Refining Environmental Sustainability Governance Reports through Fuzzy Systems Evaluation and Scoring

Abstract

Environmental, Social, and Governance (ESG) reports have become essential tools for enterprises to showcase their commitment to sustainable development and social responsibility. However, discrepancies persist regarding the criteria, assessments, and ratings disclosed in these reports. Moreover, there is a need for more objective methods to determine the weight distribution of indicator items. This study introduces a novel approach utilizing semantic variables in fuzzy theory and a multiple logic fuzzy inference system to develop an ESG environmental management performance assessment model. Therefore, this paper aims to develop a novel approach utilizing semantic variables and a multiple logic fuzzy inference system to quantitatively evaluate the sustainable performance of an environmental management plan. This research also aims to ensure fair and objective assessment outcomes, providing valuable guidance for enterprises in implementing performance management strategies. Key aspects investigated include the impact of membership functions, the extended utilization of semantic variables and logical rules, a comparative analysis of traditional weight assessments, and the limitations of applying fuzzy theory. Through comprehensive discussions and calculations, it is evident that fuzzy theory offers considerable flexibility in application. By tailoring fuzzy rules and selecting appropriate membership functions, diverse application scenarios can be accommodated. The Fuzzy systems evaluation and scoring EMP model generates EMP evaluation scores ranging from 1.76 to 8.29 for Gaussian membership, 1.80 to 8.19 for Triangular membership-A, 1.92 to 8.00 for Triangular membership-B, and 1.81 to 8.19 for Quadrilateral trapezoidal membership, based on simulated rating scenarios using the semantic variables of completeness and feasibility. This approach successfully incorporates distribution logic from subjective membership degrees to evaluate EMP scores. The findings demonstrate that fuzzy theory enables the consideration of multiple factors and facilitates the provision of objective-level membership, underscoring its potential in addressing complex evaluation challenges. This study illuminates the versatility of the fuzzy system theory, with its applications poised to extend across various domains.

1. Introduction

Refining environmental sustainability governance reports through fuzzy systems evaluation and scoring is of paramount importance in the context of evolving global sustainability standards and corporate responsibility. Since the UN Earth Summit in 1992, there has been a significant push towards enhancing environmental awareness and promoting sustainable development through various international agreements and initiatives. The introduction of the UN Global Compact and subsequent CSR and ESG guidelines underscored the need for businesses to adopt and report on sustainable practices actively.

Refining Environmental Sustainability Governance Reports through fuzzy systems evaluation and scoring is essential for accurately assessing complex environmental performance metrics. Introduced by Professor Zadeh in 1965, fuzzy theory provides a sophisticated approach to handling qualitative data by transforming it into quantitative measures through defuzzification and multiple logic rules [1,2]. This method addresses the limitations of conventional binary evaluations by converting qualitative judgments into degrees of membership ranging from 0 to 1, thus capturing a more nuanced picture of sustainability efforts. In the context of evolving global standards and the increasing need for detailed, actionable environmental reporting, fuzzy systems offer a powerful tool for enhancing the accuracy and effectiveness of sustainability assessments. This approach supports better decision-making, aligns with contemporary sustainability practices, and meets the growing demands for comprehensive and precise governance reporting.

Our research addresses the question: how can an effective ESG environmental management performance assessment model be constructed using semantic-linguistic variables and fuzzy theory to improve the evaluation of corporate sustainability practices. It aims to develop a robust model by integrating fuzzy theory and multiple logic rules to assess qualitative aspects of environmental management. The study explores the impact of various membership functions and logistic rules on evaluating environmental management plans, enhancing the accuracy and effectiveness of ESG performance assessments. This approach contributes to global sustainable development, refines ESG reporting practices, supports investment decisions, and informs regulatory development.

In 2018, Buyukozkan and Karabulut conducted a review of 128 papers focused on corporate sustainability performance evaluation (SPE) [3]. The compiled research predominantly centers on sustainability indicators and assessments, with sustainability accounting defined as the former. This encompasses qualitative data collection for sustainability, defining necessary data and item standards, and establishing indicators. Additionally, sustainability assessment involves utilizing unconventional methods or models to integrate previously mentioned sustainability data, standards, and indicators into sustainable indices, serving as benchmarks for assessing enterprise SPE. These efforts have tangible effects on business management and operations, aiming to improve sustainability indicators and performance.

Buyukozkan and Karabulut proposed several recommendations regarding Sustainable Performance Evaluation (SPE): The burgeoning research on environmental and economic sustainability reflects a growing interest in a sustainable society, necessitating practical applications to reinforce item indicators and methods, along with academic SPE research findings. Sustainability assessments should transcend mere disclosure to serve as reference tools for improvement. Clarifying the relationship between different sustainability items is crucial for accurately determining the weight and impact of each disclosed item, thus avoiding consistent deviations in assessments. Objective scientific methods are essential for determining the distribution of weights for indicator items. Research into assessing qualitative indicators is ongoing, as these items cannot easily be quantified numerically. Integrating integrated indices into management or improvement plans after converting performance into numerical values poses challenges. Overall, the recommendations underscore the need for continued research and development in SPE to enhance its effectiveness in guiding sustainable business practices.

The Analytic Hierarchy Process (AHP) and Fuzzy Analytic Hierarchy Process (FAHP) are commonly employed management methodologies for assessing the relative weights of Environmental, Social, and Governance (ESG) criteria. In their study, Rajabi, El-Sayegh, and Romdhane identified 22 Sustainability Key Performance Indicators (SKPIs) specific to the construction industry from sustainability databases and literature [4]. These SKPIs were categorized into environmental and socioeconomic axes. Subsequently, 31 experts from the field participated in pairwise comparisons using AHP to determine the weights of the SKPIs. The results of the study highlighted the prioritization of goals related to renewable energy use and construction site safety, underscoring the importance of these areas within the construction industry.

In another study, Tsai et al. utilized the fuzzy Decision-Making Trial and Evaluation Laboratory (DEMATEL) model to evaluate environmental performance in the printed circuit board (PCB) industry [5]. They selected four environmental themes and 10 sublevel standards. To address subjective perceptions and difficulties in absolute quantification, the fuzzy semantic-linguistic non-quantitative intervals method was employed to assess the relative impact of standards and establish an AHP orthogonal matrix. Both the triangular membership function and the Fuzzy DEMATEL model revealed significant direct and indirect effects of standards, facilitating the prioritization of sustainable performance standards.

Hu et al. leveraged sustainability reports of TAIEX-listed Taiwanese companies, employing the Fuzzy Delphi methods (FDM) and Fuzzy AHP methods to evaluate report quality [6]. The FDM validated 18 norms and 44 indicators, while Fuzzy AHP-generated weights for 19 norms and 44 indicators. Triangular Fuzzy Numbers (TFNs) were used to determine local weight interval values, and assessment scores for sustainability reports were established based on subjective qualitative assessments and global weights. FDM provided a practical framework for decision-making, inviting experts to assess normative indicators, while AHP served as a computational tool for distributing weights, especially when dealing with interval values using fuzzy theory.

Furthermore, the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) is a commonly utilized calculation standard in multi-criteria analysis methods, enabling selection based on positive and negative outcome differences. Shahbod et al. extracted sustainability norms and indicators from extensive literature and validated six subjects, 22 criteria, and 48 indicators through the fuzzy Delphi method, involving expert consensus [7].

FAHP and TOPSIS were employed to assess the relative importance of hospital environmental performance indicators. TOPSIS facilitates the determination of the priority of key indicator factors. Awasthi et al. utilized TOPSIS to evaluate the environmental performance of supply chains, focusing on 12 criteria, such as green management certification and production practices. Linguistic assessments by experts were used to mitigate subjective deviations in direct scoring [8]. Subsequently, weights and scores for various supplier criteria were evaluated, and TOPSIS was employed to calculate supplier performance indices, forming the basis for identifying exceptional green suppliers.

Dos Santos et al. engaged 32 experts to establish green performance criteria, utilizing Shannon entropy and TOPSIS to determine criteria weights and select manufacturers based on performance [9]. Applying TOPSIS principles, the Shannon entropy method assessed criteria entropy, indicating the dispersion degree of criteria. Fuzzy assessments using the triangular membership function were conducted on seven criteria and three suppliers, resulting in a ranking of green performance among selected suppliers.

While Awasthi et al. [8] and Dos Santos et al. [9] employed slightly different methods, their fundamental principles remained consistent. Similarly, Tsai et al. utilized the fuzzy DEMATEL model to evaluate environmental performance in the Printed Circuit Board (PCB) industry [5]. To address experts’ subjective perceptions and the challenge of absolute quantification, a fuzzy semantic-linguistic non-quantified interval method was employed to assess criteria effects and establish an Analytic Hierarchy Process (AHP) orthogonal matrix. The triangular fuzzy number and fuzzy DEMATEL models were then utilized to identify significant criteria effects and prioritize sustainable performance criteria. Furthermore, Uygum and Dede integrated criteria effects and weights to screen and select outstanding green suppliers [10]. That study was described as ushering in the era of multi-criteria decision-making methods. However, it primarily employed semantic-linguistic fuzzy membership functions in the early stages of fuzzy theory, rather than utilizing multiple logic equations and fuzzy inference calculations. These investigations exhibit a notable bias towards AHP methodology.

GERMANWATCH, based in Germany, utilizes four categories and 14 criteria to evaluate climate change performance indexes across various countries: greenhouse gas (GHG) emissions, renewable energy usage, energy consumption, and climate policy effectiveness. While the first three criteria are quantifiable, the fourth criterion pertains to environmental management plans. GERMANWATCH releases reports ranking countries’ efforts in mitigating climate change globally. A crucial aspect of evaluating climate policy management plans is assessing the extent to which countries meet the objectives of the Paris Agreement at the national level [11]. The CCPI employs non-quantifiable indicators like “international climate policy” and “national climate policy” for evaluation. However, these evaluations rely on expert rankings from 1 (weak) to 5 (strong), potentially introducing subjectivity into the scoring process. Refinitiv, an evaluation agency, adopts a similar approach in its assessment system, incorporating qualitative measures alongside traditional quantitative criteria. These qualitative measures help adjust Environmental, Social, and Governance (ESG) assessment scores based on the volume of reported negative events or controversies.

Our research fills a crucial gap by developing an effective ESG environmental management performance assessment model using semantic-linguistic variables and fuzzy theory. This model addresses the need for robust evaluation tools that integrate qualitative aspects of environmental management, which are often overlooked in current quantitative-focused models. By exploring the impact of various membership functions and logistic rules, our study enhances the accuracy and effectiveness of ESG performance assessments, contributing to global sustainable development, refining ESG reporting practices, supporting investment decisions, and informing regulatory development.

Our research is important due to its significant implications across several fields. First, it contributes to global sustainable development efforts, enhancing understanding of ESG and CSR practices in alignment with international goals set by the UN and the EU. Second, it refines ESG reporting practices, guiding regulatory bodies and businesses towards more accurate CSR and ESG disclosures, which can influence policy and corporate strategies. Third, our proposed ESG assessment model aids investors by providing reliable tools for evaluating corporate sustainability performance, aligning with the growing importance of ESG criteria in financial markets. Fourth, it supports ESG regulation development by offering a comprehensive view of disclosure standards and metrics, informing future legislation and enforcement. Finally, our research provides methodologies that advance academic studies in environmental performance evaluation and multi-criteria decision-making, enriching the field of sustainability and ESG assessments. All data sources referenced in this introduction are detailed in Appendix A.

2. Methodology and Experimental Procedures

The focus of this study is on evaluating the sustainable environmental performance of enterprises. This evaluation is achieved by calculating a total score based on various relevant indicators and their relative weights. The process is designed to help businesses identify their environmental strengths and weaknesses, as well as assess their overall environmental performance, which can lead to improvements.

The methodology acknowledges the challenge of creating a universally accepted, objective, and rational indicator evaluation system for environmental performance assessment. While the study does not aim to establish such a system, it examines the conceptual framework and thought processes behind these systems to provide a foundation for future research.

The process flowchart (Figure 1) outlines the development of a measurement for sustainability performance of environmental management plans (EMPs) proposed by industrial sectors using a fuzzy model. The primary objective is to provide an objective and precise evaluation method. The model focuses on formulating semantic variables to assess EMPs. Key evaluation criteria include plan certainty, timely execution, and quality implementation, represented by the variables measuring completeness, technology feasibility, and implementation progress, respectively. Fuzzy model inputs are variable-stimulated scores, and outputs are derived through membership functions, logistic rules, and defuzzification. To validate the fuzzy system, we compare its results to those obtained using traditional weight and crisp value methods.

2.1. Indicator Scores

The enterprise’s sustainable environmental performance was evaluated by calculating the total score based on relevant indicators. After factoring in the relative weights, individual and total indicator scores were derived. This process enables businesses to pinpoint their environmental strengths and weaknesses and gauge their standing in terms of environmental performance, thereby fostering improvements in this area. Quantifying the experimental environment is pivotal for environmental performance assessment, yet creating a universally accepted, objective, and rational indicator evaluation system presents a formidable challenge. While this study does not aim to establish a unified indicator evaluation system, it examines the conceptual framework and thought processes underlying such systems, serving as a foundational platform for future research endeavors. Previous studies have utilized spherical statistical models to score quantifiable criteria, but qualitative plans inherent in environmental management defy numerical expression. Consequently, earlier discussions have relied on expert evaluations combined with fuzzy theory models for assessments [1].

2.2. Data Analysis

The degree of membership in fuzzy logic is contingent upon the membership function and its parameters. The choice of membership function is dictated by the specific event scenario and the design of logical rules, often guided by practical experience rather than theoretical principles. Many studies employing fuzzy AHP utilize various membership functions (MF), such as the triangular function, which encompasses models like Gaussian, S-shaped, Z-shaped, Pi-shaped, Sigmoidal, Gaussian2, Triangular, Trapezoidal, Differential Sigmoidal, Linear S-shaped, Linear Z-shaped, Production Sigmoidal, and Generalized Bell functions [7,12,13].

Fuzzy theory, combined with the semantic-linguistic analysis method and multiple logic concepts, is expressed as follows:

If x = A, then y = B

(1)

However, the membership function of x or y typically ranges between zero and one. A and B represent the fuzzy set corresponding to x and y, expressed in multiple logic rules. Equation (1) can be modified to Equation (2) or (3):

If x = A and y = B, then z = C

(2)

or

If x = A or y = B, then z = C

(3)

In the above logical computation equations, if the operator is “and”, the fuzzy rule computes the lower value between Sets A and B, corresponding to the intersection of Membership Function Set C. Conversely, if the operator is “or”, the fuzzy rule calculates the higher value between Set A and Set B, corresponding to the bisector of Membership Function Set C. Subsequent results and discussions will provide a clear illustration of this computation using the Matlab fuzzy inference engine.

2.3. Data Collection

The pivotal step in fuzzy theory is defuzzification, which entails deriving precise values from uncertain and fuzzy data through a defuzzification calculation process [13]. Various defuzzification methods exist, with the most commonly utilized being the maximum degree of truth, the centroid, and the bisector [14]. The centroid and the bisector methods were used in this study. In the maximum degree of truth method, the defuzzification result value is determined by selecting the maximum membership function. The centroid method determines the center of gravity within the ranges of the respective sets. It identifies the point where a vertical line maintains equilibrium on the fuzzy set area. The equation is expressed as Equation (4) where μ(x) is membership function with x ∈ X and x′ denotes the defuzzification value [14]:

$${\mathrm{x}}^{\prime }={\displaystyle \frac{\sum _{\mathrm{i}}\mathsf{\mu }\left({\mathrm{x}}_{\mathrm{i}}\right){\mathrm{x}}_{\mathrm{i}}}{\sum _{\mathrm{i}}\mathsf{\mu }\left({\mathrm{x}}_{\mathrm{i}}\right)}}$$

(4)

The bisector method is akin to the centroid, representing the point where a vertical line bisects the fuzzy set area into two equal sub-areas. The equation is expressed as (5):

$${\int }_{\mathsf{\alpha }}^{{\mathrm{x}}^{\prime }}{\mathsf{\mu }}_{\mathrm{A}}\left(\mathrm{x}\right)\mathrm{d}\mathrm{x}={\int }_{{\mathrm{x}}^{\prime }}^{\mathsf{\beta }}{\mathsf{\mu }}_{\mathrm{A}}\left(\mathrm{x}\right)\mathrm{d}\mathrm{x}, \mathrm{if} \alpha =\min \{x|x\in X\} \mathrm{and} \beta =\max \{x|x\in X\}$$

(5)

The overall procedure of the fuzzy system is illustrated in Figure 2: (1) Fuzzification (establish semantic-linguistic variables + membership function): The membership function of input and output variables; (2) fuzzy rule base (establish IF AND/OR THEN fuzzy rules); (3) Fuzzy inference engine (compute 1 and 2); (4) Defuzzification (conversion of results in 3 to exact values).

The simulated calculations of the fuzzy model and the validation scores represent different levels of EMP performance in terms of measure completeness and technology feasibility. These levels are categorized as poor (score < 3.5), good (score between 3.5 and 7.5), and excellent (score > 7.5). By combining these two variables, nine potential scenarios were created (e.g., PP, PG, PE, GP, GG, GE, EP, EG, and EE.). Nine sets of simulated scores (A(1.82, 1.25), B(1.65, 5.34), C(2.25, 8.78), D(6.53, 1.05), E(5.80, 7.30), F(6.83, 9.25), G(9.83, 2.56), H(8.53, 6.52), and I(8.12, 9.30)), representing these scenarios, were generated and are presented in

Table 1. Three kinds of MF parameters and simulation results.

Situation	Completeness Scoring	Feasibility Scoring	Average Value	Gaussian Membership Function zmf gaussmf smf (G Model) [1.5 5] [1.25 5] [5 8.5]	Triangular Membership Function linzmf trimf linsmf (T1 Model) [1.5 5] [1.5 5 7.5] [5 8.5]	Triangular Membership Function linzmf trimf linsmf (T2 Model) [2.5 5] [2.5 5 8.5] [5 7.5]	Quadrilateral Trapezoidal Membership Function linzmf trapmf linsmf (T3 Model) [1.5 5] [2 4 6 8] [5 8.5]
A	Completeness: poor	Feasibility: poor		Results: poor	Results: poor	Results: poor	Results: poor
	1.82	1.25	1.53	1.76	1.80	1.92	1.81
B	Completeness: poor	Feasibility: good		Results: good	Results: good	Results: good	Results: good
	1.65	5.34	3.49	5.03	5.08	5.00	5.00
C	Completeness: poor	Feasibility: excellent		Results: good	Results: good	Results: good	Results: good
	2.25	8.78	5.51	5.20	5.45	5.00	5.29
D	Completeness: good	Feasibility: poor		Results: poor	Results: poor	Results: poor	Results: poor
	6.53	1.05	3.76	2.03	2.02	2.11	1.90
E	Completeness: good	Feasibility: good		Results: good	Results: good	Results: good	Results: good
	5.80	7.30	6.55	7.38	6.71	7.65	6.80
F	Completeness: good	Feasibility: excellent		Results: excellent	Results: excellent	Results: excellent	Results: excellent
	6.83	9.25	8.04	8.07	7.95	7.95	7.99
G	Completeness: excellent	Feasibility: poor		Results: poor	Results: poor	Results: poor	Results: poor
	9.83	2.56	6.19	2.89	3.91	2.1	3.82
H	Completeness: excellent	Feasibility: good		Results: excellent	Results: excellent	Results: excellent	Results: excellent
	8.53	6.52	7.41	7.88	7.98	7.88	8.10
I	Completeness: excellent	Feasibility: excellent		Results: excellent	Results: excellent	Results: excellent	Results: excellent
	8.12	9.30	8.71	8.29	8.19	8.08	8.19

The simulated scores represent different levels of EMP performance in terms of measure completeness and technology feasibility, categorized as poor (<3.5), good (3.5–7.5), and excellent (>7.5). By combining these two variables, nine potential scenarios were created (e.g., poor poor, poor good, poor excellent, etc.).

. The evaluation process begins with expert assessments of plan completeness and feasibility, considering the practicality of the company’s environmental performance. It is essential to note that plan completeness without feasibility is ineffective for environmental sustainability, resulting in a poor overall evaluation. To incentivize proactive sustainability efforts, the higher-scoring variable between completeness and feasibility determines the final evaluation, unless feasibility is rated as poor. This approach highlights the interdependent nature of these two factors and the importance of both for achieving positive environmental outcomes. Consequently, we developed a set of logic rules and a process module to calculate the final evaluation score based on these considerations.

3. Findings and Interpretation

In a prior study examining the application of fuzzy theory in scoring the potential effectiveness of environmental management projects, two scoring items were utilized as semantic-linguistic variables: the completeness of environmental management plans and the feasibility of planned target implementation technology [1]. Due to the unavailability of actual data on the management plans and goals established by evaluated enterprises, statistical comparisons of performance with others in the same trade were not feasible. Environmental plans have significant impacts, yet a Boolean approach is unsuitable for determining whether enterprises possess plans. Consequently, the assessment of management plans necessitates review and evaluation by experts in the relevant field. Corporate management plans encompass critical components such as management strategies and goal setting, crucial for enhancing environmental performance and achieving enterprise sustainability. Ensuring that plans are comprehensive, feasible, and encompass all necessary field factors is paramount. Insufficient detail or failure to consider relevant factors renders it impossible to address environmental concerns effectively. Feasibility refers to the ability to successfully implement something under practical conditions, considering manpower, logistics, technology, resources, finance, the environment, and other pertinent factors.

Moreover, reviewers from diverse backgrounds provide varied subjective evaluations and perspectives. The definitions of comprehensiveness and feasibility scores for plan representation differ, demonstrating multiple values and fuzzy uncertainty in semantic-linguistic terms. Consequently, converting this fuzzy uncertainty into an estimated quantified score is pivotal in evaluating qualitative indicator performance, which aligns with the true purpose of fuzzy theory. The completeness and feasibility of evaluation plans based on fuzzy theory employ poor, good, and excellent as evaluation standards. Expert reviews are utilized in this evaluation method, wherein completeness is assessed first, followed by feasibility, while considering the pragmatic aspects of environmental performance. Even if an enterprise’s plans demonstrate completeness, lacking feasibility renders them vague and general, offering little contribution to environmental sustainability. In such cases, the assessment results would be deemed “poor”. Additionally, except for “poor” feasibility, the higher of the two evaluation results serves as the basis for evaluation, as plan completeness and feasibility are interdependent factors, each influencing the evaluation of the other. Nine types of multiple logic rules were generated using fuzzy intersect calculation based on fuzzy theory.

Matlab_R2023a software was utilized for evaluation calculations. Situational simulation results demonstrate that employing the fuzzy method enables the integration of evaluation plans into logical rules while mitigating absolute subjective effects. This surpasses the capabilities of traditional weight methods used to assess qualitative plans. However, various other influencing factors and limitations arise when applying fuzzy theory to qualitative environmental management plans. These aspects necessitate comprehensive discussion, and the advanced discussion outcomes in this section are outlined below:

3.1. Impact of Membership Functions on Evaluation

Figure 3, Figure 4 and Figure 5 illustrate the typical triangular and trapezoidal membership functions employed in this study. The horizontal axis represents semantic variable and total rated EMP scores, ranging from 0 to 10. The vertical axis represents the membership degree, indicating the percentage distribution of a score within a specific membership function. A membership degree of 1 signifies a complete belonging to a particular category (e.g., poor, good, or excellent). For instance, a score of 3.0 might be classified as 55% poor and 45% good. The shape and width of membership functions significantly influence the distribution of rating percentages, as evident in the comparison of Figure 4 and Figure 5.

Table 1 summarizes the function parameters and simulation results for these four MF simulation types. A Gaussian membership function was first selected for the three linguistic semantic variables of nine sets of simulation scores. The control parameters are as follows: smf [1.5 5.0], gaussmf [1.25 5], and zmf [5 8.5]. Remarkably, the nine input semantic-linguistic variable simulations yielded consistent values, with Situation G exhibiting slightly noticeable differences. The membership function calculation resulted in values of 2.89, 3.91, 2.1, and 3.82. However, a statistical paired T-test revealed a significance level of 0.05, with relevant test values presented in

Table 2. Statistical paired t-test of various paired MF groups.

Paired MF	G~T1	G~T2	G~T3	T1~T2	T1~T3	T2~T3
Mean Difference	−0.0622	0.0933	−0.04	0.1555	0.0222	−0.1333
Standard Error	0.1469	0.1020	0.1332	0.2413	0.0320	0.2274
T-Statistic	−0.4233	0.9145	−0.3001	0.6444	0.6924	−0.5861
Prob Level	0.6832	0.3872	0.77176	0.5373	0.5082	0.5739

Abbreviations: G (G model), T1, T2, T3 (T1, T2, T3 models as defined in Table 1).

. The probability level for the six types of pairing is significantly higher than 0.05, indicating no difference between the four types of membership functions when compared in pairs. This similarity is due to their very similar geometric overlap despite differences in mathematical equations. The input membership functions, control parameters, and output memberships exhibit no discernible differences in terms of geometric spatial distribution, approximating the total score of the computed fuzzy results.

To mitigate highly subjective crisp determination scores, evaluation grade membership employs fuzzy theory and computing logic. Distinct total scores are generated by settings and calculations utilizing logical rules, offering tangible representations rather than single scores. The examination of total scores (see Table 1) reveals two phenomena: Rough equivalence between the total score and the average value of sub-item scores, as observed in Situation I, where the completeness score was 8.12, the feasibility score was 9.3, and the average value was 8.71. There is greater variation between the total score and the average value of sub-item scores, as seen in Situations B, D, and G. For instance, Situation G had a completeness score of 9.83, a feasibility score of 2.56, and an average value of 6.195. The total scores for the four types of membership function (MF) were: 2.89 (G), 3.91 (T1), 2.1 (T2), and 3.82 (T3). The completeness and feasibility of the overall plan were evaluated comprehensively.

In Category 2, the total and average sub-item scores exhibited more variation, classified into Situation B, where the average score of sub-item scores exceeded the total score, and Situations D and G, where the average value of sub-item scores was less than the total score. Situation B’s linguistic variable-based logic rules are as follows: If completeness is “poor” and feasibility is “good”, the overall rating is “good”. Consequently, the fuzzy inference-based result score was around 5.00 (good). Situations D and G followed similar logic rules based on linguistic variables. In Situations D and G, the logic rule design is based on the absolute weight of feasibility in enhancing semantic-linguistic variable technology. Given its significance as a key factor, feasibility plays a decisive role in determining the overall assessment level. This exemplifies a key application feature of fuzzy theory systems. For instance, if completeness is rated as “good” and feasibility as “poor”, the overall rating is determined as “poor”, resulting in fuzzy inference-based scores of around 2.00 and 3.00 (poor). Conversely, in Situation G, where completeness is deemed excellent, the score approaches 4.00.

3.2. Expanding the Application of Linguistic Variables and Logistic Rules

In this context, the semantic-linguistic variables previously discussed represent fuzzy inferences about two key aspects: the completeness of plans and technological feasibility. To further enhance the evaluation of environmental plan performance, an additional criterion, namely the “semantic-linguistic variable” plan implementation schedule, has been introduced. This addition aims to incentivize businesses to accelerate their environmental improvement initiatives. However, eligibility for this extra point is contingent upon receiving completeness and feasibility ratings of “good or higher”, without impacting the overall assessment level. According to this criterion, only situations E, F, H, and I from the original binary logic system qualify for schedule extra points.

By incorporating the schedule rating of 8.00 into the logic inference engine, centroid, and defuzzification with the maximum value, total scores of 7.38~8.29 increased by up to 17% to about 8.30~9.09, as shown in

Table 3. The impact of the membership factor and multiple logistic rules on the final scores.

Situation	Completeness Scoring	Feasibility Scoring	Progress Schedule Score	Gaussian Membership Function Binary Logistic zmf gaussmf smf [1.5 5] [1.25 5] [5 8.5]	Gaussian Membership Function (G) Ternary Logistic (Centroid) zmf gaussmf smf [1.5 5] [1.25 5] [5 8.5]	Gaussian Membership Function (G) Ternary Logistic (Maximum Degree of Truth) zmf gaussmf smf [1.5 5] [1.25 5] [5 8.5]
A	Completeness: poor	Feasibility: poor		Results: poor
	1.82	1.25		1.76
B	Completeness: poor	Feasibility: good		Results: good
	1.65	5.34		5.03
C	Completeness: poor	Feasibility: excellent		Results: good
	2.25	8.78		5.20
D	Completeness: good	Feasibility: poor		Results: poor
	6.53	1.05		2.03
E	Completeness: good	Feasibility: good	Schedule: excellent	Results: good	Results: good	Results: good
	5.80	7.30	8.00	7.38	7.86	8.65
F	Completeness: good	Feasibility: excellent	Schedule: excellent	Results: excellent	Results: excellent	Results: excellent
	6.83	9.25	8.00	8.07	8.11	8.45
G	Completeness: excellent	Feasibility: poor		Results: poor
	9.83	2.56		2.89
H	Completeness: excellent	Feasibility: good	Schedule: excellent	Results: excellent	Results: excellent	Results: excellent
	8.53	6.52	8.00	7.88	7.99	8.30
I	Completeness: excellent	Feasibility: excellent	Schedule: excellent	Results: excellent	Results: excellent	Results: excellent
	8.12	9.30	8.00	8.29	8.30	9.09

. This highlights the potential of fuzzy theory in extending its applications beyond traditional methodologies.

3.3. Comparative Analysis of Traditional Weight Assessments

Both fuzzy theory and traditional qualitative weight assessments aim to estimate numerical scores for qualitative indices, but they employ different methodologies. Traditional qualitative weight assessments assign scores to empirical assessment sub-items in plans based on default weight distribution ratios and the scores of the respective sub-items. In contrast, fuzzy theory assessment methods consider specific situational logic and key factor considerations to calculate scores, aiming to mitigate absolute subjective effects during the review process.

To compare the characteristics of qualitative weight assessment and fuzzy theory, simulations were conducted. Sub-item completeness and feasibility weight ratios were set at 35–65%, 50–50%, and 65–35%, representing different levels of importance assigned to completeness and feasibility. Simulated sub-item values used previously were then compared. The situational simulation results in

Table 4. Comparison of traditional weight assessments with Fuzzy simulation.

Situation	Completeness Scoring	Feasibility Scoring	Fuzzy Assessment (Centroid)	Weight Assessment Completeness 35% Feasibility 65%	Weight Assessment Completeness 50% Feasibility 50%	Weight Assessment Completeness 65% Feasibility 35%
A	Completeness: poor	Feasibility: poor	Results: poor	Results: poor	Results: poor	Results: poor
	1.82	1.25	1.76	1.45	1.54	1.62
B	Completeness: poor	Feasibility: good	Results: good	Results: good	Results: poor/good	Results: poor
	1.65	5.34	5.03	4.05	3.50	2.94
C	Completeness: poor	Feasibility: excellent	Results: good	Results: good	Results: good	Results: good
	2.25	8.78	5.20	6.49	5.52	4.54
D	Completeness: good	Feasibility: poor	Results: poor	Results: poor	Results: poor/good	Results: good
	6.53	1.05	2.03	2.97	3.79	4.61
E	Completeness: good	Feasibility: good	Results: good	Results: good	Results: good	Results: good
	5.80	7.30	7.38	6.78	6.55	6.33
F	Completeness: good	Feasibility: excellent	Results: excellent	Results: excellent	Results: excellent	Results: excellent
	6.83	9.25	8.07	8.40	8.04	7.68
G	Completeness: excellent	Feasibility: poor	Results: poor	Results: good	Results: good	Results: good
	9.83	2.56	2.89	5.10	6.20	7.29
H	Completeness: excellent	Feasibility: good	Results: excellent	Results: excellent	Results: excellent	Results: excellent
	8.53	6.52	7.88	7.22	7.53	7.83
I	Completeness: excellent	Feasibility: excellent	Results: excellent	Results: excellent	Results: excellent	Results: excellent
	8.12	9.30	8.29	8.89	8.71	8.53

display the total scores of situations A, E, F, H, and I, along with the weight assessment results using fuzzy inference, which exhibited minor differences. Slight variations among situations B, C, D, and G were observed.

To gauge the level of numerical discretion, standard deviations of the two groups were examined. For situations A, E, F, H, and I, the standard deviations were 0.13, 0.45, 0.29, 0.30, and 0.25, respectively, while for situations B, C, D, and G, they were 0.89, 0.81, 1.11, and 1.87, respectively. These results indicate fundamental structural differences between fuzzy inferences and weight calculations, particularly noticeable at level of sub-item assessment.

For instance, in Situation G, where completeness was rated as “excellent (9.83)”, while feasibility was rated as “poor (2.56)”, the overall assessment score was deemed “poor”, with a fuzzy total of poor 2.89 because of the designed logic rules to downgrade the overall assessment to poor level. However, under three different weight settings, the assessment consistently yielded ratings of “good” or higher, ranging from 5.10 to 7.29 without considering the critical poor feasibility. Similarly, in Situation D, with completeness and feasibility assessed as “good” and “poor”, respectively, the fuzzy computing score was poor 2.03. Yet, due to weight ratios, the weight calculation resulted in a score of good 4.61 at completeness weight 65%, approximating the “good” assessment. While in situation B, where completeness was rated as “poor” (1.65) and feasibility was rated as “good” (5.34), the overall assessment score due to logic rule was “good” with a fuzzy total of 5.03. Nevertheless, the assessment scores of the three weight settings increased from 4.05 to 3.50 to 2.94, indicating the overweight of completeness. This discrepancy underscores the influence of fuzzy logic in the assessment process, wherein overall scores may differ from those obtained through traditional weight methods.

Traditional weight methods lack the flexibility to incorporate fuzzy logic thinking factors, especially when dealing with sub-items of similar levels and scores. The application of fuzzy theory in assessing qualitative plans allows for the integration of logical rules while mitigating subjective effects, surpassing the capabilities of traditional weight methods in evaluating quality plans.

Limitations exist in the application of any theory or tool, and fuzzy theory is no exception. Even Newton’s law of universal gravity requires adjustments to account for regional variations. In the operational framework of the fuzzy theory system (Figure 2), comprising fuzzy, a fuzzy inference engine, and defuzzification, the impact of membership factors and multiple logistic multi-value logic rules was discussed earlier, with the final defuzzification method also influencing the total score.

An examination of Table 4 reveals that the total score of Situation I (ranging from 8.08 to 8.29) is similar to the completeness score (8.12) but seemingly lower than the technology feasibility score (9.3) and the average score (8.71). Increasing both scores to 9.5 would result in total scores for the four types of MF as follows: G (8.32), T1 (8.25), T2 (8.08), and T3 (8.25). This suggests that when sub-item scores approach perfection, the defuzzification score tends to approximate the upper limit rather than the perfect score.

Examining the intersection of the fuzzy inference engine output set reveals that at a perfect score of 10 points for both completeness and feasibility, the intersection encompasses the entire set space of output membership (Figure 6). The final total score derived from centroid defuzzification approaches an upper limit of approximately 8.32, which is not perfect 10 points. The reason for this underscored (8.32) result is because of the specific defuzzification method used.

Additionally, centroid defuzzification imposes a limit on the total score, although defuzzification methods such as the maximum method and the bisector also exist. The maximum method can raise the total score to 9.25, reflecting a more professional use of fuzzy calculations. Moreover, increasing the upper limit of the total score involves narrowing the set space of the output membership function. For instance, modifying the quadrilateral trapezoidal membership function of T3 to a narrower linzmf (1 2), identical trapmf (2 4 6 8), and narrower linsmf (8 9) alters the functional pattern (Figure 7), resulting in low- and high-score areas being pushed to the sides. When the maximum method is used for defuzzification, the total score becomes 9.5.

These discussions and calculations may underscore the flexibility of fuzzy theory in application. Fuzzy rule design and membership function setting can generate a considerable application space tailored to specific targets. Grasping the ingenuity of fuzzy systems will lead to limitless and boundless applications.

While the centroid, maximum, and bisector defuzzification methods employed in this study impose certain limitations on the total EMP score, they provide comparable basic results when used consistently. Future research could focus on refining defuzzification methods to more accurately reflect the nuances of EMP evaluation. Additionally, applying the fuzzy model to evaluate national and international climate policies, as exemplified by the GERMANWATCH Climate Change Performance Index, could demonstrate its broader applicability and potential for generating more objective and precise assessments.

4. Conclusions

While quantifiable environmental standards are relatively straightforward to evaluate, environmental management plans serve as essential blueprints for sustainable objectives, strategies, implementation methods, and timelines. Assessing the completeness, technological feasibility, work schedules, and other qualitative aspects of these plans is crucial for effective sustainability management.

In both research and practical applications, discussions concerning mathematical assessment standards are often lacking. Traditional methods such as statistical ranking and the Boolean approach fall short in evaluating environmental management plans due to their qualitative nature. Therefore, this study adopts a novel approach by integrating multiple logistic-valued logic rules using fuzzy systems, which align with logical factor thinking while mitigating human subjective biases. The fuzzy system offers a precise assessment of plan performance, avoiding the subjective interpretations typical of traditional methods.

Evaluating the three semantic variables—measure completeness, technology feasibility, and implementation progress, representing EMP completeness, technology feasibility, and implementation progress, respectively—is fundamental to constructing a fuzzy systems evaluation and scoring EMP model. The process involves selecting suitable membership functions and defuzzification methods, followed by developing logistic rules to assign simulation scores (1–10) to each variable. These scores are subsequently input into the fuzzy model to determine the final EMP evaluation score.

The fuzzy systems evaluation and scoring EMP model generates EMP evaluation scores ranging from 1.76 to 8.29 for Gaussian membership, 1.80 to 8.19 for Triangular membership-A, 1.92 to 8.00 for Triangular membership-B, and 1.81 to 8.19 for Quadrilateral trapezoidal membership, based on simulated rating scenarios using the semantic variables of completeness and feasibility. This approach successfully incorporates distribution logic from subjective membership degrees to evaluate EMP scores. However, the average method’s reliance on equal weighting limits its ability to capture the full range of membership degree distributions. This enables the evaluation of EMP scores by effectively integrating distribution logic from subjective membership degrees. However, the average method’s limitation lies in its consideration of equal criteria weights, neglecting the distribution of membership degrees. In contrast, the fuzzy model can dynamically adjust evaluations through logical pattern design. For instance, an EMP with an exceptional completeness score (9.80) but poor feasibility (2.56) would receive a low overall score (2.89) using the fuzzy model, rather than a misleading average score of 6.19. This highlights the model’s ability to accurately reflect the complex interplay between different semantic variables. Consequently, a low EMP value should be assigned in such cases, rather than an inflated average. To further enhance the model’s performance, increasing the number of semantic variables, refining logic rules, or experimenting with different membership function types and defuzzification methods could be explored.

Traditional weight methods lack the flexibility to incorporate fuzzy logic thinking factors, especially when dealing with sub-items of similar levels and scores. The fuzzy system offers a precise assessment of plan performance, avoiding the subjective interpretations typical of traditional methods. However, fuzzy systems do have limitations, particularly regarding membership function types and defuzzification methods, which can influence assessment values and levels. The assessment quantification model for plan thinking aims to provide exploratory insights rather than serving as an absolute standard. The objective is to stimulate further reflection and discussion to enhance the rationality of Environmental, Social, and Governance (ESG) assessments and contribute to improved environmental sustainability.