418	0.0213	0.0213	0.0221	0.0221	0.0662	0.0662	0.0000	0.0237	0.0260	0.0269	0.0284	0.0216	0.0175	0.0194	0.0226	0.0210	0.0213	0.0158	0.0400	0.0400	0.0425	0.0092	0.0082	0.0103	0.0086	0.0087	0.0095	0.0198	0.0200	0.0212	0.0175	0.0153	0.0171	0.0189	0.0201	0.0186	0.0214
f1	0.0106	0.0125	0.0097	0.0104	0.0100	0.0099	0.0104	0.0104	0.0137	0.0159	0.0158	0.0000	0.0152	0.0101	0.0101	0.0051	0.0051	0.0057	0.0066	0.0062	0.0062	0.0046	0.0112	0.0112	0.0120	0.0073	0.0065	0.0082	0.0068	0.0069	0.0075	0.0157	0.0158	0.0168	0.0139	0.0122	0.0135	0.0150	0.0159	0.0147	0.0169
f2	0.0116	0.0137	0.0107	0.0114	0.0109	0.0108	0.0114	0.0114	0.0151	0.0174	0.0173	0.0101	0.0000	0.0101	0.0101	0.0101	0.0056	0.0061	0.0071	0.0067	0.0068	0.0050	0.0121	0.0121	0.0130	0.0080	0.0071	0.0090	0.0075	0.0076	0.0083	0.0172	0.0174	0.0185	0.0152	0.0133	0.0148	0.0164	0.0175	0.0162	0.0186
f3	0.0120	0.0142	0.0110	0.0118	0.0113	0.0112	0.0118	0.0118	0.0156	0.0181	0.0179	0.0101	0.0051	0.0000	0.0101	0.0051	0.0058	0.0064	0.0074	0.0069	0.0070	0.0052	0.0126	0.0126	0.0135	0.0083	0.0074	0.0093	0.0077	0.0079	0.0086	0.0178	0.0180	0.0191	0.0157	0.0138	0.0154	0.0170	0.0181	0.0167	0.0192
f4	0.0127	0.0150	0.0117	0.0125	0.0119	0.0118	0.0124	0.0124	0.0165	0.0191	0.0189	0.0051	0.0101	0.0152	0.0000	0.0202	0.0061	0.0067	0.0078	0.0073	0.0074	0.0055	0.0132	0.0132	0.0142	0.0087	0.0078	0.0098	0.0082	0.0083	0.0090	0.0188	0.0190	0.0202	0.0166	0.0146	0.0162	0.0180	0.0191	0.0177	0.0203
f5	0.0097	0.0114	0.0089	0.0095	0.0091	0.0090	0.0095	0.0095	0.0126	0.0145	0.0144	0.0000	0.0051	0.0101	0.0051	0.0000	0.0046	0.0051	0.0059	0.0055	0.0056	0.0041	0.0100	0.0100	0.0107	0.0066	0.0059	0.0075	0.0062	0.0063	0.0069	0.0143	0.0145	0.0154	0.0127	0.0111	0.0124	0.0137	0.0146	0.0135	0.0155
f19	0.0078	0.0092	0.0072	0.0077	0.0074	0.0073	0.0077	0.0077	0.0102	0.0118	0.0117	0.0077	0.0083	0.0086	0.0091	0.0069	0.0000	0.0030	0.0060	0.0060	0.0060	0.0000	0.0088	0.0088	0.0095	0.0054	0.0048	0.0061	0.0051	0.0051	0.0056	0.0116	0.0117	0.0125	0.0103	0.0090	0.0100	0.0111	0.0118	0.0109	0.0126
f20	0.0086	0.0102	0.0080	0.0085	0.0081	0.0081	0.0085	0.0085	0.0112	0.0130	0.0129	0.0085	0.0092	0.0095	0.0100	0.0076	0.0089	0.0000	0.0089	0.0060	0.0060	0.0030	0.0097	0.0097	0.0104	0.0059	0.0053	0.0067	0.0056	0.0057	0.0062	0.0128	0.0130	0.0138	0.0113	0.0099	0.0111	0.0123	0.0130	0.0121	0.0139
f21	0.0101	0.0119	0.0093	0.0099	0.0095	0.0094	0.0099	0.0099	0.0131	0.0152	0.0151	0.0099	0.0107	0.0111	0.0117	0.0088	0.0060	0.0060	0.0000	0.0060	0.0089	0.0060	0.0113	0.0113	0.0122	0.0069	0.0062	0.0078	0.0065	0.0066	0.0072	0.0150	0.0151	0.0161	0.0132	0.0116	0.0129	0.0143	0.0152	0.0141	0.0162
f22	0.0094	0.0111	0.0086	0.0092	0.0088	0.0088	0.0092	0.0092	0.0122	0.0141	0.0140	0.0092	0.0100	0.0104	0.0109	0.0083	0.0089	0.0089	0.0060	0.0000	0.0089	0.0060	0.0106	0.0106	0.0114	0.0065	0.0058	0.0073	0.0061	0.0061	0.0067	0.0139	0.0141	0.0150	0.0123	0.0108	0.0120	0.0133	0.0142	0.0131	0.0151
f23	0.0095	0.0112	0.0087	0.0093	0.0089	0.0089	0.0093	0.0093	0.0123	0.0143	0.0142	0.0094	0.0101	0.0105	0.0111	0.0084	0.0030	0.0060	0.0089	0.0060	0.0000	0.0060	0.0107	0.0107	0.0115	0.0065	0.0058	0.0074	0.0061	0.0062	0.0068	0.0141	0.0142	0.0151	0.0125	0.0109	0.0122	0.0135	0.0143	0.0132	0.0152
f24	0.0071	0.0083	0.0065	0.0069	0.0066	0.0066	0.0069	0.0069	0.0092	0.0106	0.0105	0.0069	0.0075	0.0078	0.0082	0.0062	0.0060	0.0030	0.0089	0.0030	0.0060	0.0000	0.0080	0.0080	0.0085	0.0049	0.0043	0.0055	0.0046	0.0046	0.0050	0.0105	0.0106	0.0112	0.0093	0.0081	0.0090	0.0100	0.0106	0.0098	0.0113
f25	0.0178	0.0211	0.0164	0.0175	0.0168	0.0167	0.0175	0.0175	0.0232	0.0268	0.0267	0.0224	0.0243	0.0252	0.0265	0.0200	0.0132	0.0146	0.0170	0.0159	0.0161	0.0119	0.0000	0.0260	0.0390	0.0123	0.0110	0.0138	0.0115	0.0117	0.0127	0.0265	0.0267	0.0284	0.0234	0.0205	0.0228	0.0253	0.0269	0.0249	0.0286
f26	0.0178	0.0211	0.0164	0.0175	0.0168	0.0167	0.0175	0.0175	0.0232	0.0268	0.0267	0.0224	0.0243	0.0252	0.0265	0.0200	0.0132	0.0146	0.0170	0.0159	0.0161	0.0119	0.0260	0.0000	0.0390	0.0123	0.0110	0.0138	0.0115	0.0117	0.0127	0.0265	0.0267	0.0284	0.0234	0.0205	0.0228	0.0253	0.0269	0.0249	0.0286
f27	0.0190	0.0224	0.0175	0.0186	0.0179	0.0177	0.0186	0.0186	0.0247	0.0285	0.0283	0.0240	0.0260	0.0270	0.0284	0.0215	0.0142	0.0157	0.0182	0.0170	0.0172	0.0128	0.0260	0.0260	0.0000	0.0130	0.0117	0.0147	0.0122	0.0124	0.0135	0.0282	0.0284	0.0302	0.0249	0.0218	0.0243	0.0269	0.0286	0.0265	0.0304
f10	0.0092	0.0109	0.0085	0.0090	0.0087	0.0086	0.0090	0.0090	0.0120	0.0138	0.0138	0.0073	0.0080	0.0083	0.0087	0.0066	0.0054	0.0059	0.0069	0.0065	0.0065	0.0049	0.0123	0.0123	0.0130	0.0000	0.0044	0.0044	0.0022	0.0066	0.0044	0.0114	0.0115	0.0123	0.0090	0.0079	0.0087	0.0097	0.0078	0.0073	0.0084
f11	0.0082	0.0097	0.0076	0.0081	0.0078	0.0077	0.0081	0.0081	0.0107	0.0124	0.0123	0.0065	0.0071	0.0074	0.0078	0.0059	0.0048	0.0053	0.0062	0.0058	0.0058	0.0043	0.0110	0.0110	0.0117	0.0044	0.0000	0.0044	0.0022	0.0044	0.0066	0.0102	0.0103	0.0109	0.0080	0.0070	0.0078	0.0086	0.0070	0.0065	0.0075
f28	0.0104	0.0123	0.0096	0.0102	0.0098	0.0097	0.0102	0.0102	0.0135	0.0156	0.0155	0.0082	0.0090	0.0093	0.0098	0.0075	0.0061	0.0067	0.0078	0.0073	0.0074	0.0055	0.0138	0.0138	0.0147	0.0066	0.0066	0.0000	0.0066	0.0066	0.0089	0.0128	0.0130	0.0138	0.0101	0.0089	0.0098	0.0109	0.0088	0.0082	0.0095
f29	0.0086	0.0102	0.0080	0.0085	0.0081	0.0081	0.0085	0.0085	0.0112	0.0130	0.0129	0.0068	0.0075	0.0077	0.0082	0.0062	0.0051	0.0056	0.0065	0.0061	0.0061	0.0046	0.0115	0.0115	0.0122	0.0044	0.0066	0.0022	0.0000	0.0066	0.0066	0.0107	0.0108	0.0115	0.0084	0.0074	0.0082	0.0090	0.0073	0.0068	0.0078
f30	0.0088	0.0104	0.0081	0.0086	0.0083	0.0082	0.0086	0.0086	0.0114	0.0132	0.0131	0.0069	0.0076	0.0079	0.0083	0.0063	0.0051	0.0057	0.0066	0.0061	0.0062	0.0046	0.0117	0.0117	0.0124	0.0044	0.0000	0.0022	0.0044	0.0000	0.0044	0.0109	0.0110	0.0117	0.0085	0.0075	0.0083	0.0092	0.0075	0.0069	0.0080
f31	0.0095	0.0113	0.0088	0.0094	0.0090	0.0089	0.0094	0.0094	0.0124	0.0144	0.0143	0.0075	0.0083	0.0086	0.0090	0.0069	0.0056	0.0062	0.0072	0.0067	0.0068	0.0050	0.0127	0.0127	0.0135	0.0044	0.0022	0.0044	0.0022	0.0044	0.0000	0.0118	0.0120	0.0127	0.0093	0.0082	0.0090	0.0100	0.0081	0.0075	0.0087
f32	0.0199	0.0235	0.0183	0.0195	0.0187	0.0186	0.0195	0.0195	0.0258	0.0299	0.0297	0.0157	0.0172	0.0178	0.0188	0.0143	0.0116	0.0128	0.0150	0.0139	0.0141	0.0105	0.0265	0.0265	0.0282	0.0114	0.0102	0.0128	0.0107	0.0109	0.0118	0.0000	0.0369	0.0246	0.0172	0.0151	0.0168	0.0186	0.0151	0.0140	0.0161
f33	0.0201	0.0237	0.0185	0.0197	0.0189	0.0188	0.0197	0.0197	0.0261	0.0302	0.0300	0.0158	0.0174	0.0180	0.0190	0.0145	0.0117	0.0130	0.0151	0.0141	0.0142	0.0106	0.0267	0.0267	0.0284	0.0115	0.0103	0.0130	0.0108	0.0110	0.0120	0.0246	0.0000	0.0246	0.0175	0.0153	0.0170	0.0188	0.0152	0.0142	0.0163
f34	0.0213	0.0252	0.0196	0.0210	0.0201	0.0199	0.0209	0.0209	0.0277	0.0321	0.0319	0.0168	0.0185	0.0191	0.0202	0.0154	0.0125	0.0138	0.0161	0.0150	0.0151	0.0112	0.0284	0.0284	0.0302	0.0123	0.0109	0.0138	0.0115	0.0117	0.0127	0.0492	0.0492	0.0000	0.0186	0.0163	0.0181	0.0200	0.0162	0.0151	0.0174
f35	0.0176	0.0208	0.0162	0.0173	0.0165	0.0164	0.0172	0.0172	0.0228	0.0264	0.0262	0.0139	0.0152	0.0157	0.0166	0.0127	0.0103	0.0113	0.0132	0.0123	0.0125	0.0093	0.0234	0.0234	0.0249	0.0060	0.0053	0.0067	0.0056	0.0057	0.0062	0.0172	0.0175	0.0186	0.0000	0.0140	0.0209	0.0279	0.0237	0.0220	0.0254
f36	0.0154	0.0182	0.0142	0.0151	0.0145	0.0144	0.0151	0.0151	0.0200	0.0232	0.0230	0.0122	0.0133	0.0138	0.0146	0.0111	0.0090	0.0099	0.0116	0.0108	0.0109	0.0081	0.0205	0.0205	0.0218	0.0052	0.0047	0.0059	0.0049	0.0050	0.0054	0.0151	0.0153	0.0163	0.0070	0.0000	0.0140	0.0140	0.0208	0.0193	0.0223
f37	0.0171	0.0202	0.0158	0.0168	0.0161	0.0160	0.0168	0.0168	0.0223	0.0258	0.0256	0.0135	0.0148	0.0154	0.0162	0.0124	0.0100	0.0111	0.0129	0.0120	0.0122	0.0090	0.0228	0.0228	0.0243	0.0058	0.0052	0.0066	0.0054	0.0055	0.0060	0.0168	0.0170	0.0181	0.0140	0.0209	0.0000	0.0209	0.0230	0.0214	0.0247
f38	0.0190	0.0224	0.0175	0.0187	0.0179	0.0178	0.0186	0.0186	0.0247	0.0286	0.0284	0.0150	0.0164	0.0170	0.0180	0.0137	0.0111	0.0123	0.0143	0.0133	0.0135	0.0100	0.0253	0.0253	0.0269	0.0064	0.0057	0.0073	0.0060	0.0061	0.0067	0.0186	0.0188	0.0200	0.0209	0.0209	0.0140	0.0000	0.0255	0.0237	0.0273
f39	0.0202	0.0238	0.0186	0.0198	0.0190	0.0189	0.0198	0.0198	0.0262	0.0304	0.0302	0.0159	0.0175	0.0181	0.0191	0.0146	0.0118	0.0130	0.0152	0.0142	0.0143	0.0106	0.0269	0.0269	0.0286	0.0078	0.0070	0.0088	0.0073	0.0075	0.0081	0.0151	0.0152	0.0162	0.0178	0.0156	0.0173	0.0191	0.0000	0.0279	0.0279
f40	0.0187	0.0221	0.0172	0.0184	0.0176	0.0175	0.0183	0.0183	0.0243	0.0281	0.0279	0.0147	0.0162	0.0167	0.0177	0.0135	0.0109	0.0121	0.0141	0.0131	0.0132	0.0098	0.0249	0.0249	0.0265	0.0073	0.0065	0.0082	0.0068	0.0069	0.0075	0.0140	0.0142	0.0151	0.0165	0.0145	0.0160	0.0178	0.0279	0.0000	0.0279
f41	0.0215	0.0254	0.0198	0.0211	0.0202	0.0201	0.0210	0.0211	0.0279	0.0323	0.0321	0.0169	0.0186	0.0192	0.0203	0.0155	0.0126	0.0139	0.0162	0.0151	0.0152	0.0113	0.0286	0.0286	0.0304	0.0084	0.0075	0.0095	0.0078	0.0080	0.0087	0.0161	0.0163	0.0174	0.0190	0.0167	0.0185	0.0205	0.0558	0.0419	0.0000

.

4.4. Identification of Key Factors

After obtaining the super-IDR matrices ${\overline{X}}_{1:1}$, ${\overline{X}}_{2:1}$, and ${\overline{X}}_{3:1}$, we apply classical DEMATEL to each to obtain the three total relationship matrices ${\overline{T}}_{1:1}$, ${\overline{T}}_{2:1}$, and ${\overline{T}}_{3:1}$, respectively. Next, we rearrange the influences in ${\overline{T}}_{2:1}$ and ${\overline{T}}_{3:1}$ according to natural number order to align them with ${\overline{T}}_{1:1}$; (i.e., $F=\left\{f_i|i=1,\dots ,41\right\}$). At this point, the above total relationship matrix and the weights assigned in Section 4.1 are substituted into Equation (3), and the overall relation matrix $\overline{T}={[\overline{t_{ij}}]}_{41\times 41}$ of PCAES can be obtained, which is shown in

Table A4. The overall total relation matrix $\overline{T}$ in PCAES system.

Factor	f1	f2	f3	f4	f5	f6	f7	f8	f9	f10	f11	f12	f13	f14	f15	f16	f17	f18	f19	f20	f21	f22	f23	f24	f25	f26	f27	f28	f29	f30	f31	f32	f33	f34	f35	f36	f37	f38	f39	f40	f41
f1	0.0191	0.0936	0.0366	0.0394	0.0333	0.0552	0.0665	0.0547	0.0542	0.0477	0.0515	0.0157	0.0161	0.0167	0.0191	0.0232	0.0246	0.0244	0.0195	0.0206	0.0223	0.0161	0.0174	0.0141	0.0159	0.0159	0.0173	0.0099	0.0112	0.0095	0.0107	0.0153	0.0147	0.0136	0.0171	0.0127	0.0115	0.0122	0.0193	0.0178	0.0203
f2	0.0667	0.0199	0.0360	0.0388	0.0338	0.0547	0.0659	0.0542	0.0536	0.0470	0.0506	0.0160	0.0164	0.0170	0.0194	0.0236	0.0251	0.0249	0.0196	0.0207	0.0224	0.0163	0.0175	0.0142	0.0164	0.0164	0.0179	0.0101	0.0114	0.0097	0.0110	0.0158	0.0153	0.0142	0.0175	0.0132	0.0120	0.0127	0.0198	0.0183	0.0208
f3	0.0467	0.0474	0.0130	0.0428	0.0274	0.0452	0.0544	0.0447	0.0444	0.0384	0.0412	0.0140	0.0144	0.0149	0.0168	0.0207	0.0221	0.0219	0.0163	0.0173	0.0188	0.0132	0.0142	0.0114	0.0147	0.0147	0.0160	0.0098	0.0097	0.0084	0.0094	0.0142	0.0138	0.0140	0.0152	0.0117	0.0119	0.0127	0.0173	0.0160	0.0182
f4	0.0542	0.0571	0.0611	0.0160	0.0740	0.0538	0.0648	0.0533	0.0529	0.0461	0.0496	0.0160	0.0165	0.0170	0.0194	0.0236	0.0252	0.0251	0.0190	0.0201	0.0218	0.0152	0.0163	0.0132	0.0166	0.0166	0.0180	0.0112	0.0110	0.0095	0.0107	0.0159	0.0154	0.0156	0.0172	0.0131	0.0133	0.0141	0.0195	0.0180	0.0205
f5	0.0416	0.0441	0.0414	0.0268	0.0103	0.0418	0.0504	0.0414	0.0411	0.0359	0.0386	0.0124	0.0128	0.0132	0.0150	0.0183	0.0195	0.0194	0.0149	0.0158	0.0171	0.0119	0.0128	0.0103	0.0128	0.0128	0.0139	0.0087	0.0087	0.0075	0.0084	0.0123	0.0120	0.0121	0.0135	0.0102	0.0103	0.0109	0.0153	0.0141	0.0161
f6	0.0258	0.0271	0.0226	0.0244	0.0203	0.0228	0.0650	0.0423	0.0425	0.0340	0.0365	0.0335	0.0344	0.0356	0.0410	0.0431	0.0457	0.0452	0.0273	0.0290	0.0311	0.0233	0.0251	0.0203	0.0334	0.0334	0.0363	0.0150	0.0099	0.0088	0.0189	0.0149	0.0146	0.0195	0.0150	0.0211	0.0164	0.0172	0.0171	0.0158	0.0179
f7	0.0326	0.0342	0.0284	0.0307	0.0256	0.0875	0.0348	0.0870	0.0533	0.0437	0.0469	0.0422	0.0434	0.0448	0.0518	0.0546	0.0578	0.0571	0.0344	0.0366	0.0393	0.0294	0.0317	0.0257	0.0420	0.0420	0.0455	0.0190	0.0124	0.0111	0.0243	0.0184	0.0180	0.0244	0.0187	0.0269	0.0205	0.0215	0.0213	0.0197	0.0223
f8	0.0252	0.0264	0.0219	0.0237	0.0198	0.0422	0.0644	0.0219	0.0400	0.0337	0.0362	0.0327	0.0336	0.0347	0.0402	0.0422	0.0447	0.0441	0.0268	0.0285	0.0306	0.0227	0.0245	0.0199	0.0324	0.0324	0.0352	0.0147	0.0096	0.0085	0.0186	0.0142	0.0139	0.0188	0.0144	0.0206	0.0158	0.0166	0.0164	0.0151	0.0172
f9	0.0258	0.0271	0.0226	0.0244	0.0203	0.0517	0.0615	0.0513	0.0180	0.0387	0.0509	0.0342	0.0351	0.0363	0.0428	0.0457	0.0487	0.0482	0.0270	0.0289	0.0308	0.0241	0.0260	0.0211	0.0302	0.0302	0.0328	0.0152	0.0077	0.0072	0.0188	0.0127	0.0126	0.0197	0.0116	0.0208	0.0164	0.0172	0.0135	0.0124	0.0141
f10	0.0207	0.0217	0.0174	0.0189	0.0159	0.0433	0.0523	0.0430	0.0395	0.0118	0.0372	0.0274	0.0281	0.0290	0.0350	0.0384	0.0408	0.0403	0.0226	0.0240	0.0254	0.0196	0.0213	0.0174	0.0230	0.0230	0.0250	0.0126	0.0057	0.0060	0.0161	0.0097	0.0096	0.0160	0.0088	0.0174	0.0131	0.0137	0.0096	0.0089	0.0101
f11	0.0217	0.0226	0.0179	0.0195	0.0165	0.0458	0.0553	0.0455	0.0398	0.0367	0.0135	0.0287	0.0294	0.0304	0.0368	0.0402	0.0426	0.0421	0.0237	0.0253	0.0267	0.0205	0.0223	0.0183	0.0237	0.0237	0.0258	0.0133	0.0059	0.0057	0.0175	0.0095	0.0094	0.0163	0.0087	0.0181	0.0134	0.0139	0.0095	0.0088	0.0100
f12	0.0219	0.0232	0.0198	0.0212	0.0176	0.0265	0.0313	0.0257	0.0237	0.0160	0.0168	0.0102	0.0243	0.0309	0.0308	0.0289	0.0303	0.0300	0.0147	0.0158	0.0173	0.0286	0.0312	0.0254	0.0342	0.0342	0.0373	0.0144	0.0084	0.0083	0.0168	0.0143	0.0144	0.0194	0.0112	0.0174	0.0145	0.0154	0.0132	0.0121	0.0137
f13	0.0212	0.0224	0.0191	0.0205	0.0170	0.0257	0.0303	0.0249	0.0229	0.0156	0.0163	0.0163	0.0102	0.0236	0.0170	0.0278	0.0291	0.0289	0.0142	0.0153	0.0167	0.0275	0.0300	0.0245	0.0329	0.0329	0.0358	0.0139	0.0081	0.0080	0.0163	0.0137	0.0138	0.0187	0.0108	0.0169	0.0140	0.0149	0.0127	0.0117	0.0132
f14	0.0225	0.0237	0.0202	0.0217	0.0180	0.0271	0.0320	0.0263	0.0242	0.0164	0.0172	0.0169	0.0307	0.0112	0.0243	0.0294	0.0309	0.0306	0.0150	0.0162	0.0177	0.0292	0.0319	0.0260	0.0349	0.0349	0.0380	0.0147	0.0086	0.0085	0.0172	0.0146	0.0147	0.0199	0.0114	0.0178	0.0148	0.0158	0.0135	0.0124	0.0140
f15	0.0239	0.0253	0.0214	0.0230	0.0191	0.0278	0.0328	0.0270	0.0249	0.0170	0.0178	0.0249	0.0322	0.0259	0.0127	0.0487	0.0526	0.0524	0.0168	0.0181	0.0196	0.0393	0.0432	0.0355	0.0444	0.0444	0.0485	0.0172	0.0107	0.0108	0.0197	0.0176	0.0178	0.0230	0.0124	0.0187	0.0158	0.0168	0.0146	0.0135	0.0152
f16	0.0289	0.0306	0.0261	0.0280	0.0232	0.0434	0.0517	0.0422	0.0337	0.0224	0.0236	0.0313	0.0323	0.0333	0.0332	0.0214	0.0438	0.0438	0.0251	0.0269	0.0291	0.0398	0.0434	0.0355	0.0505	0.0505	0.0550	0.0193	0.0137	0.0131	0.0272	0.0217	0.0216	0.0262	0.0179	0.0304	0.0192	0.0204	0.0209	0.0192	0.0218
f17	0.0315	0.0334	0.0289	0.0310	0.0255	0.0466	0.0554	0.0452	0.0369	0.0237	0.0247	0.0349	0.0360	0.0371	0.0370	0.0577	0.0251	0.0687	0.0285	0.0306	0.0333	0.0451	0.0493	0.0402	0.0571	0.0571	0.0622	0.0213	0.0154	0.0149	0.0293	0.0249	0.0249	0.0295	0.0201	0.0296	0.0213	0.0228	0.0235	0.0217	0.0245
f18	0.0303	0.0321	0.0278	0.0298	0.0246	0.0446	0.0531	0.0433	0.0355	0.0226	0.0236	0.0338	0.0349	0.0359	0.0358	0.0565	0.0568	0.0240	0.0278	0.0299	0.0324	0.0440	0.0480	0.0392	0.0555	0.0555	0.0605	0.0206	0.0149	0.0144	0.0286	0.0242	0.0242	0.0286	0.0194	0.0289	0.0206	0.0220	0.0227	0.0209	0.0237
f19	0.0182	0.0190	0.0154	0.0167	0.0141	0.0170	0.0202	0.0167	0.0121	0.0094	0.0098	0.0148	0.0152	0.0157	0.0157	0.0222	0.0235	0.0233	0.0061	0.0139	0.0222	0.0292	0.0322	0.0259	0.0282	0.0282	0.0308	0.0137	0.0114	0.0106	0.0141	0.0160	0.0158	0.0174	0.0127	0.0130	0.0121	0.0128	0.0133	0.0123	0.0138
f20	0.0198	0.0207	0.0168	0.0182	0.0153	0.0185	0.0219	0.0181	0.0133	0.0102	0.0107	0.0164	0.0169	0.0174	0.0174	0.0246	0.0260	0.0257	0.0296	0.0072	0.0307	0.0322	0.0356	0.0292	0.0312	0.0312	0.0341	0.0150	0.0125	0.0117	0.0155	0.0176	0.0174	0.0192	0.0137	0.0142	0.0132	0.0140	0.0146	0.0134	0.0151
f21	0.0213	0.0223	0.0182	0.0197	0.0165	0.0201	0.0238	0.0197	0.0145	0.0111	0.0115	0.0174	0.0179	0.0184	0.0185	0.0261	0.0276	0.0273	0.0225	0.0226	0.0085	0.0330	0.0370	0.0304	0.0325	0.0325	0.0355	0.0159	0.0133	0.0124	0.0164	0.0189	0.0186	0.0205	0.0164	0.0154	0.0144	0.0153	0.0159	0.0147	0.0165
f22	0.0303	0.0316	0.0262	0.0285	0.0242	0.0190	0.0226	0.0186	0.0170	0.0135	0.0142	0.0102	0.0106	0.0109	0.0117	0.0151	0.0159	0.0158	0.0127	0.0133	0.0138	0.0163	0.0655	0.0471	0.0369	0.0369	0.0406	0.0365	0.0313	0.0325	0.0352	0.0451	0.0456	0.0461	0.0225	0.0185	0.0197	0.0214	0.0270	0.0249	0.0280
f23	0.0317	0.0331	0.0274	0.0298	0.0253	0.0197	0.0235	0.0193	0.0176	0.0141	0.0148	0.0106	0.0109	0.0113	0.0121	0.0156	0.0164	0.0163	0.0121	0.0133	0.0149	0.0475	0.0189	0.0469	0.0382	0.0382	0.0420	0.0381	0.0327	0.0339	0.0367	0.0470	0.0475	0.0481	0.0234	0.0192	0.0205	0.0223	0.0281	0.0259	0.0292
f24	0.0260	0.0271	0.0224	0.0244	0.0207	0.0160	0.0190	0.0157	0.0142	0.0115	0.0122	0.0084	0.0087	0.0090	0.0096	0.0124	0.0130	0.0129	0.0106	0.0105	0.0125	0.0292	0.0465	0.0125	0.0313	0.0313	0.0344	0.0315	0.0270	0.0281	0.0304	0.0387	0.0391	0.0396	0.0191	0.0156	0.0166	0.0181	0.0229	0.0211	0.0238
f25	0.0423	0.0445	0.0364	0.0394	0.0331	0.0375	0.0445	0.0367	0.0368	0.0297	0.0314	0.0231	0.0238	0.0246	0.0252	0.0315	0.0326	0.0322	0.0126	0.0135	0.0152	0.0556	0.0610	0.0503	0.0258	0.0597	0.0793	0.0439	0.0316	0.0335	0.0467	0.0490	0.0499	0.0568	0.0242	0.0319	0.0286	0.0309	0.0294	0.0271	0.0304
f26	0.0423	0.0445	0.0364	0.0394	0.0331	0.0375	0.0445	0.0367	0.0368	0.0297	0.0314	0.0231	0.0238	0.0246	0.0252	0.0315	0.0326	0.0322	0.0126	0.0135	0.0152	0.0556	0.0610	0.0503	0.0597	0.0258	0.0793	0.0439	0.0316	0.0335	0.0467	0.0490	0.0499	0.0568	0.0242	0.0319	0.0286	0.0309	0.0294	0.0271	0.0304
f27	0.0440	0.0463	0.0380	0.0410	0.0345	0.0391	0.0464	0.0383	0.0385	0.0311	0.0328	0.0242	0.0249	0.0257	0.0264	0.0329	0.0340	0.0336	0.0132	0.0141	0.0159	0.0579	0.0635	0.0523	0.0600	0.0600	0.0296	0.0455	0.0327	0.0347	0.0484	0.0507	0.0516	0.0589	0.0252	0.0332	0.0298	0.0322	0.0306	0.0281	0.0316
f28	0.0651	0.0679	0.0502	0.0547	0.0473	0.0307	0.0368	0.0303	0.0296	0.0251	0.0269	0.0136	0.0139	0.0144	0.0170	0.0200	0.0215	0.0214	0.0163	0.0173	0.0187	0.0206	0.0225	0.0185	0.0204	0.0204	0.0222	0.0109	0.0275	0.0271	0.0336	0.0425	0.0430	0.0455	0.0418	0.0363	0.0409	0.0464	0.0517	0.0475	0.0533
f29	0.0515	0.0538	0.0415	0.0452	0.0391	0.0286	0.0342	0.0282	0.0252	0.0212	0.0232	0.0120	0.0123	0.0127	0.0147	0.0191	0.0202	0.0200	0.0127	0.0135	0.0146	0.0173	0.0189	0.0155	0.0177	0.0177	0.0193	0.0172	0.0074	0.0211	0.0281	0.0359	0.0365	0.0365	0.0329	0.0316	0.0326	0.0359	0.0394	0.0363	0.0405
f30	0.0527	0.0552	0.0425	0.0463	0.0401	0.0277	0.0332	0.0273	0.0253	0.0213	0.0221	0.0115	0.0118	0.0122	0.0144	0.0180	0.0193	0.0191	0.0122	0.0130	0.0140	0.0165	0.0181	0.0148	0.0173	0.0173	0.0188	0.0210	0.0205	0.0076	0.0221	0.0367	0.0360	0.0378	0.0339	0.0322	0.0336	0.0371	0.0413	0.0380	0.0424
f31	0.0604	0.0632	0.0486	0.0529	0.0458	0.0440	0.0530	0.0436	0.0369	0.0318	0.0339	0.0192	0.0197	0.0204	0.0226	0.0270	0.0281	0.0250	0.0143	0.0152	0.0164	0.0209	0.0228	0.0188	0.0271	0.0271	0.0295	0.0249	0.0155	0.0202	0.0139	0.0382	0.0387	0.0427	0.0372	0.0416	0.0380	0.0417	0.0461	0.0424	0.0475
f32	0.0683	0.0717	0.0564	0.0612	0.0526	0.0390	0.0467	0.0383	0.0358	0.0286	0.0302	0.0184	0.0189	0.0195	0.0222	0.0284	0.0306	0.0305	0.0179	0.0191	0.0209	0.0237	0.0257	0.0208	0.0273	0.0273	0.0297	0.0339	0.0282	0.0300	0.0337	0.0165	0.0503	0.0396	0.0452	0.0427	0.0447	0.0494	0.0544	0.0500	0.0559
f33	0.0672	0.0705	0.0555	0.0602	0.0517	0.0380	0.0455	0.0373	0.0352	0.0280	0.0296	0.0180	0.0185	0.0191	0.0218	0.0277	0.0299	0.0298	0.0174	0.0186	0.0203	0.0231	0.0250	0.0202	0.0268	0.0268	0.0291	0.0333	0.0279	0.0284	0.0331	0.0384	0.0165	0.0387	0.0446	0.0420	0.0441	0.0488	0.0539	0.0495	0.0553
f34	0.0773	0.0810	0.0615	0.0668	0.0573	0.0395	0.0473	0.0387	0.0384	0.0305	0.0322	0.0196	0.0201	0.0208	0.0237	0.0287	0.0312	0.0313	0.0208	0.0222	0.0243	0.0262	0.0284	0.0230	0.0292	0.0292	0.0318	0.0382	0.0311	0.0325	0.0352	0.0606	0.0611	0.0195	0.0511	0.0448	0.0501	0.0554	0.0629	0.0578	0.0648
f35	0.0465	0.0488	0.0389	0.0422	0.0360	0.0446	0.0534	0.0439	0.0398	0.0319	0.0341	0.0234	0.0240	0.0249	0.0296	0.0365	0.0392	0.0390	0.0274	0.0288	0.0306	0.0379	0.0416	0.0342	0.0393	0.0393	0.0429	0.0175	0.0147	0.0137	0.0180	0.0222	0.0220	0.0240	0.0142	0.0325	0.0378	0.0458	0.0386	0.0355	0.0397
f36	0.0412	0.0432	0.0344	0.0373	0.0318	0.0498	0.0598	0.0492	0.0424	0.0351	0.0376	0.0258	0.0265	0.0274	0.0314	0.0393	0.0355	0.0354	0.0210	0.0224	0.0241	0.0333	0.0366	0.0301	0.0408	0.0408	0.0445	0.0158	0.0111	0.0106	0.0208	0.0176	0.0175	0.0214	0.0212	0.0150	0.0290	0.0300	0.0332	0.0306	0.0342
f37	0.0434	0.0454	0.0344	0.0373	0.0316	0.0365	0.0437	0.0358	0.0355	0.0281	0.0299	0.0206	0.0211	0.0219	0.0266	0.0303	0.0332	0.0332	0.0237	0.0252	0.0272	0.0343	0.0377	0.0310	0.0355	0.0355	0.0388	0.0145	0.0125	0.0119	0.0131	0.0198	0.0197	0.0221	0.0299	0.0338	0.0121	0.0376	0.0375	0.0345	0.0386
f38	0.0463	0.0486	0.0370	0.0400	0.0340	0.0393	0.0471	0.0385	0.0385	0.0303	0.0323	0.0223	0.0228	0.0237	0.0288	0.0328	0.0359	0.0360	0.0254	0.0270	0.0291	0.0370	0.0406	0.0334	0.0386	0.0386	0.0421	0.0154	0.0131	0.0127	0.0139	0.0212	0.0211	0.0223	0.0371	0.0344	0.0291	0.0144	0.0403	0.0371	0.0415
f39	0.0561	0.0589	0.0467	0.0507	0.0433	0.0534	0.0640	0.0526	0.0481	0.0393	0.0420	0.0277	0.0284	0.0294	0.0356	0.0431	0.0464	0.0462	0.0321	0.0341	0.0367	0.0460	0.0506	0.0417	0.0473	0.0473	0.0516	0.0207	0.0162	0.0154	0.0212	0.0238	0.0237	0.0270	0.0445	0.0409	0.0417	0.0456	0.0206	0.0520	0.0533
f40	0.0525	0.0551	0.0437	0.0474	0.0405	0.0500	0.0599	0.0492	0.0450	0.0368	0.0393	0.0259	0.0266	0.0275	0.0333	0.0403	0.0434	0.0432	0.0300	0.0319	0.0343	0.0430	0.0473	0.0390	0.0442	0.0442	0.0483	0.0194	0.0152	0.0144	0.0199	0.0222	0.0221	0.0252	0.0417	0.0383	0.0390	0.0427	0.0529	0.0177	0.0522
f41	0.0631	0.0662	0.0524	0.0569	0.0486	0.0600	0.0719	0.0591	0.0541	0.0442	0.0473	0.0310	0.0318	0.0329	0.0399	0.0482	0.0519	0.0516	0.0359	0.0382	0.0410	0.0517	0.0569	0.0469	0.0530	0.0530	0.0579	0.0232	0.0181	0.0172	0.0238	0.0265	0.0264	0.0302	0.0497	0.0458	0.0467	0.0510	0.0901	0.0719	0.0239

. The calculation process is as follows:

$$\overline{T}=0.5\times {\overline{T}}_{1:1}+0.3\times {\overline{T}}_{2:1}+0.2\times {\overline{T}}_{3:1}={[\overline{t_{ij}}]}_{41\times 41}.$$

(8)

We draw a heat map based on the total relationship matrix $\overline{T}$ (shown in Figure 6) to visually depict the degree of influence of each factor on the other factors (the redder the color, the greater the degree of influence).

Finally, we calculate the centrality degree and cause degree of each factor in the overall total relation matrix $\overline{T}$, resulting in the data presented in

Table 6. The centrality and cause degree of each factor in PCAES system.

Factor	di + ci	Ranking	di- − ci	Factor Type	Factor	di + ci	Ranking	di- − ci	Factor Type
f1	2.6742	12	−0.5807	result factor	f22	2.3075	24	−0.2008	result factor
f2	2.7576	9	−0.7036	result factor	f23	2.4743	20	−0.3258	result factor
f3	2.2520	26	−0.4738	result factor	f24	2.0189	33	−0.2717	result factor
f4	2.5243	17	−0.3496	result factor	f25	2.8712	4	0.1130	cause factor
f5	2.0657	31	−0.4520	result factor	f26	2.8712	4	0.1130	cause factor
f6	2.7141	10	−0.4677	result factor	f27	3.0644	3	−0.0015	result factor
f7	3.3462	1	−0.4235	result factor	f28	2.1622	29	0.4601	cause factor
f8	2.6608	13	−0.4701	result factor	f29	1.7482	36	0.4158	cause factor
f9	2.5460	15	−0.2777	result factor	f30	1.7461	37	0.4184	cause factor
f10	2.0593	32	−0.2210	result factor	f31	2.2967	25	0.4167	cause factor
f11	2.1770	28	−0.2673	result factor	f32	2.5223	18	0.4465	cause factor
f12	1.7395	38	−0.0171	result factor	f33	2.4958	19	0.3946	cause factor
f13	1.7351	39	−0.1243	result factor	f34	2.7912	7	0.5007	cause factor
f14	1.8169	34	−0.0867	result factor	f35	2.3425	22	0.4080	cause factor
f15	2.0948	30	−0.0086	result factor	f36	2.3348	23	0.2344	cause factor
f16	2.5357	16	−0.0540	result factor	f37	2.1925	27	0.2375	cause factor
f17	2.7596	8	0.0529	cause factor	f38	2.3699	21	0.2291	cause factor
f18	2.7036	11	−0.0005	result factor	f39	2.8197	6	0.4718	cause factor
f19	1.5376	41	−0.1276	result factor	f40	2.6163	14	0.4730	cause factor
f20	1.6643	40	−0.0722	result factor	f41	3.0655	2	0.7149	cause factor
f21	1.7846	35	−0.1227	result factor	-	-	-	-	-

.

Based on Table 6, we plot the causality diagram as shown in Figure 7. Note that factors f₂₅ and f₂₆ have the same centrality degree and cause degree; thus, they overlap in the Figure 7. Also, in Figure 7 the solid red circles indicate the main causal factors, the solid red triangles indicate the main factors, and the red hollow circles indicate the other factors.

According to the literature [53,62,63,64], centrality degree indicates the degree of importance of a factor in a system, and elements with higher centrality degree values are deemed more critical, warranting higher prioritization owing to their potential to induce substantial systemic perturbations. Furthermore, the Pareto principle postulates that the efficacious resolution of about 20% of the most critical issues can yield 80% amelioration in outcomes. Therefore, about 20% of the 41 indicators—that is, the top eight (about 19.5%) or nine (about 21.5%)—in terms of centrality degree should be retained as key factors in this study.

To determine the appropriate number of key factors, we examined the distribution of the top 7, 8, 9, and 10 indicators across the DPSIRM subsystems. As shown in

Table 7. Distribution of key factors under different scenarios.

Subsystems	A (Seven)	B (Eight)	C (Nine)	D (Ten)
D	0	0	1 (f2)	1
P	1 (f7)	1	1	2 (f6, f7)
S	1 (f17)	1	1	1
I	3 (f25, f26, f27)	3	3	3
R	0	1 (f34)	1	1
M	2 (f39, f41)	2	2	2

, selecting the top nine indicators (i.e., $d_i+c_i\ge 2.75$) ensures that none of the six subsystems is omitted—each subsystem is represented by at least one key factor. The ranking of centrality degree among these key factors is delineated as follows: f₇ > f₄₁ > f₂₇ > f₂₅ = f₂₆ > f₃₉ > f₃₄ > f₁₇ > f₂.

Cause degree refers to the extent of a factor’s influence on other factors. By examining centrality, we can identify the key factors, while cause degree allows us to differentiate between cause factors and result factors. When a factor’s cause degree exceeds zero $(d_i-c_i>0)$, it wields more influence than it receives, categorizing it as a cause factor. Such factors, when altered, propagate their effects throughout the system. Conversely, if a factor’s cause degree is less than zero $(d_i-c_i<0)$, it is mainly influenced by other factors, rendering it a result factor. When causal factors change, they affect result factors, necessitating a strategic consideration of their interplay to optimize the overall system effect. Result factors, while they might not influence cause factors, contribute to the system’s response and should not be disregarded. Therefore, we also identify the cause factors (f₁₇, f₂₅, f₂₆, f₃₄, f₃₉, and f₄₁) and result factors (f₂, f₇, and f₂₇) among the above nine key factors in conjunction with Table 6.

In conclusion, the PCAES system must prioritize the following nine key factors: urbanization rate (f₂), per capita arable land area (f₇), biodiversity indices (f₁₇), soil erosion situation (f₂₅), vegetation degradation situation (f₂₆), losses from anthropogenic or natural disasters (f₂₇), intensity of investment in pollution control (f₃₄), comprehensive mechanization rate of major crops (f₃₉), and intensity of agricultural R&D investment (f₄₁).

5. Discussion and Recommendations

5.1. Interactions Between Key Factors

To achieve PCAES, it is necessary to identify and manage the key factors and base management practices on those factors. In Section 4, we identify nine key factors affecting PCAES and determine which are causal factors and which are result factors. Changes in causal factors can affect the result factors; thus, it is important to focus on causality to optimize the influence of causal factors and closely monitor the outcome factors as they can, to some extent, reflect changes in PCAES.

In order to clearly illustrate the causal relationships between these key factors, we plotted the influence relationships between these factors as shown in Figure 8, which has the same meanings of red solid circles, red solid triangles and red hollow circles as in Figure 7.

During the plotting process, we set a threshold value with reference to previous studies [53,65,66,67]. in view of the large number of influential relationships involved. This threshold is calculated by adding 1.5 times the standard deviation to the mean value of all factors in Figure 6 (i.e., 0.0289 + 1.5 × 0.0142 = 0.0502). Consequently, Figure 8 only displays the effects between key factors with influence values exceeding this threshold.

In Figure 8, the value labeled on the connecting line at the arrow represents the degree of influence of the factor at the tail of the arrow on the factor at the tip of the arrow; this value can be obtained from Table A4. For example, the urbanization rate (f₂) is mainly influenced by three factors (f₃₄, f₃₉, and f₄₁ → f₂), with the intensity of investment in pollution control (f₃₄) having the most significant effect. The slowdown in the urbanization of some highland areas is often caused by delays in pollution control measures (f₃₄ → f₂). This is because the area has to cope with not only the pollution caused by industrial and agricultural production but also the large amount of domestic pollution caused by rapid urbanization [68]. To address these challenges, it is important to advance cooperative regional development. By fostering cross-regional collaboration and strategic coordination, these regions can synergize their complementary strengths to achieve holistic growth, thereby amplifying economic, social, and environmental benefits.

Similarly, per capita arable land area (f₇) is mainly affected by three factors (f₁₇, f₃₉, and f₄₁ → f₇), with the intensity of agricultural R&D investment (f₄₁) having the strongest effect on f₇. In plateau areas, cultivated land is scarce, and high-quality arable land resources are limited [69], necessitating substantial investment in agricultural R&D (f₄₁ → f₇). By leveraging advanced technological systems such as big data analytics, cloud computing, and artificial intelligence, intelligent real-time land-management systems can be constructed. Such efforts can help reveal the evolution of plateaus’ arable land quality and governance laws, ultimately promoting the effective use of arable land resources.

Losses from natural or anthropogenic disasters (f₂₇) are mainly affected by five factors (f₁₇, f₂₅, f₂₆, f₃₉, and f₄₁ → f₂₇), among which soil erosion (f₂₅) and vegetation degradation (f₂₆) have a stronger effect on f₂₇. Insufficient vegetation cover exacerbates soil erosion, leading to natural disasters such as landslides, mudslides, droughts, and pest infestations (f₂₅ and f₂₆ → f₂₇). Enhancing the rational development and utilization of soil and water resources is imperative for achieving sustainable development [70]. For this reason, it is necessary to protect natural forests and existing vegetation, implement soil conservation measures, prevent indiscriminate logging, and plan for the fallowing of steep-slope arable land in a phased manner. Moreover, we should promote the development of economic forestry and grasslands, accelerate the structural adjustment of agricultural production, and increase the pace of returning farmland to forests and grasslands to restore and build good environments. Finally, we should undertake the comprehensive management of small watersheds.

5.2. Management Suggestions

The PCA development environment is becoming increasingly complex, presenting both opportunities and challenges. To promote the sustainable development of the sector and ensure the stability of PCAES, it is necessary to identify and systematically manage the key factors. Enhancing their positive effects while mitigating their negative effects will greatly improve the stability and self-regulation capacity of agroecosystems.

This study takes Yunnan Province as a representative case to analyze the performance of key factors and propose targeted management strategies for improving plateau-characteristic agroecological security. As of 2023, the urbanization rate (f₂) in Yunnan reached 52.92% [71], while arable land resources (f₇) have become increasingly scarce [72], and land-use conflicts between urban and rural areas remain significant. In the context of rapid urban expansion, it is essential to optimize land-use structures, strictly control the occupation of high-quality farmland, and promote intensive land use. For example, around Kunming, some high-quality arable land faces encroachment due to urban sprawl. Local governments may draw on precision agriculture practices from countries like the Netherlands, applying advanced irrigation and fertilization technologies to improve land productivity and reduce the need for new farmland. Additionally, promoting efficient, facility-based, and eco-agriculture is key to improving yield per unit area and alleviating the tension between limited arable land and ecological security. In places like Dali and Lijiang, greenhouse-based off-season vegetable and flower production can enhance economic returns while reducing land dependence.

Yunnan has the richest biodiversity (f₁₇) in China [73], and its plateau ecosystems show strong natural resilience. Maintaining biodiversity helps stabilize agricultural systems, enhance their self-regulatory and productive capacities, and ensure food security. To further leverage these ecological advantages, biodiversity protection should be integrated into farmland planning and use. Standards for farmland classification should be aligned with regional ecological characteristics, and eco-friendly certification systems should be introduced to encourage farmers and enterprises to adopt diversified cropping patterns. For instance, in the Honghe Hani Rice Terraces, the combination of terrace rice and livestock has fostered a model of ecological agriculture that both conserves the landscape and increases farmers’ income. Structurally, techniques such as intercropping, relay cropping, and understory planting can improve habitat complexity, promote the presence of beneficial insects and birds, reduce pesticide dependence, and increase the ecological value of agricultural products. In Pu’er’s tea-growing regions, integrated planting of tea shrubs with trees and herbaceous plants has been shown to attract insectivorous birds, reduce pest populations, and minimize pesticide use.

However, soil erosion (f₂₅) and vegetation degradation (f₂₆) remain prominent challenges, particularly in ecologically fragile areas [74,75]. The plateau’s steep terrain and uneven rainfall exacerbate erosion risks, while human activities further intensify degradation. A zoned management approach is needed. In severely affected areas, local governments should implement watershed-based ecological restoration projects, including terracing, contour farming, and reforestation. For example, in Shangri-La, a combination of terracing and the establishment of soil-conservation forests has effectively reduced erosion. In moderately affected areas, legal enforcement should be strengthened to prevent construction-induced disturbance. In agricultural zones, the focus should be on protecting vegetation cover and enhancing ecological stability through localized land remediation and habitat restoration. To effectively address vegetation degradation, local governments should conduct systematic resource surveys and identify the underlying causes of degradation in each region. Based on this analysis, drought- and cold-resistant species should be promoted according to local ecological conditions. In high-altitude areas of Nujiang Prefecture, alpine meadow plants such as Oxytropis and Elymus nutans—which offer strong adaptability and soil conservation benefits—are well suited for restoration. Soil improvement should also be prioritized, including the application of organic fertilizers and structural amendments to enhance fertility and water retention, thereby creating a more favorable environment for vegetation recovery. Additionally, container seedling technologies may be used to cultivate native species in controlled conditions before transplantation, increasing survival rates and long-term restoration success.

In addition, agricultural economic losses (f₂₇) caused by natural and anthropogenic disasters in Yunnan reached CNY 8.65 billion in 2024 [76], highlighting severe deficiencies in disaster preparedness. The complex topography and volatile climate of plateau regions make them particularly vulnerable to extreme weather events. Local authorities should strengthen early-warning systems and rural infrastructure to cope with climate extremes. In regions such as Zhaotong, which demonstrate a high degree of susceptibility to substantial precipitation, the establishment of networks dedicated to the monitoring of rainfall and the implementation of measures to ensure preparedness in the event of flooding is imperative. Regarding pollution control (f₃₄), a diversified ecological compensation mechanism should be established. Given the fragility of plateau ecosystems, the compensation mechanism should offer tailored support for environmental protection and restoration. Greater effort should be made to attract social and international green finance into sustainable agricultural development. Additionally, establishing a carbon trading mechanism between agriculture and industry could help promote the green transformation of agriculture while enhancing the ecosystem’s economic regulatory function.

Currently, Yunnan’s level of agricultural modernization remains relatively low. In 2025, the comprehensive mechanization rate for major crops (f₃₉) was only 55.00% [37]. R&D investment in agricultural science and technology (f₄₁) related to PCA is also limited compared to developed regions. The geographic and climatic constraints of plateau areas increase the difficulty and cost of agricultural mechanization and innovation. Moving forward, the region should increase funding for agricultural research, improve talent recruitment and training, and implement policy incentives to encourage innovation. For example, the provincial government has partnered with leading agricultural universities to establish dedicated research funds supporting highland agricultural innovation. Mechanization across all stages of crop production should be accelerated, with a focus on automated feeding, forage harvesting, and the demonstration and promotion of new equipment, such as agricultural drones. Furthermore, investment in agricultural information technology should be increased. A digital platform for showcasing, trading, and promoting agricultural technologies should be developed to bridge the gap between R&D supply and market demand, thus accelerating the integration of scientific innovations into the plateau agricultural industry. For instance, a provincial agricultural big data platform could be used to track crop growth conditions and support precision farming in highland zones.

6. Conclusions

Modern PCA epitomizes new, high-quality productive forces. It involves a series of PCA enterprise clusters, which can lay a solid foundation for the economic transformation, upgrading, and leapfrog development of economically underdeveloped mountainous plateau regions. The development environment of PCA is becoming more complex, presenting both opportunities and challenges. Ensuring local AES is a critical issue that needs to be addressed. The main contributions of this study are as follows:

(1) Systematic identification of the factors affecting PCAES: Addressing the limitations of existing agroecosystem indicator systems, which generally focus on the macro level while lacking a micro-level perspective, this study innovatively examines the factors affecting PCAES at the macro, meso, and micro levels. It integrates the unique characteristics of plateau agriculture to construct an evaluation indicator system covering 41 factors. This approach not only overcomes the inadequacies of single-level or fragmented factor analyses in previous studies but also lays a foundation for systematic analyses of PCAES.

(2) Using hierarchical DEMATEL-DTP, we identify the key factors that influence PCAES. We construct a new DTP framework based on DPSIRM, TERE, and POS, analyzing the intrinsic mechanisms of the factors and their interrelationships from multiple perspectives. We propose a hierarchical DEMATEL-DTP method and identify the nine key factors (e.g., the biodiversity index and the intensity of agricultural R&D investment) that have the strongest effects on PCAES. These factors highlight the main contradictions affecting PCAES and suggest targeted guidance for optimal management.

(3) Targeted management recommendations based on the causal relationships among the key factors: We not only identify nine key factors affecting PCAES but also make management recommendations based on the causal relationships between the factors. These recommendations have the following distinctive features: First, they are focused, ensuring the priority management of key factors for efficient resource use. Second, they are highly operable, taking into account the actual situation in Yunnan Province and proposing countermeasures that fit the characteristics of local ecological security. Third, they emphasize sustainability, focusing not only on short-term goals but also on the balanced development of long-term ecological and economic benefits.

This study nevertheless has some shortcomings. First, because the hierarchical DEMATEL-DTP approach focuses on identifying key factors, we do not assess PCAES in a specific region. Future research could extend the method to the evaluation of specific regions or design a scientific evaluation method based on hierarchical DEMATEL, inviting more experts to conduct detailed assessments of the ecological security status of a specific region. Second, the integration of GIS with DEMATEL could be explored to spatially visualize the relationships between different factors, enabling more targeted and operational solutions based on regional characteristics. Third, we do not fully consider the emergent effects inherent in complex systems. Emergence refers to the phenomenon in which many small interactions among individuals lead to the creation of a larger whole that exhibits new characteristics not present in the individual components. Future research should consider incorporating system dynamics or agent-based modeling to explore how small changes in key factors can lead to significant changes in the system, thereby providing deeper insights into the sustainable management of PCAES.