Evaluation of Energy Saving and Emission Reduction in Steel Enterprises Using an Improved Dempster–Shafer Evidence Theory: A Case Study from China

Abstract

As global warming and environmental issues become increasingly prominent, steel enterprises, as a carbon-intensive industry, face urgent challenges in energy saving and emission reduction (ESER). This study develops a novel evaluation model integrating the WSR methodology, the cloud matter-element model, and an improved D-S evidence theory to address the fuzziness, randomness, and uncertainty in ESER assessments. A case study demonstrates that this approach can address the correlation between ESER indicators; quantify the evaluation process; and optimize issues related to fuzziness, randomness, and uncertainty. This finding provides a systematic evaluation framework for ESER in steel enterprises operating under the long-process production model (the blast furnace-converter model), offering valuable insights for formulating comprehensive ESER strategies throughout the entire production process.

1. Introduction

In the context of escalating climate change, promoting ESER and mitigating greenhouse gas emissions have become key challenges that countries must address [1]. Many countries have set corresponding “carbon reduction” targets and implemented a series of policy measures to promote low-carbon transformation in response to this challenge. For instance, the Chinese government has committed to reaching peak carbon emissions by 2030 and achieving carbon neutrality by 2060 [2]. The European Union has proposed the European Green Deal, aiming to achieve carbon neutrality by 2050. The deal includes measures such as carbon taxes, carbon emission trading, and improved regulation of energy-intensive industries [3]. The United States has also set emission reduction targets for the power and manufacturing sectors through initiatives such as the Clean Power Plan and the Inflation Reduction Act, promoting the adoption of clean energy [4,5]. These policies have had a particularly significant impact on high carbon emission industries, making ESER measures increasingly urgent for these sectors.

According to statistics from the World Steel Association, in 2022, the steel industry recorded a CO₂ emission intensity of 1.91 tons per tons of crude steel produced, accompanied by an energy intensity of 21.02 GJ per tons of crude steel for industrial carbon emissions [6]. Therefore, strengthening ESER efforts in the steel industry is imperative. Among these, the different steelmaking production processes significantly affect carbon emissions. Steel production processes are typically divided into long-process and short-process methods [7]. The long-process steelmaking route, primarily utilizing the blast furnace—basic oxygen furnace (BF-BOF) method, employs coke and iron ore as its principal raw materials. Production fundamentally involves ironmaking within a blast furnace, followed by steelmaking in a basic oxygen furnace. This integrated process is characterized by high production efficiency and significant cost advantages, establishing it as the predominant manufacturing pathway for the majority of the global steel industry [8]. While some research on ESER in the steel industry exists, it primarily focuses on individual factors, such as energy utilization efficiency, energy saving technologies, emission reduction technologies, and their potential. However, a systematic evaluation and analysis of the multiple factors affecting ESER in the actual production processes of steel industries has not been conducted. Consequently, existing evaluation systems lack the comprehensiveness needed to accurately reflect ESER at different stages. Furthermore, existing evaluation methods for ESER, such as fuzzy clustering analysis, fuzzy matter-element theory, and system dynamics theory, exhibit several limitations. These include inadequate handling of uncertainty and multi-source data integration.

To address these challenges, this study focuses on the long-process process (blast furnace-converter method) within the steel industry. By adopting the Wuli–Shili–Renli (WSR) methodology [9], the study holistically accounts for multiple factors influencing energy-saving and emission-reduction (ESER) efforts in steel enterprises, thereby overcoming the limitations of single-indicator evaluation methods [10,11]. Drawing on the dimensions of WuLi (physical), ShiLi (process), and RenLi (human) factors, a comprehensive evaluation framework is established, comprising 7 primary indicators and 23 secondary indicators. Furthermore, the integration of the cloud matter-element model with the improved Dempster–Shafer (D-S) evidence theory [12] effectively addresses issues related to fuzziness, uncertainty, and evidence conflict during the evaluation process. This approach enhances the ability to process multi-source data, thereby improving the reliability and accuracy of the evaluation results.

Consequently, a comprehensive evaluation model for ESER in steel enterprises is developed, offering a systematic approach to assessing the effectiveness of such initiatives. Finally, the model was applied in a case study involving MC Steel Corporation. The findings demonstrate a high degree of alignment between the actual outcomes and the evaluation results, confirming the model’s validity. The following sections discuss the five components: literature review, methodology, case study, results and discussion, and conclusions.

2. Literature Review

2.1. Energy Saving and Emission Reduction Evaluation Research

The industrial sector accounts for over 60% of global energy-related carbon emissions, making energy saving and emission reduction (ESER) a critical priority. Reflecting this urgency, high-emission industries such as electricity [13], steel [14], tobacco [15], cement [14,16], and petrochemicals [17] have increasingly focused research on both implementing ESER measures and developing methods to evaluate their effectiveness. As research progresses, ESER evaluations have gradually evolved into multi-dimensional, multi-level integrated systems that more comprehensively and accurately reflect the complex needs of different industries. For example, Xie and Jiang [18] proposed an ESER performance assessment model based on fuzzy comprehensive evaluation (FCE), which assessed the performance of ESER in road transport enterprises from six perspectives. Ma and Gao [19] employed an extended evaluation method to assess the ESER effects of distributed energy, integrating system dynamics and demand response models to evaluate the effectiveness of distributed energy systems. Zhou et al. [20] integrated the advantages of the analytic hierarchy process (AHP) and entropy methods to establish a comprehensive evaluation indicator system that includes 6 primary indicators and 23 secondary indicators, offering a comprehensive reflection of the energy saving and emission reduction status in urban transportation [21]. These analyses highlight the broad scope of ESER evaluations, with diverse methods tailored to distinct contexts. However, many models inadequately address the challenges of uncertainty, potentially introducing biases that affect evaluation accuracy.

However, prevalent evaluation models often inadequately address uncertainties, potentially introducing biases that undermine assessment accuracy. For instance, fuzzy comprehensive evaluation (FCE) relies on subjective membership functions, which can cause results to diverge from objective reality [22]. The analytic hierarchy process (AHP) is sensitive to the consistency of expert judgments and struggles with conflicting data [23]. Similarly, the entropy method exhibits limitations in integrating heterogeneous data from multiple sources [24]. Consequently, these constraints restrict the effective application of conventional methods in complex ESER evaluation contexts.

2.2. Energy Saving and Emission Reduction Research in Steel Enterprises

According to the International Energy Agency (IEA), the steel industry, as one of the most resource-intensive sectors, accounts for 8% of global energy consumption and 7% of CO₂ emissions within the energy sector [25]. Additionally, due to the generally low energy efficiency in production processes, the high energy consumption in the steel industry results in significant energy waste. Consequently, promoting ESER in steel enterprises is paramount for achieving global carbon reduction targets [26]. Existing studies suggest that improving the energy structure, enhancing energy efficiency, and advancing production technologies are key factors influencing ESER in steel enterprises [27,28,29,30]. Hasanbeigi et al. [31], focusing on the blast furnace steelmaking process, summarized 12 emerging alternative steelmaking technologies designed to improve energy efficiency, reduce CO₂ and other air pollutant emissions, and promote the sustainable development of the steel industry. In terms of energy efficiency and energy saving potential, Ma et al. [19] and Na et al. [32] have researched waste heat and energy recovery technologies, demonstrating that optimizing process flows and improving energy utilization efficiency can effectively reduce carbon emissions during steel production.

Based on the above analysis, it is evident that while experts and scholars have conducted both qualitative and quantitative analyses of ESER in steel enterprises, most studies focus on the ESER potential of individual measures or factors. However, there is a lack of research on ESER from the perspective of the entire production process.

2.3. Dempster–Shafer Evidence Theory and Its Application Research

Current research on ESER in steel enterprises continues to face challenges in addressing the complexity of uncertainty and the fusion of multi-source information. To address these challenges, researchers have explored Dempster–Shafer (D-S) evidence theory and its improved methods, finding that it is highly effective in handling ESER evaluations in complex systems [12,33]. D-S evidence theory, a method for managing uncertainty and fuzzy information, has broad applications in group decision making and multi-information fusion analysis [33,34].

As modern engineering projects become increasingly complex, D-S evidence theory has been continuously refined to enhance its applicability. For instance, Wang et al. [35] introduced conflict and reliability factors to mitigate the impact of unreliable evidence when significant evidence conflict occurs, thereby significantly improving result accuracy. Other researchers have employed techniques such as weighting [36] and weight factor redistribution to ensure that higher-quality evidence predominates in the decision-making process, thereby improving decision rationality. Additionally, Yang et al. [37] introduced an improved multi-source data fusion algorithm, which improved the capacity of D-S theory to process large-scale data, making it more suitable for complex ESER evaluation systems.

From the above analysis, this body of research demonstrates that D-S evidence theory, particularly with its subsequent enhancements, offers a robust methodology for tackling uncertainty, fuzzy information, and related complexities. These capabilities make it a powerful tool for navigating the intricacies of ESER evaluation, especially within industries like steelmaking characterized by multidimensional and uncertain factors.

3. Methodology

3.1. Research Framework

The research process began with a comprehensive review of the literature on ESER in steel enterprises, sourced from Web of Science, Google Scholar, and relevant regulations and standards. These databases provide access to peer-reviewed articles, technical reports, and other academic resources, while the referenced regulations and standards are issued by authoritative bodies (e.g., ISO, national ministries), ensuring their credibility. This comprehensive review aimed to systematically identify the critical factors influencing ESER, with the credibility and reliability of the sources further reinforced by their capacity for cross-referencing with other reputable publications or standards.

Subsequently, the WSR methodology, in conjunction with expert interviews, was employed to refine and select the relevant risk factors, thereby constructing an evaluation indicator system for ESER in steel enterprises. Based on this framework, the cloud matter-element model was applied to assign weights to the indicators. Subsequently, an improved D-S evidence theory was employed to develop the ESER model.

The detailed research framework is illustrated in Figure 1.

3.2. Indicator System Construction

3.2.1. Initial Identification of Influencing Factors

Initially, research outcomes related to ESER in the steel industry were analyzed to preliminarily identify the influencing factors. Searches were conducted on Web of Science and Google Scholar using the following search terms: TS = (“Energy Saving and Emission Reduction” or “ESER” and “Iron and Steel”), TS = (“Carbon Emission” or “CO₂ emission” and “Iron and Steel”), TS = (“Energy Consumption” and “Steel Industry”).

Following the screening of literature highly relevant to the research theme, 21 core papers were meticulously selected for in-depth interpretation and analysis. Through the consolidation of content from these peer-reviewed articles, an initial set of 30 potential influencing factors was identified. To further ensure the comprehensiveness and authoritativeness of these factors, the research team consulted relevant national and industry technical standards in China, extracting 8 supplementary key factors.

Finally, a preliminary list of 28 ESER influencing factors was established through cross-comparison, validation, and integrated analysis of the factors derived from both literature and standards. This refinement involved several steps: Firstly, factors with similar meanings or strong correlations were consolidated. For instance, “Sinter and pellet ratio” and “Blast furnace pulverized coal injection ratio” were merged into the more comprehensive indicator “Physicochemical index of furnace burden”. Secondly, the phrasing of certain factors was modified for precision; for example, the original factor “Blast furnace top gas pressure recovery” was redefined as “Blast furnace top gas pressure recovery utilization rate”. This process resulted in the initial list of 28 influencing factors presented in

Table 1. Initial processing of influencing factors.

Serial Number	Influencing Factors	Source References	Initial Processing	Processing Results	Standard Specifications
1	Fuel particle size	[38,39]	Retained	1 Fuel particle size
2	Iron ore quality	[32,40,41]	Modified	2 Furnace iron ore quality	[42]
3	Harmful substances in raw material	[43]	Retained	3 Harmful substances in raw material
4	Raw material granularity	[41,44]	Retained	4 Raw material granularity
5	Sintering and pellet ratio	[40]	Merged	5 Raw material index	[45]
6	Blast furnace coal 6 injection ratio	[46]
7	Sintering machine performance	[32,47]	Retained	6 Sintering machine performance
8	Blast furnace equipment performance	[48]	Retained	7 Blast furnace equipment performance
9	Heating furnace equipment performance	[48,49,50]	Retained	8 Heating furnace performance
10	Solvent unit consumption	[51]	Retained	9 Solvent unit consumption
11	Fuel unit consumption	[39]	Retained	10 Fuel unit consumption
12	Coke ratio	[52,53]	Retained	11 Coke ratio
13	Coal ratio	[52,53]	Retained	12 Coal ratio
14	Blast furnace burden structure	[46]	Merged	13 Iron-to-steel ratio	[54,55]
15	Iron-to-steel ratio	[56]
16	Oxygen demand for steelmaking		Added	14 Oxygen demand for steelmaking	[45]
17	Converter coal gas consumption		Added	15 Converter coal gas consumption	[45]
18	Desulfurized ash usage	[44]	Retained	16 Desulfurized ash usage
19	Flue gas waste heat utilization	[57]	Merged	17 Flue gas waste heat rate	[45]
20	Residual heat recovery efficiency	[53]
21	Blast furnace gas utilization rate	[43,47]	Retained	18 Blast furnace gas utilization rate
22	Gas recovery equipment maintenance level	[54,58]	Modified	19 Gas recovery equipment maintenance level	[45,54]
23	Blast furnace pressure recovery	[53]	Retained	20 Blast furnace pressure recovery rate
24	Converter coal gas recovery	[59]	Retained	21 Converter coal gas recovery
25	Hot delivery equipment	[32]	Retained	22 Hot delivery equipment
26	Degree of process Integration	[57]	Merged	23 Automation control level	[45]
27	Automation control degree	[51]
28	Sintering operation skills	[51]	Retained	24 Sintering operation skills
29	Blast furnace operation skills	[52]	Retained	25 Blast furnace operation skills
30	Converter operation skills	[51]	Retained	26 Converter operation skills
31	Heating operation skills	[57]	Retained	27 Heating operation skills
32	Converter equipment maintenance level	[57]	Retained	28 Converter equipment maintenance level

.

3.2.2. Finalization of Influencing Factors

To optimize the influencing factors for ESER evaluation, this study employed an expert consultation method. Acknowledging the complexity, multiple stages, and extended workflow characteristic of long-process steel production, alongside potential biases arising from diverse expert backgrounds and perspectives [60], a panel of 15 experts was meticulously selected. Selection criteria emphasized broad expertise covering overall planning, material procurement, technology implementation, process optimization, equipment maintenance, and ESER assessment (refer to

Table A1. Statistical information of experts.

No.	Expert Name	Organization	Job Category
1	Expert A	Sintering Plant, MG Co., Ltd.	production supervisor
2	Expert B	Sintering Plant, MG Co., Ltd.	deputy chief engineer of production
3	Expert C	Sintering Plant, MG Co., Ltd.	plant manager
4	Expert D	Sintering Plant, MG Co., Ltd.	deputy plant manager
5	Expert E	CJ Steel Co.	director of energy and environmental center
6	Expert F	CJ Steel Co.	head of manufacturing department
7	Expert G	CJ Steel Co.	assistant to general manager
8	Expert H	WH Steel Co.	chief engineer of production
9	Expert I	WH Steel Co.	director of production department
10	Expert J	Sintering Plant, BG Co., Ltd.	deputy plant manager
11	Expert K	Sintering Plant, BG Co., Ltd.	chief engineer of production
12	Expert L	Sintering Plant, BG Co., Ltd.	technical supervisor
13	Expert M	Sintering Plant, BG Co., Ltd.	plant manager
14	Expert N	CG Steel Co.	deputy chief engineer
15	Expert O	CG Steel Co.	senior technical manager

for expert details).

The consultation utilized a two-round iterative process. In the first round, experts received briefings on the research background, objectives, and initial definitions of potential ESER evaluation factors for steel enterprises. They subsequently reviewed the initial list, providing judgments and suggestions for refinement. Feedback from this round was analyzed, leading to modifications of the factor list. In the second round, experts reevaluated the revised list of factors based on the first-round feedback and subsequent revisions. Following the collection of evaluation forms, the data were processed and analyzed. Applying a pre-defined significance threshold, factors failing to achieve an 80% consensus rate among experts were eliminated from the final list.

This rigorous, iterative consultation process resulted in the final identification of 23 key influencing factors, which are detailed in

Table 2. Final determination of influencing factors for steel enterprises.

Serial Number	Influencing Factors	Serial Number	Influencing Factors
1	Fuel particle size (C11)	13	Gas consumption in rolling (C36)
2	Furnace iron ore quality (C12)	14	Flue gas heat recovery rate (C41)
3	Harmful substances in raw materials (C13)	15	Blast furnace gas utilization rate (C42)
4	Furnace chemical and physical index (C14)	16	Blast furnace pressure recovery utilization rate (C43)
5	Sintering machine performance (C21)	17	Converter gas recovery per ton of steel (C44)
6	Blast furnace equipment performance (C22)	18	Hot delivery rate (C51)
7	Heating furnace equipment performance (C23)	19	Automated control degree (C52)
8	Solvent consumption per unit (C31)	20	Operational skills level (C61)
9	Fuel unit consumption (C32)	21	Equipment maintenance level (C62)
10	Fuel ratio (C33)	22	Employee training level (C71)
11	Iron to steel ratio (C34)	23	Management system improvement level (C72)
12	Oxygen consumption in steelmaking (C35)

.

3.2.3. Establishment of the Evaluation Indicator System

This research employed the WSR (physical–process–human) system methodology for a systematic analysis of factors influencing ESER in steel enterprises. The WSR methodology decomposes complex problems into three dimensions—physical (Wuli), process (Shili), and human (Renli)—to facilitate a comprehensive understanding of all aspects.

The physical dimension (Wuli) focuses on foundational conditions and resources like raw materials, equipment, and resource usage, leading to the establishment of three primary indicators: raw material quality (B1), equipment performance (B2), and resource consumption (B3). The process dimension (Shili) centers on operational flow and efficiency, resulting in two primary indicators: secondary energy utilization (B4) and process integration (B5). The human dimension (Renli) pertains to personnel and management aspects, yielding two primary indicators: professional skills (B6) and institutional training (B7). The definitions for these primary indicators are detailed in

Table 3. Determination process and meaning of primary indicators.

Dimension	Primary Indicator	Optimized Meaning
WuLi (physical)	Raw material quality (B1)	Evaluates the quality and performance of raw materials used in the production process to ensure efficient production flow and minimize pollutant emissions.
	Equipment performance (B2)	Assesses the technical condition and maintenance level of production equipment. Properly maintained equipment significantly reduces energy consumption and environmental emissions.
	Resource consumption (B3)	Analyzes the usage of resources such as water, electricity, and fuel during production. Optimizing resource utilization minimizes system inefficiencies and enhances overall sustainability.
ShiLi (process)	Secondary energy utiliza-tion (B4)	Highlights the importance of recycling and reusing waste heat and waste gas generated during production processes to improve energy efficiency and reduce overall energy losses.
	Process integration (B5)	Focuses on enhancing coordination and ensuring smooth transitions between production processes. Proper integration reduces resource waste and improves operational efficiency.
Renli (human)	Professional skills (B6)	Evaluates the skill level and expertise of operators. Enhancing professional skills optimizes resource utilization and boosts efficiency throughout the production lifecycle.
	Institutional training (B7)	Emphasizes the establishment of effective management systems and employee training programs to promote energy saving awareness, strengthen emission reduction capabilities, and support the achievement of sustainable development goals.

.

Based on the characteristics of the long-process production model in steel enterprises, the 23 refined key secondary indicators were mapped to these respective primary indicators, forming the ESER evaluation indicator system for steel enterprises, as illustrated in Figure 2.

3.2.4. Generalizability Analysis of the Indicator System

The generalizability of the proposed ESER indicator system is supported by several factors inherent to the global steel industry. Firstly, the widespread adoption of the long-process production model provides a strong foundation. According to the World Steel Association, this route accounted for approximately 71.1% of global crude steel output in 2022, establishing it as the mainstream choice worldwide, not merely typical in China [61].

Secondly, core production processes exhibit remarkable consistency across long-process steel plants globally. Major stages—sintering, ironmaking, steelmaking, and rolling—share fundamental principles and operational flows, irrespective of the producer, such as China’s Baowu Steel or international counterparts like ArcelorMittal. This process standardization ensures that indicators directly reflecting these stages possess inherent relevance worldwide. For instance, metrics like “Flue gas waste heat recovery rate (C41)”, “Blast Furnace Gas utilization rate (C42)”, and “Iron-to-steel ratio (C34)” are intrinsically linked to critical long-process operations. Similarly, indicators assessing core equipment, including “Blast furnace equipment performance (C22)” and “Heating furnace equipment performance (C23)”, address universally critical factors for ESER in such facilities.

Furthermore, the human and management dimensions are universally crucial. The inherent complexity and high-risk nature of long-process steelmaking necessitate global reliance on operator expertise and rigorous maintenance protocols for safe, stable, and energy-efficient operations. Consequently, human-factor indicators like “Process operation skill level (C61)” and “Equipment maintenance level (C62)” are fundamental prerequisites worldwide. Additionally, amidst increasingly stringent global ESER standards and technological advancements, effective “Management personnel training (C71)” and robust “Management systems (C72)” are indispensable for any long-process producer pursuing sustainable adaptation and optimal ESER performance, as technology alone cannot achieve desired outcomes without proficient personnel and sound management structures.

In conclusion, the ESER indicator system developed in this study provides a robust and valuable assessment model applicable not only in China but also globally for steel enterprises utilizing the long-process model. While the system offers broad relevance due to the aforementioned factors, companies can tailor specific indicators—referencing the definitions and adjustment principles provided—to align with their unique equipment, technology, or local regulatory contexts, ensuring targeted and effective application.

3.3. Construction of the Evaluation Model

3.3.1. Classification of Energy Saving and Emission Reduction Levels

To facilitate the determination of ESER evaluation levels for steel enterprises, this study adopted the classification method outlined in the Energy Management Performance Evaluation Guidelines for the Steel Industry (GB/T 40084-2021) [62]. A grading set was defined as follows:

Evaluation Set = {S1, S2, S3, S4, S5}

The levels of ESER were classified into five categories: excellent (S1): (90, 100]; good (S2): (80, 90]; average (S3): (70, 80]; below average (S4): (60, 70]; poor (S5): (0, 60].

Experts were subsequently invited to rate each indicator affecting ESER in steel enterprises. Through a review of relevant literature and visits to steel enterprises, along with national standards such as the Steel Industry Energy Management Performance Evaluation Guidelines, Sintering Process Energy Efficiency Evaluation Guidelines, Blast Furnace Process Energy Efficiency Evaluation Guidelines, and the IPCC 2006 National Greenhouse Gas Inventory Guidelines (2019 Revision), 13 quantitative indicator grading standards were compiled (refer to

Table A4. Quantitative indicator evaluation levels.

No.	Evaluation Indicator	Unit	Excellent	Good	Average	Blow Average	Poor
1	Fuel particle size (C11)	%	Proportion of 0.5–5 mm particles > 70%	Proportion of 0.5–5 mm particles [70–60%)	Proportion of 0.5–5 mm particles [60–50%)	Proportion of 0.5–5 mm particles [50–40%)	Proportion of 0.5–5 mm particles ≤ 40%
2	Furnace iron ore quality (C12)	%	>57	[57–56)	[56–55)	[55–54)	≤54
3	Solvent unit consumption (C31)	kg/t	<130	[130–140)	[140–150)	[150–160)	≥160
4	Fuel unit consumption (C32)	kg/t	<48	[48–50)	[50–52)	[52–54)	≥54
5	Fuel ratio (C33)	kg/t	<500	[500–520)	[520–540)	[540–550)	≥550
6	Iron-to-steel ratio (C34)	%	<80	[80–85)	[85–90)	[90–95)	≥95
7	Oxygen consumption for steelmaking (C35)	m3/t	<45	[45–48)	[48–51)	[51–53)	≥53
8	Gas consumption per unit in rolling mill (C36)	m3/t	<260	[260–280)	[280–290)	[290–300)	≥300
9	Flue gas heat recovery rate (C41)	%	>70	[70–65)	[65–60)	[60–55)	≤55
10	Blast furnace gas utilization rate (C42)	%	>50	[50–45)	[45–40)	[40–35)	≤35
11	Recovery utilization rate (C43)	%	>90	[90–70)	[70–50)	[50–40)	≤40
12	Converter gas recovery per ton of steel (C44)	m3/t	>120	[120–110)	[110–100)	[100–90)	≤90
13	Hot delivery rate (C51)	%	>90	[90–80)	[80–70)	[70–60)	≤60

). Additionally, with reference to standards such as the Energy Conservation Design Standards for Steel Enterprises, Metallurgical Coke Quality Standards, Technical Standards for Iron Sintering Enterprises in Large Blast Furnaces, and Energy Conservation Design Technical Specifications for Steel Rolling Heating Furnaces, 10 qualitative indicator grading standards were compiled (refer to

Table A5. Qualitative indicator evaluation levels.

No.	Evaluation Indicator	Excellent	Good	Average	Below Average	Poor
1	Harmful substances in raw materials (C13)	Almost no harmful components in raw materials.	Few harmful impurities in raw materials.	Harmful impurities present but within national standards.	Significant harmful impurities, content near upper limit of national standards.	High quantity of harmful impurities, exceeding national standards.
2	Furnace stability (C14)	Highly stable physical and chemical indicators.	Indicators show slight fluctuations with high stability.	Indicators generally stable but occasionally show significant fluctuations.	Significant deviations in indicators, low stability.	Large deviations in indicators, poor stability.
3	Sintering equipment performance (C21)	Ultra-large sintering machines with advanced ESER facilities; within 5 years of operation; world-class design indicators.	Large sintering machines with mature facilities; within 10 years of operation; no air leakage at critical points; domestically advanced.	Equipment within 15 years of operation; minor air leaks manageable through regular maintenance.	Equipment over 15 years old; facilities outdated; low efficiency and high energy consumption.	Equipment over 20 years old; severe air leakage; outdated and in need of replacement.
4	Blast furnace equipment performance (C22)	Within 10 years of operation; volume > 2000 m3; advanced control and feeding systems; leading energy facilities.	Within 15 years of operation; volume > 1000 m3; advanced feeding and control systems; modern energy facilities.	Equipment over 15 years old; volume < 1000 m3; outdated energy systems requiring continuous upgrades.	Equipment over 20 years old; volume < 800 m3; incomplete energy facilities; outdated.	Equipment over 25 years old; volume < 400 m3; no energy facilities; approaching end of life.
5	Heating furnace equipment performance (C23)	Advanced regenerative step-hearth furnace with composite insulation; excellent heat retention and control.	Regenerative step-hearth furnace with honeycomb ceramic insulation; good thermal inertia and flexible operation.	Step-hearth furnace with basic regenerative design; inadequate insulation, high energy loss.	Step-hearth furnace with ordinary refractory insulation; poor heat retention and low efficiency.	Pusher-type furnace; high energy consumption and low efficiency; obsolete technology.
6	Automation level (C52)	Intelligent manufacturing technology with centralized control of major processes.	Full integration of basic and process automation across all production lines.	Key lines automated, but process control lacks full integration.	Few lines with integrated automation, minimal automation in other areas.	Traditional manual equipment with no automation, labor-intensive operations.
7	Operational skills (C61)	Over 50% of key operators hold senior technician qualifications or have won national-level skill competitions; possess over 5 years of relevant work experience.	40–50% of key operators hold technician qualifications or have won provincial-level skill competitions; possess 3–5 years of relevant work experience.	40–60% of key operators hold intermediate worker qualifications or higher; possess 2–3 years of relevant work experience.	30–40% of key operators hold junior worker qualifications; possess 1–2 years of relevant work experience.	Less than 20% of key operators hold any qualification certificates; lack relevant work experience.
8	Equipment maintenance level (C62)	High maintenance level, almost no unplanned repairs.	Relatively high level of equipment maintenance; low frequency of unscheduled maintenance. 3–4 instances of unscheduled maintenance annually.	Average level of equipment maintenance; moderate frequency of unscheduled maintenance. 5–6 instances of unscheduled maintenance annually.	Low level of equipment maintenance; high frequency of unscheduled maintenance. 7–9 instances of unscheduled maintenance annually.	Very low level of equipment maintenance; ≥10 instances of unscheduled maintenance annually.
9	Management training (C71)	Management personnel participate in energy saving and emission reduction (ESER)-related training ≥ 7 times per year, with each session lasting ≥ 4 h.	Management personnel participate in ESER-related training 5–6 times per year, with each session lasting ≥ 3 h.	Management personnel participate in ESER-related training 4–5 times per year, with each session lasting ≥ 2 h.	Management personnel participate in ESER-related training 2–3 times per year, with each session lasting < 2 h.	Management personnel participate in ESER-related training < 2 times per year, or have not participated in any relevant training.
10	Management system maturity (C72)	Comprehensive and well-established energy-saving and emission-reduction management system.	Fairly complete management system.	Relevant management system in place but requires further improvement.	Management system exists but is not fully developed.	No management system for energy-saving and emission-reduction.

).

Since the grading of ESER evaluation indicators is based on intervals, particularly for qualitative indicators, the boundaries of these intervals may be subject to randomness and ambiguity. Therefore, the cloud model can be utilized to effectively address these issues.

3.3.2. Establishment of the Grading Matrix Based on the Cloud Model

The cloud matter-element model is developed based on matter element theory, integrating the cloud model. The cloud model, proposed by Academician Deyi Li in 1995, is a mathematical framework that combines traditional fuzzy mathematics with probability theory to map qualitative concepts to quantitative data, addressing the inherent randomness in determining fuzzy membership degrees. The cloud model exists in various forms, depending on the underlying probability distribution functions. The normal cloud model, which is based on the normal distribution in probability theory and the Gaussian membership function in fuzzy sets, quantifies the overall characteristics of qualitative concepts through cloud digital features. These features include the expectation ($\mathrm{Ex}$), which represents the central position of the cloud; entropy ($\mathrm{En}$), which indicates the degree of uncertainty or fuzziness; discreteness, which reflects the extent of dispersion; and hyper-entropy (He), which measures the rate of change of entropy. By substituting the feature values v in the Matter Element Model $\mathrm{R}=\left(\mathrm{N},\mathrm{c},\mathrm{v}\right)$ with normal clouds $\left(\mathrm{Ex},\mathrm{En},\mathrm{He}\right)$, the cloud matter-element model is derived. In this model:

N represents the evaluation object;

C represents the features of the object;

V represents the specific value of C.

The specific expression is as follows:

$$R=\left[\begin{array}{c}{R}_1\\ R_2\\ ⋮\\ R_n\end{array}\right]=\left[\begin{array}{cc}{N}_1& C_1\\ & C_2\\ & ⋮\\ & C_n\end{array}\begin{array}{c}\\ \end{array}\begin{array}{c}{V}_1\\ V_2\\ \\ V_n\end{array}\right]=\left[\begin{array}{c}N\\ \\ \\ \end{array}\begin{array}{cc}{C}_1& \left(E{x}_1,E{n}_1,H{e}_1\right)\\ C_2& \left(E{x}_2,E{n}_2,H{e}_2\right)\\ & ⋮\\ {\mathrm{C}}_n& \left(E{x}_n,E{n}_{n}H{e}_n\right)\end{array}\right]$$

(1)

The initial step in applying the cloud matter-element model is to determine the normal cloud parameters (Ex, En, He). The calculation is performed based on the grading intervals of the evaluation indicators, using the following formula:

$$Ex=\left(a+b\right)/2$$

(2)

$$En=\left(b-a\right)/2\sqrt{2\ln 2}$$

(3)

$$He=t\times En$$

(4)

The calculation yields five numerical characteristics, where a and b represent the lower and upper bounds of the grading intervals, and t is a constant that can be adjusted according to the specific fuzziness and randomness of the system. In this study, t = 0.5, under which He equals half of En, defining the moderate fluctuation level of the system’s initial fuzziness.

In the process of energy-saving and emission-reduction evaluation for steel enterprises, the average score $x_j$ provided by experts for each evaluation indicator serves as a cloud. The membership degree $\mathrm{\mu }\left(\mathrm{x}\right)$ between the indicator value $x_j$ and the clouds of different grading levels is calculated using the following formula, objectively quantifying the extent to which the indicator value belongs to each grading cloud.

$$\mu \left(x\right)=\exp \left[-{\left(x_j-Ex\right)}^2/2{\left({En}^{\prime }\right)}^2\right]$$

(5)

$$E{n}^{\prime }=r\times He+En$$

(6)

In the formula, ${\mathrm{E}\mathrm{n}}^{\prime }$ represents the expected value of En, and He is the standard deviation of the normal cloud. A random variable r is introduced, following a standard normal distribution, ensuring that each calculation introduces slight variations to simulate the randomness inherent in real-world systems. Accordingly, this study conducted 1000 simulations, using the median value as the membership degree for the ESER evaluation indicators of steel enterprises.

To enhance the model’s ability to manage fuzziness and reduce the impact of uncertainty on evaluation results, the Dempster–Shafer (D-S) evidence theory was applied to integrate multi-indicator information during the ESER evaluation for steel enterprises.

3.3.3. Optimization of ESER Evaluation Based on D-S Evidence Theory

Dempster–Shafer theory (DST), originating from Dempster’s work (1967) [63] and Shafer’s subsequent extensions involving belief functions and probability bounds, provides a robust framework for reasoning under uncertainty. Unlike Bayesian inference, which necessitates prior probabilities often difficult to ascertain accurately amidst incomplete or noisy data, DST processes evidence directly via basic probability assignments (BPAs). Crucially, DST inherently distinguishes between “lack of evidence” and “conflicting evidence”, a capability not readily available in Bayesian approaches [64,65]. Compared to Fuzzy logic, which employs subjective membership functions for ambiguity but encounters limitations in multi-source data fusion [40], DST offers more nuanced uncertainty management through belief and plausibility functions [66]. Building upon these foundational strengths, this study introduces an improved DST methodology specifically tailored for ESER evaluation.

Our optimized approach utilizes the Dempster combination rule but incorporates key refinements for improved performance [67]. Specifically, evidence combination weights are dynamically adjusted based on two metrics: the distance between evidence bodies (measuring conflict) and the uncertainty of each evidence body (quantified using Shannon entropy). This allows the model to adaptively assign more influence to more reliable and consistent evidence sources. Furthermore, the BPAs associated with the evaluation indicators undergo a weighted average correction prior to fusion. This optimized methodology enhances the precision and reliability of ESER assessments, particularly when grappling with the multi-source heterogeneous data and complex uncertainties inherent in steel manufacturing.

The primary innovations of this improved D-S approach for ESER evaluation include the following:

Dynamic evidence weighting: Employing Shannon entropy and evidence distance enables adaptive prioritization of information sources, significantly improving fusion accuracy and reliability when handling heterogeneous or conflicting data.

Targeted BPA correction: The pre-fusion weighted correction of BPAs allows the model to more accurately reflect the true influence of each evaluation factor, mitigating biases from incomplete or subjective initial assessments.

Improved practical utility: These methodological improvements translate directly into greater practical effectiveness, empowering steel enterprises to more reliably identify energy inefficiencies and emission reduction potentials, thereby fostering the development of more scientific and targeted ESER strategies.

Detailed steps and corresponding equations for this improved D-S methodology are presented in Figure 3.

4. Case Study

4.1. Overview of the Case

MC Steel Enterprise is situated in Dangtu County, Maanshan, Anhui Province, China. It is a representative long-process steel enterprise encompassing the entire industrial chain, from iron ore processing to the production of finished steel products. The company’s production processes include sintering, ironmaking, steelmaking, and rolling. It operates three 192-square-meter sintering machines, two 1080-cubic-meter blast furnaces, one 1250-cubic-meter blast furnace, two 120-ton converters, one 140-ton electric arc furnace, and four production lines for bar and high-speed wire rod products, with a total annual steel production capacity of approximately 5 million tons.

By the end of 2022, MC Steel had produced 3.96 million tons of pig iron, 4.61 million tons of steel billets, and 4.65 million tons of various wire rod products. However, alongside this capacity expansion, the company faced a substantial increase in energy consumption and emissions. Under increasingly stringent ESER regulations, the enterprise faces immense pressure and urgently requires the establishment of a comprehensive and scientifically rigorous evaluation system for ESER. This system would facilitate a comprehensive assessment and optimization of its ESER management strategies.

4.2. Calculation of Energy Saving and Emission Reduction Levels for Indicators

To ensure assessment rigor and accuracy, this study engaged ten senior managers specializing in energy saving and emission reduction (ESER) from MC Steel Enterprise. These experts, possessing extensive professional knowledge and practical ESER management experience, were tasked with evaluating the current performance of each established indicator.

Prior to the evaluation, the expert panel received comprehensive materials: detailed indicator definitions (

Table A3. Evaluation index system for ESER in steel enterprises.

Dimension	Primary Indicator	Secondary Indicator	Indicator Definition
WuLi (Physical)	Raw material quality (B1)	Fuel particle size (C11)	Percentage of fuel particles with sizes ranging between 25 and 80 mm, ensuring optimal combustion efficiency.
		Furnace iron ore quality (C12)	Average grade of furnace iron ore input, reflecting material quality.
		Harmful substances in raw materials (C13)	Distribution and concentration of harmful impurities in raw materials, affecting production quality.
		Furnace chemical and physical index (C14)	Stability and consistency of the chemical and physical properties of the furnace materials, crucial for ensuring efficient and safe operations.
	Equipment performance (B2)	Sintering machine performance (C21)	Installation quality and operational reliability of sintering equipment.
		Blast furnace equipment performance (C22)	Comprehensive performance of blast furnace equipment, including operational stability and maintenance standards.
		Heating furnace equipment performance (C23)	Performance of heating furnace equipment, assessing efficiency and stability during operation.
ShiLi (Process)	Resource consumption (B3)	Solvent consumption per unit (C31)	Total solvent consumption divided by the weight of the product produced by sintering
		Fuel unit consumption (C32)	Total fuel consumption divided by total product obtained from sintering production
		Fuel ratio (C33)	Combined amount of coke and coal consumed per ton of iron produced in the blast furnace
		Iron to steel ratio (C34)	Ratio of molten iron in the furnace to steel output in the steelmaking converter production process
		Oxygen consumption in steelmaking (C35)	Oxygen consumption per ton of steel in the steelmaking process
		Gas consumption in rolling (C36)	Amount of gas consumed per ton of steel in the billet setting process
	Secondary energy utilization (B4)	Flue gas heat recovery rate (C41)	Ratio of energy gained through flue gas waste heat recovery to total waste heat in the flue gas.
		Blast furnace gas utilization rate (C42)	Proportion of the reducing components C0 and H2 in the gas involved in the reduction reaction and the proportion of heat absorbed by the charge.
		Blast furnace pressure recovery utilization rate (C43)	Energy recovered by residual pressure in the blast furnace divided by the total energy of residual pressure in the blast furnace.
		Converter gas recovery per ton of steel (C44)	The amount of gas produced during the smelting of one ton of iron into qualified steel, i.e., the amount of gas recovered from the gas cabinet at equal pressure.
	Process integration (B5)	Hot delivery rate (C51)	Billet into the heating furnace surface temperature ≥ 400 °C billet share.
		Automated control degree (C52)	Degree of automation of production lines.
Renli (Human)	Professional skills (B6)	Operational skills level	Skill level, proficiency of staff.
		Equipment maintenance level	High and low levels of equipment maintenance.
	Institutional training (B7)	Employee training level (C71)	Number of training sessions on ESER attended by managers.
		Management system improvement level (C72)	Whether the management system of ESER is perfect.

), indicator grading criteria (Table A4 and Table A5), and relevant 2022 ESER production data from MC Steel Enterprise (

Table 4. Data related to ESER of MC Steel Enterprise in 2022.

No.	Evaluation Index	Unit	2022 Data
1	Fuel particle size (C11)	%	65–70
2	Furnace iron ore quality (C12)	%	55.6–55.8
3	Solvent unit consumption (C31)	kg/t	145
4	Fuel unit consumption (C32)	kg/t	48
5	Fuel ratio (C33)	kg/t	511.59
6	Iron-to-steel ratio (C34)	%	83.80%
7	Oxygen consumption for steelmaking (C35)	m3/t	46.83
8	Gas consumption per unit in rolling mill (C36)	m3/t	295.96
9	Flue gas heat recovery rate (C41)	%	58
10	Blast furnace gas utilization rate (C42)	%	44.74
11	Recovery utilization rate (C43)	%	75–80
12	Converter gas recovery per ton of steel (C44)	m3/t	110
13	Hot delivery rate (C51)	%	85–90

). During the assessment, experts scored the current performance of each ESER indicator, integrating these provided materials with their professional judgment and experience.

Following the evaluation, the final score for each indicator was determined by averaging all expert ratings. We assessed the consistency of these ratings using the coefficient of variation (CV), a statistical measure of relative dispersion where values below 10% typically signify high agreement. The analysis revealed that 21 out of 23 indicators (approximately 91%) exhibited a CV below 10%, demonstrating strong consensus and confirming the reliability and credibility of the assessment for most indicators. The slightly higher CVs observed for indicators C61 and C62 are attributable to the qualitative nature of these human-factor indicators, where judgments can inherently vary based on individual experience. This variability was considered acceptable, particularly given the rigorous two-round consultation process previously employed for factor identification. Average scores and CVs for all indicators are detailed in

Table 5. Evaluation of ESER indicators: experts’ scores and average values for MC Steel Enterprises.

Secondary Indicator	Average Score	Coefficient Variation (CV)	Average Score	Secondary Indicator	Coefficient Variation (CV)
C11	86.70	1.37%	C36	76.70	1.75%
C12	77.10	1.47%	C41	68.90	1.02%
C13	88.20	5.09%	C42	78.90	0.68%
C14	84.10	7.42%	C43	78.90	0.89%
C21	84.10	6.46%	C44	89.00	0.71%
C22	85.90	8.06%	C51	86.20	1.62%
C23	85.30	5.5%	C52	87.50	5.29%
C31	77.30	1.3%	C61	73.70	12.03%
C32	86.80	1.69%	C62	75.70	16.55%
C33	77.10	1.35%	C71	82.30	8.15%
C34	87.10	1.3%	C72	81.40	9.58%
C35	86.50	1.57%

.

4.3. Establishment of the Indicator Grading Matrix Based on the Cloud Matter Element Model

Based on the scores and average values provided by experts for MC Steel’s ESER evaluation indicators (refer to Table 5), along with the normal cloud numerical characteristics for the steel enterprises’ energy-saving and emission-reduction levels: (95, 4.25, 2.12), (85, 4.25, 2.12), (75, 4.25, 2.12), (65, 4.25, 2.12), and (30, 25.48, 2.12), the cloud membership degrees between each indicator and the different grading levels were calculated according to Formulas (5) and (6).

The results are presented in

Table 6. Cloud membership of ESER indicators in MC Steel Enterprises.

Secondary Indicator	Excellent	Good	Average	Blow Average	Poor
C11	0.2950	0.9487	0.0869	0.0002	0.2040
C12	0.0036	0.3231	0.9247	0.0706	0.3410
C13	0.4346	0.8374	0.0452	0.0001	0.1832
C14	0.1267	0.9857	0.2282	0.0016	0.2425
C21	0.1256	0.9856	0.2274	0.0016	0.2349
C22	0.2237	0.9857	0.1158	0.0004	0.2175
C23	0.1887	0.9984	0.1561	0.0007	0.2210
C31	0.0042	0.3498	0.9104	0.0672	0.3315
C32	0.3111	0.9420	0.0833	0.0002	0.2027
C33	0.0035	0.3262	0.9242	0.0718	0.3297
C34	0.3346	0.9235	0.0746	0.0002	0.1992
C35	0.2785	0.9616	0.0940	0.0003	0.2064
C36	0.0025	0.2952	0.9495	0.0882	0.3432
C41	0.0000	0.0106	0.5193	0.7637	0.4712
C42	0.0109	0.5204	0.7585	0.0324	0.3055
C43	0.0103	0.5151	0.7610	0.0320	0.3046
C44	0.5315	0.7519	0.0312	0.0000	0.1796
C51	0.2555	0.9749	0.1039	0.0004	0.2184
C52	0.3608	0.8922	0.0621	0.0001	0.1968
C61	0.0004	0.1061	0.9704	0.2667	0.3999
C62	0.0014	0.2173	0.9915	0.1332	0.3611
C71	0.0576	0.8777	0.3898	0.0047	0.2655
C72	0.0363	0.7967	0.4781	0.0101	0.2690

.

In the ESER evaluation of steel enterprises, the indicators are considered independent. During the grading evaluation of the indicators, the cloud membership degree between each indicator and its corresponding grading level can be treated as the basic probability assignment (BPA) in the context of evidence theory. However, since the sum of the cloud membership degrees for each indicator’s grading levels does not equal 1, an uncertainty probability, $\mathrm{m}\left(\mathrm{\Phi }\right)$ representing the probability that the indicator does not belong to any grading level, must be introduced. Furthermore, by calculating the uncertainty probability $\mathrm{m}\left(\mathrm{\Phi }\right)$ and the BPA $\mathrm{m}\left(\mathrm{A}\right)$, D-S evidence theory is applied to integrate the basic probability assignments for the energy-saving and emission-reduction evaluation indicators of MC Steel. The results are presented in

Table 7. BPA table for ESER indicators in MC Steel Enterprises.

Secondary Indicator	Excellent	Good	Average	Blow Average	Poor	$\mathbf{m}\left(\mathbf{\Phi }\right)$
C11	0.1823	0.5864	0.0537	0.0001	0.1261	0.0513
C12	0.0020	0.1797	0.5142	0.0393	0.1896	0.0753
C13	0.2425	0.4673	0.0252	0.0000	0.1023	0.1626
C14	0.0788	0.6131	0.1419	0.0010	0.1508	0.0143
C21	0.0786	0.6167	0.1423	0.0010	0.1470	0.0144
C22	0.1429	0.6296	0.0739	0.0003	0.1390	0.0143
C23	0.1204	0.6371	0.0996	0.0004	0.1410	0.0016
C31	0.0023	0.1915	0.4984	0.0368	0.1815	0.0896
C32	0.1904	0.5765	0.0510	0.0001	0.1240	0.0580
C33	0.0019	0.1821	0.5160	0.0401	0.1841	0.0758
C34	0.2017	0.5567	0.0450	0.0001	0.1201	0.0765
C35	0.1738	0.6001	0.0586	0.0002	0.1288	0.0384
C36	0.0014	0.1670	0.5371	0.0499	0.1941	0.0505
C41	0.0000	0.0046	0.2247	0.3305	0.2039	0.2363
C42	0.0051	0.2425	0.3535	0.0151	0.1424	0.2415
C43	0.0048	0.2415	0.3568	0.0150	0.1428	0.2390
C44	0.2674	0.3783	0.0157	0.0000	0.0904	0.2481
C51	0.1604	0.6120	0.0652	0.0002	0.1371	0.0251
C52	0.2129	0.5265	0.0366	0.0001	0.1161	0.1078
C61	0.0002	0.0590	0.5401	0.1485	0.2226	0.0296
C62	0.0008	0.1264	0.5767	0.0775	0.2101	0.0085
C71	0.0317	0.4829	0.2145	0.0026	0.1461	0.1223
C72	0.0182	0.3991	0.2395	0.0051	0.1348	0.2033

.

4.4. Optimization of ESER Evaluation Based on D-S Evidence Theory

Based on the improved D-S evidence theory method described above, the distances between evidence bodies $d\left(m_1,m_2\right)$ and the evidence body entropy E shown in Figure 3 were calculated. Specifically, the basic probability assignments of the evaluation indicators were adjusted by combining the distances between evidence bodies with Shannon entropy, which effectively reduces the impact of evidence conflicts. Next, the average distance ${\mathrm{d}}_{\mathrm{j}}$ between each evidence body and the others was calculated, yielding the evidence body fusion weights ${\mathrm{w}}_{\mathrm{j}}$. Shannon entropy was used to quantify the uncertainty E of the evidence, and the results were normalized to obtain ${\mathrm{u}}_{\mathrm{j}}$. The adjusted fusion weights ${{\mathrm{w}}^{\prime }}_{\mathrm{j}}$ were then derived and used to perform a weighted average correction and fusion of the basic probability assignments for the evaluation indicators. The results are presented in

Table 8. Integrated weight analysis of ESER evaluation indicators for MC Steel Enterprises.

Indicator	$\mathbf{Average} \mathbf{Distance} {\mathbf{d}}_{\mathbf{j}}$	$\mathbf{Weight} {\mathbf{w}}_{\mathbf{j}}$	Entropy E	$\mathbf{Normalization} {\mathbf{u}}_{\mathbf{j}}$	$\mathbf{Adjusted} \mathbf{Weight} {{\mathbf{w}}^{\prime }}_{\mathbf{j}}$
C11	0.2162	0.0472	1.1950	0.0459	0.0496
C12	0.2584	0.0395	1.3001	0.0413	0.0374
C13	0.2504	0.0407	1.3208	0.0405	0.0378
C14	0.1910	0.0534	1.1303	0.0490	0.0599
C21	0.1916	0.0532	1.1252	0.0492	0.0601
C22	0.2199	0.0464	1.0992	0.0505	0.0537
C23	0.2211	0.0461	1.0614	0.0524	0.0555
C31	0.2480	0.0411	1.3248	0.0403	0.0380
C32	0.2173	0.0469	1.2102	0.0452	0.0486
C33	0.2578	0.0396	1.2997	0.0413	0.0375
C34	0.2199	0.0464	1.2405	0.0438	0.0466
C35	0.2168	0.0470	1.1679	0.0472	0.0509
C36	0.2768	0.0368	1.2605	0.0430	0.0363
C41	0.4932	0.0207	1.3912	0.0377	0.0179
C42	0.2253	0.0453	1.4219	0.0366	0.0380
C43	0.2255	0.0452	1.4197	0.0367	0.0380
C44	0.2921	0.0349	1.3490	0.0393	0.0315
C51	0.2174	0.0469	1.1388	0.0485	0.0522
C52	0.2264	0.0450	1.2791	0.0422	0.0436
C61	0.3936	0.0259	1.2232	0.0446	0.0265
C62	0.3404	0.0300	1.1512	0.0479	0.0329
C71	0.1583	0.0644	1.3444	0.0395	0.0584
C72	0.1776	0.0574	1.4025	0.0373	0.0491

.

Finally, the BPA of the ESER evaluation indicators for MC Steel Enterprise were integrated with the fusion weights of the indicators to derive the weighted average evidence m*, as illustrated in

Table 9. Weighted average evidence results based on D-S evidence theory.

Level	Excellent	Good	Average	Blow Average	Poor	$\mathbf{m}\left(\mathbf{\Phi }\right)$
m*	0.0990	0.4399	0.2088	0.0203	0.1469	0.0850

.

Using Formula (4), the Dempster combination rule, a Python 3.13 script was applied to perform 22 iterations of fusion on the weighted average evidence. The resulting probabilities were

[6.5391 × 10⁻¹², 9.9999 × 10⁻¹, 4.4738 × 10⁻⁶, 3.9604 × 10⁻¹⁸, 7.1116 × 10⁻⁷, 2.3378 × 10⁻²¹]

It is evident that the second element had the highest value, while the probabilities of other elements were nearly zero. These indicate that during the fusion process, the probability of the evaluation grade “good” gradually approaches 1, while the probabilities of other evaluation grades approach 0. Therefore, based on the calculation using the Dempster combination rule, the final basic probability assignment for MC Steel Enterprise’s current ESER status was as shown in

Table 10. Final fusion results based on D-S evidence theory.

Level	Excellent	Good	Average	Blow Average	Poor	$\mathbf{m}\left(\mathbf{\Phi }\right)$
$m\left(A\right)$	0	1.0000	0	0	0	0

.

Based on the maximum membership degree principle and the data presented in Table 9, it can be concluded that MC Steel Enterprise’s current energy-saving and emission-reduction evaluation grade is classified as “good”.

4.5. Local Sensitivity Analysis (LSA)

This study employed local sensitivity analysis (LSA), rather than global sensitivity analysis (GSA), to evaluate the model’s robustness specifically around the current parameter values derived from MC Steel Enterprise’s operational data. LSA enables the efficient identification of key indicators exerting the most significant influence on energy saving and emission reduction (ESER) evaluation results by analyzing the effects of perturbations near these specific parameter points. While GSA explores the entire parameter space, LSA offers superior computational efficiency and a targeted focus appropriate for this study, where parameters possess a clear real-world basis and constrained variation [68].

For the analysis, we selected six indicators identified with higher importance weights in Table 8 (C14, C21, C22, C23, C51, and C71). We applied perturbations to the weights of these selected indicators within a ±30% range relative to their original values, using a 10% step size. Crucially, following each individual weight perturbation, the resulting combined evidence (m*) was recalculated using the improved D-S fusion process.

The sensitivity analysis involved systematically altering the weight of each selected indicator (within the ±30% range) and measuring the corresponding impact on the combined evidence outcome (m*). This ±30% perturbation range was chosen to represent a significant interval of potential weight uncertainty, facilitating a robust assessment of model stability. The indicators eliciting the largest changes in m* were identified as the most sensitive, signifying the factors with the greatest impact on ESER performance at MC Steel. The results, presented in Figure 4 (focusing on the “good” performance grade), demonstrated minimal output fluctuation despite these substantial weight perturbations; the maximum observed fluctuation in the combined evidence (m*) attributable to sensitivity was less than 0.5%.

Key findings indicate that “Heating furnace equipment performance (C23)” exerted the most significant influence on the enterprise’s ESER evaluation, followed by “Sintering machine performance (C21)” and “Blast furnace equipment performance (C22)”. Conversely, “Employee training level (C71)” demonstrated the least sensitivity among the tested indicators. Throughout the analysis, the fused probability consistently converged to the “good” grade, signifying substantial model stability even under considerable indicator weight variations; output fluctuations remained negligible. This stability stems primarily from two factors: the high initial basic probability assignment (BPA) values associated with key indicators under the “good” grade, and the improved D-S evidence theory’s effective conflict management. These findings collectively validate the reliability and robustness of the developed ESER evaluation model, reinforcing its credibility for practical application.

5. Results and Discussion

5.1. Analysis and Discussion of Results

Evaluating the energy saving and emission reduction (ESER) performance of steel enterprises is a critical factor for enhancing operational efficiency and holds significant importance for mitigating climate change and addressing the global energy crisis. Based on the basic probability assignment (BPA) results for each secondary ESER indicator presented in Table 6, it is evident that most secondary indicators achieved high evaluation grades. Although some indicators did not reach the ideal “good” level, the overall assessment derived from our evaluation model reasonably concludes that MC Steel Enterprise’s ESER performance is currently in a “good” stage.

Furthermore, this evaluation outcome aligns with the results of China Baowu Steel Group’s internal selection for the “Best Practice Energy Efficiency Enterprise under the Dual Carbon Goals”. This concordance further validates the effectiveness and feasibility of the proposed ESER evaluation model, which integrates the cloud model and improved D-S evidence theory. Nevertheless, despite the overall positive assessment, certain specific areas require targeted improvements to further elevate the steel enterprise’s ESER levels.

Analysis of specific indicators from Table 6 reveals key areas for attention:

Flue gas waste heat recovery rate (C41): This indicator exhibited its highest probability mass concentrated in the “poor” and “fair” grades, with a combined probability of 0.5344. Conversely, the combined probability for “excellent” and “good” was extremely low at 0.0046. This strongly indicates a significant deficiency in MC Steel Enterprise’s flue gas waste heat recovery practices, particularly concerning the efficiency of recovering medium-to-low temperature gases. The primary underlying reason is that the enterprise’s current system—utilizing dual-pressure waste heat boilers and supplementary steam turbines for flue gas heat recovery—primarily captures only the high-temperature gas (>280 °C) generated by the sinter plant’s circular cooler. Significant volumes of gas in the medium-to-low temperature range (150 °C to 280 °C) are consequently discharged directly into the atmosphere without effective recovery. Therefore, it is recommended that the enterprise invests in technological upgrades to enable the full recovery and utilization of these 150 °C to 280 °C gases. This would enhance the overall waste heat recovery efficiency and significantly improve the performance score for indicator C41.

Process operation skill level (C61) and Equipment maintenance level (C62): For these indicators, the combined probabilities for achieving “excellent” and “good” grades were notably low (0.0592 and 0.1272, respectively). In contrast, the probability of being assessed as “average” was high for both (0.6886 and 0.6542, respectively). This highlights existing shortcomings in the enterprise’s process operation capabilities and equipment maintenance standards. A major contributing factor stems from the relatively lower overall educational background and vocational skill levels of the workforce inherited from earlier operational periods. Although skill levels have seen improvement following the enterprise’s integration into the Baowu Steel Group—facilitated by the recruitment of specialized technical talent and experienced management personnel—a discernible gap persists when compared to other leading steel enterprises. Consequently, the company should prioritize strengthening employee vocational training programs, adopting advanced production philosophies and technologies as well as engaging external experts for on-site guidance. These actions are crucial to narrowing the performance gap, especially in process operation and equipment maintenance, thereby contributing to an improved overall ESER performance for the enterprise.

Fuel ratio (C33) and Rolling mill gas consumption per ton (C36): These indicators demonstrated high probabilities associated with the “average” and “poor” grades (0.5561 and 0.5870, respectively). This suggests that significant challenges remain in resource utilization, manifesting as issues like inefficient solvent use and incomplete fuel combustion. To address this, the enterprise should focus on improving resource utilization efficiency and reducing overall consumption. This involves establishing clear resource management policies and targets, along with implementing a robust resource consumption tracking system. Adopting a “refined materials” or burden optimization strategy, ensuring rational control over flux usage during production, and actively working to lower the fuel ratio at its source are essential steps towards achieving low-carbon ironmaking, energy conservation, and ultimately improved ESER outcomes.

Input iron ore grade (C12): The probabilities assigned to the “excellent” and “good” grades for this indicator were low (0.0020 and 0.1797, respectively), while the combined probability for “average” and “poor” reached 0.5534. This clearly indicates that there is substantial room for improvement concerning the quality (grade) of iron ore utilized by MC Steel Enterprise. Enhancing the quality of raw materials is a well-established strategy for improving smelting efficiency and concurrently reducing energy consumption during the production process.

5.2. Discussion on Uniformity

In the improved D-S evidence theory model, the final evaluation grade is typically determined by applying the maximum likelihood rule to the fused basic probability assignment (BPA) results. For the MC Steel Enterprise ESER evaluation presented in this study, this process yielded a definitive conclusion, as the fused BPA for the “good” grade significantly exceeded those for other grades (Table 9).

However, complex evaluation scenarios may arise where indicator scores are closely distributed, leading to numerically similar BPA values across multiple grades (e.g., BPA(“good”) = 0.45, BPA (“average”) = 0.40). While the maximum likelihood rule still selects the grade with the highest BPA (“good” in this example), the small margin introduces uncertainty regarding the evaluation outcome. To address such ambiguity and enhance the model’s interpretability and reliability, particularly when encountering closely distributed BPAs, we propose the following auxiliary decision-making framework.

Firstly, when fused BPA values for different grades are proximate, analyzing the BPA distribution characteristics alongside the degree of evidence conflict is crucial. Evidence conflict can be quantified using the uncertainty probability (denoted as Φ), which represents the belief mass unassigned to any specific grade after fusion; its magnitude reflects the level of conflict or ambiguity among the evidence sources. A low Φ value suggests minimal conflict, implying that proximate BPAs may reflect inherent system ambiguity rather than contradictory evidence. Conversely, a high Φ value might signal underlying data inconsistencies or problematic indicator assignments. It is noteworthy that in the MC Steel case, the calculated uncertainty probability Φ was low at 0.0850 (Table 8), reinforcing confidence in the “good” grade conclusion based on the primary decision rule.

Nevertheless, if a hypothetical scenario yielded closely distributed BPAs and a significant Φ value (indicating substantial conflict), the following corrective measures would be advisable: (1) Data verification: thoroughly review the data collection pipeline and indicator assignment procedures for accuracy and consistency. (2) Indicator optimization: identify indicators contributing heavily to the conflict (potentially via sensitivity analysis) and consider targeted adjustments—such as refining evaluation criteria or modifying weights—to reduce model uncertainty and improve the decisiveness of the results.

6. Conclusions

Confronted with the severe challenges of global climate change and energy crises, developing comprehensive evaluation models for energy saving and emission reduction (ESER) within energy-intensive industries like steel manufacturing is critically important. This research integrated theoretical frameworks with practical application, starting with an analysis of the steel industry’s ESER status and priorities. We constructed a tailored ESER evaluation system for steel enterprises using the WSR (physical–process–human) methodology. Individual indicator grades, accounting for inherent fuzziness and randomness, were determined using the cloud matter-element model. Subsequently, an improved Dempster–Shafer (D-S) evidence theory was employed to effectively mitigate evidence conflict during results fusion. Findings from the case study of MC Steel Enterprise demonstrate that the model’s assessment results align closely with the company’s operational reality, thereby validating the model’s effectiveness and practical feasibility.

Key contributions and findings are summarized as follows:

Firstly, a novel integrated evaluation model was developed, combining the WSR methodology, the cloud matter-element model, and an improved D-S evidence theory. This resulted in a comprehensive ESER evaluation system (7 primary, 23 secondary indicators) that effectively addresses key ESER dimensions. The cloud matter-element model adeptly manages indicator fuzziness and randomness, while the improved D-S theory significantly reduces the interference of high-conflict evidence in multi-source data fusion, improving upon traditional methods and enhancing overall assessment reliability. This multi-method fusion approach offers a valuable theoretical perspective and scientific basis for ESER evaluation in complex industrial systems.

Secondly, the empirical analysis using MC Steel Enterprise validated the model’s real-world reliability and practical utility. The assessment results were consistent with the enterprise’s actual ESER status and management perceptions, and they successfully identified critical areas needing improvement, such as insufficient flue gas heat recovery, suboptimal resource utilization efficiency, and inadequate process operation skill levels. Based on these findings, targeted recommendations were formulated, focusing on improving Raw material quality management (B1), optimizing Resource consumption (B3), enhancing Secondary energy utilization (B4), and elevating Professional skills (B6). Furthermore, sensitivity analysis confirmed the model’s stability and robustness under parameter variations.

Despite the significant progress achieved, this research has limitations that present avenues for future work:

(1)

The current findings are primarily based on the long-process model within Chinese steel enterprises. Further validation is required to ascertain applicability across different production modes, enterprise scales, and international contexts. Future research should incorporate multi-case comparative studies involving diverse enterprises to enhance model generalizability.

(2)

Relying solely on experts from Chinese enterprises for indicator validation might limit the system’s global universality. Future studies could engage international experts and potentially employ data-driven methods (e.g., statistical validation) to refine or corroborate the indicator set, thereby improving robustness.

(3)

The analysis adopts an enterprise-centric view within the production phase. Future research could benefit from a broader life cycle assessment (LCA) perspective, encompassing data on steel usage efficiency and recycling across various sectors to evaluate ESER factors throughout the entire product lifecycle, offering valuable insights for policy development.

(4)

The current study utilizes data from a specific period, thus capturing a static snapshot of ESER performance. Future work should incorporate time-series data to establish a dynamic analysis framework, enabling the assessment of ESER trends and the longitudinal effectiveness of improvement initiatives within steel enterprises.