An ESG Assessment Approach with Multi-Agent Preference Differences: Based on Fuzzy Reasoning and Group Decision-Making

Abstract

The adoption of Environmental, Social, and Governance (ESG) to measure the green development, social responsibility, and public interest of companies is a commonly accepted theme and approach in the industry and academia at present. As ESG assessment is characterized by heterogeneity of subjects, complexity of contents, diversity of scales, and uncertainty of weights, it has led to the variability of ESG assessment results given by different assessment organizations in the same company, which has attracted a lot of criticism. This paper proposes a group decision-making method based on the preferences of multiple subjects to solve the problem of heterogeneity of subjects in ESG assessment. Specifically, for the given ESG evaluation data, the first step is to identify the preferences of subjects and structure the initial group matrix; secondly, the fuzzy inference system is employed to mine the hidden preference information; further, the initial group matrix is revised using the preference information; and finally, the TOPSIS method is applied to aggregate the information and obtain the final ESG score and ranking of each company. This study was tested using statistics from 30 companies released by Harvest Fund in May 2021, which verified the validity and advantages of the method proposed in this paper. The proposed method integrates the preferences of heterogeneous subjects and mines the possible hidden preference information, which increases the interpretation of the information contained in the original ESG data and facilitates the achievement of group consensus.

1. Introduction

ESG is a measure of environmental (E), social (S), and governance (G) that focuses not only on the performance of financial indicators but also on non-financial indicators (e.g., environmental protection, social responsibility, etc.). Ishizaka et al. (2021) point out that banks, investors, regulators, corporations, and governments are increasingly inclined to assess investment or corporate performance through ESG [1]. For analysts or investors, ESG assessments can help them find companies that are more environmentally conscious, more willing to take on social responsibilities and have better corporate governance. For companies, excellent ESG scores can help them build a good corporate image and attract significant investments [2].

With the increasing concern of countries about climate change, environmental protection, and corporate responsibility, ESG assessment is becoming a widely accepted method to measure corporate sustainability [3]. According to statistics, there are currently more than 600 ESG rating agencies around the world, covering a variety of organizations such as professional rating companies and non-profit groups, among which the more influential ones are MSCI (Morgan Stanley Capital International Indexes), Bloomberg, Thomson Reuters, DJSI (Dow Jones Sustainability Indexes), Sustainalytics, HSSUS (Hang Seng Corporate Sustainability Indexes), etc. In recent years, nations have been paying attention to water, climate, and other environmental issues and have successively proposed carbon neutrality goals (e.g., the European Union proposes to achieve carbon neutrality by 2050, and China proposes to achieve it by 2060). ESG rating provides a path and method for the nation to achieve the development concepts of carbon peaking and carbon neutrality.

Based on this, scholars have conducted a lot of research on ESG-related issues. Mori and Christodoulou (2012) reviewed various sustainability indices and indicators based on environmental, economic, and social developments to develop an urban sustainability index [4]. María Jesús Muñoz-Torres et al. (2019) proposed that ESG could be used as a measure of supply chain performance [5]. Castillo et al. (2018) argue that ESG scores can be used as a competitive comparison standard, thus helping companies understand how different environments and mechanisms affect sustainable development [6]. Bryan et al. (2017) conducted a study on the impact of internal and outsourced governance on ESG performance [7]. His study found that both internal and external governance help to improve ESG performance, which maximizes ESG performance in a synergistic environment. Rahdari and Rostamy (2015) identified the 70 most common indicators that are used in rating systems and guidelines for ESG [8]. Managers and researchers can extract the appropriate indicators from these indicators to generate sustainability evaluation systems. A noteworthy issue is that the ESG ratings of the same company are often inconsistent when calculated by different rating agencies [9,10]. The variability of ESG rating results to some extent restricts the application and development of ESG ratings; thus, it is important and practical to propose an ESG rating method that satisfies the needs of heterogeneous multi-subject preferences [11].

There are two main problems for ESG evaluation in the existing studies [12]: (1) Due to the existence of many reasons, such as information disclosure rules and the irrational behaviors of corporate managers, the assessment information is incomplete or hidden. If precise values are used for ESG rating, it will make the results less credible. (2) Because ESG assessment is multidimensional and decision-makers or analysts are not necessarily homogeneous, the ESG rating results will be biased by subjective judgment. If only a single scenario or a single decision-maker is used for the evaluation, the results obtained are inaccurate. Based on this, this paper proposes an ESG evaluation method that considers heterogeneous multi-subject preferences by combining fuzzy theory, group decision-making, and TOPSIS (Technique for Order Preference by Similarity to an Ideal Solution). The proposed method considers the possible differences in preferences of all decision-makers, which is conducive to achieving group consensus. This paper aims to fill the research gap in ESG rating based on the preferences of multiple subjects.

In Section 2, this paper will present a paper on the relevant research results. Section 3 gives the method proposed in this paper. Section 4 is the case study to demonstrate the proposed method. Section 5 concludes the whole paper.

2. Literature

2.1. Enterprise Performance and ESG

In recent years, the study of Environmental, Social, and Governance (ESG) responsibility and its consequences have remained an important topic of concern for the company’s stakeholders, including governmental and non-governmental organizations, investors, and researchers [13]. Wu and Li (2023) used multiple linear regression and stata on 2707 companies listed in Chinese A-shares during the period 2010–2021 to show that ESG performance can be a reference tool for corporate managers and government departments to make decisions [14]. Suttipun (2023) showed that there is a negative relationship between ESG performance and corporate financial risk, which means that improving ESG performance can reduce corporate financial risk. Thus, the authors suggest that senior management and shareholders should pay attention to corporate ESG performance to ensure that the company achieves sustainable growth [15]. During the COVID-19 pandemic, the performance of firms in all countries around the world was significantly affected. Al Amosh and Khatib (2023) applied statistical analysis to examine the relationship between corporate financial performance and the environmental, social, and governance (ESG) performance of companies in nine of the G20 countries during 2016–2021. The results of the study showed that companies with ESG management activities had less impact on their financial performance during the pandemic period [16]. Ahmad et al. (2023) found that ESG, company size, and corporate governance as strategic tools can improve firm performance, especially during the financial crisis, in a panel data analysis of 351 UK companies from 2002–2018 [17]. Luo et al. (2023) explored the relationship between comprehensive ESG ratings of companies and credit financing in financial markets, finding that ESG can effectively increase companies’ access to trade credit by mitigating information asymmetry, improving operational efficiency, and reducing risk [18]. The study by Lian et al. (2023) further shows that ESG performance helps to alleviate financing constraints, enhance human capital levels, and improve management layout, thus positively influencing corporate green innovation [19]. Cheng et al. (2023) used the DEA method to measure the relationship between the achievement of ESG goals and financial performance, and the analysis of data from 1108 Chinese companies revealed a positive relationship between efficiency and financial performance [20].

2.2. ESG Rating Discrepancy

With the development of ESG, scholars have paid attention to the issue of ESG rating discrepancies. Escrig-Olmedo et al. (2014) used a fuzzy multi-criteria decision-making approach to integrate the preferences of multiple investors, playing the subjective role of the decision-maker in the assessment [21]. More recently, Escrig-Olmedo et al. (2017) also investigated preference information for heterogeneous subjects in different scenarios [12]. The study by Billio et al. (2021) points out the lack of commonality in the definitions of ESG characteristics, attributes, and criteria used by the rating agencies, a problem that leads to the variability of the same company under different rating criteria [22]. The results of Barkemeyer et al. (2023) show that ESG evaluation discrepancies are disputed due to significant selection bias, which poses a hidden risk to investors [23]. Balp and Strampelli (2022) point to issues of variability and opacity in ESG rating indices and criteria, coupled with inconsistent corporate sustainability disclosure frameworks, which make it difficult for investors to obtain reliable assessments [24]. Wan and Dawod (2022) explored the relationship between their ESG ratings and capital ownership preferences for the 2015–2020 period for Shanghai and Shenzhen 300 listed companies [25].

3. Method

With the development of the concepts of carbon peak and carbon neutrality, several professional rating agencies and social organizations have emerged around the world. They measure companies’ performance in ESG from three aspects: environmental, social, and governance. In some cases, the ESG score can be a guiding signal for investors in the financial market. However, ESG analysts or decision-makers have different sets of information and/or different interpretations of information, resulting in ESG scores for the same company often varying significantly across rating agencies. Differential ratings hinder the development and application of ESG, so it is important and significant to assess ESG with the preferences of analysts or decision-makers [26]. In this paper, we propose an ESG group decision method that takes into account the preferences of multiple subjects.

3.1. Group Decision-Making

ESG is a value concept and assessment tool that focuses on environmental, social, and governance, initiated and promoted by the United Nations Principles for Responsible Investment (UNPRI). Environmental (E) concerns carbon and greenhouse gas emissions, environmental policies, waste pollution, etc.; social (S) concerns employee health and safety, management training, labor practices, etc.; governance (G) concerns corruption and bribery policies, anti-unfair competition, risk management, etc.

Due to differences in knowledge background and investment needs, etc., subjects give different personal judgments on the important order of the three dimensions, and there are six ($A_3^3=6$) scenarios, i.e., $\mathrm{E}\succ \mathrm{S} \succ \mathrm{G}$, $\mathrm{E} \succ \mathrm{G}\succ \mathrm{S}$, $\mathrm{S} \succ \mathrm{E}\succ \mathrm{G}$, $\mathrm{S} \succ \mathrm{G}\succ \mathrm{E}$, $\mathrm{G}\succ \mathrm{S} \succ \mathrm{E}$, $\mathrm{G} \succ \mathrm{E}\succ \mathrm{S}$, respectively [27]. The first scenario ($\mathrm{E}\succ \mathrm{S} \succ \mathrm{G}$) is selected for analysis here, and the analysis of the other scenarios is consistent with this. Let $w_1$, $w_2$, $w_3$ denote the importance of E, S, and G (i.e., indicator weights) given by the subject, and then the ESG score of the ith company measured by $E{S}_1$ can be expressed as follows:

$$\begin{array}{l}{s}_{i1}=\max {\displaystyle \sum _{j=1}^3{x}_{ij}^{*}{w}_j}\\ \begin{array}{cc}s.t.& w_1\ge \end{array}{w}_2\ge w_3\\ \begin{array}{cc}& \end{array}{\displaystyle \sum _{j=1}^3{w}_j}=1\\ \begin{array}{cc}& \end{array}{w}_j\ge 0\end{array}$$

(1)

here, $s_{i1}$ denotes the ESG value of $C_i$ given by $E{S}_1$. $x_{ij}^{*}$ is a normalized value, which can be calculated by Equation (2).

$$x_{ij}^{*}=\frac{x_{ij}-\underset{i}{\min }\left\{x_{ij}\right\}}{\underset{i}{\max }\left\{x_{ij}\right\}-\underset{i}{\min }\left\{x_{ij}\right\}}$$

(2)

where, $x_{ij}$ denotes the score of $C_i$ on $d_j$, $i=1,2,...,m$, $j=1,2,3$.

Theorem 1. 

According to Song’s study [28], subjects can perform a closed assessment of a company’s ESG, and this assessment does not require the determination of precise weights. Based on this, the ESG score of $C_i$ given by $E{S}_1$ can be expressed as follows.

$$s_{i1}=\max \left\{x_{i1}^{*},\frac{x_{i1}^{*}+x_{i2}^{*}}{2},\frac{x_{i1}^{*}+x_{i2}^{*}+x_{i3}^{*}}{3}\right\}$$

(3)

The method does not require the exact weights of each indicator, thus making the results more objective and the process simpler. Based on the above, the six scenarios are analyzed to form a group decision-making matrix.

$$S_{m\times 6}=\left[\begin{array}{cccc}{s}_{11}& s_{12}& \cdots & s_{16}\\ s_{21}& s_{22}& \cdots & s_{26}\\ ⋮& ⋮& \cdots & ⋮\\ s_{m1}& s_{m2}& \cdots & s_{m6}\end{array}\right]$$

(4)

where, $s_{ip}$ denotes the ESG score of pth subject on the production operation of ith company, $i=1,2,\cdots ,m$, $p=1,2,\cdots ,6$.

3.2. Preference Information Measurement

The group decision-making matrix derived based on Equation (4) responds to the preferences of heterogeneous subjects. However, the attribute characteristics of the exact values make the preference information of the subject hidden. To further explore the preference information of the subjects, this paper adopts the fuzzy inference system (FIS) to fuzzify the exact numbers and derive the complete preference information. FIS is a widely used method for sustainability assessment [29,30]. The main steps are shown in Figure 1.

Figure 1 shows the inference process from fuzzification to defuzzification of the fuzzy inference system. The first is the fuzzification process. In this paper, the exact values are fuzzified using an affiliation function. Through the fuzzification process, a clear (non-fuzzy) value is transformed into an affiliation level for each linguistic term in the fuzzy set. Linguistics are an effective way for decision-makers to express preference information in complex decision problems [31]. In this paper, the triangular fuzzy number is chosen to fuzzify the exact value. Let $a=\left(a^l,a^m,a^b\right)$ is a triangular fuzzy number, and its corresponding affiliation function formula is shown in Equation (5).

$$u_A(x)=\{\begin{array}{ccc}0& if& x\le a^l\\ \frac{x-a^l}{a^m-a^l}& if& a^l<x\le a^m\\ \frac{a^b-x}{a^b-a^m}& if& a^m<x\le a^b\\ 0& if& a^b\le x\end{array}$$

(5)

In this paper, the five-level linguistic variables are selected to fuzzify their exact values, and their relevant information is shown in

Table 1. Language variables and scores.

Language Variables	Affiliation Function
Poor Sustainability (PS)	(0, 0, 0.25)
Low Sustainability (LS)	(0, 0.25, 0.5)
Medium Sustainability (MS)	(0.25, 0.5, 0.75)
High Sustainability (HS)	(0.5, 0.75, 1)
Top Sustainability (TS)	(0.75, 1, 1)

. From this, the preferences of subjects for each company can be derived. Taking $E{S}_1$ as an example, the affiliation of an ith company ($C_i$) can be expressed as Equation (6).

$$U_i^1=\frac{u_{PS}\left(s_{i1}\right)}{s_{i1}}+\frac{u_{LS}\left(s_{i1}\right)}{s_{i1}}+\frac{u_{MS}\left(s_{i1}\right)}{s_{i1}}+\frac{u_{HS}\left(s_{i1}\right)}{s_{i1}}+\frac{u_{TS}\left(s_{i1}\right)}{s_{i1}}$$

(6)

where the “+” does not represent a summation, but rather a generalization of the set. “$\frac{u_{PS}\left(s_{i1}\right)}{s_{i1}}$” is also not a point, it indicates $s_{i1}$ the affiliation to the fuzzy set PS.

Next, we need to analyze the fuzzy rule base. The obtained affiliation is usually analyzed using the “if-then” inference rule. Here, the fuzzy values are aggregated using fuzzy operators. Currently, there are four types of fuzzy operators, namely “Min-Max” fuzzy operator ($R\left(\min ,\max \right)$), “Min-product” fuzzy operator ($R\left(\min ,\oplus \right)$), “Max-product” fuzzy operator ($R\left(\max ,\oplus \right)$), and “product-sum” fuzzy operator ($R\left(•,\oplus \right)$) [32]. We choose $R\left(•,\oplus \right)$ to perform information aggregation in this paper, which can be expressed as Equation (7).

$$R=\left(\begin{array}{cccc}{r}_{11}& r_{12}& \cdots & r_{11}\\ r_{21}& r_{22}& \cdots & r_{2n}\\ ⋮& ⋮& \cdots & ⋮\\ r_{m1}& r_{m2}& \cdots & r_{mn}\end{array}\right)\times \left(\begin{array}{c}{a}_1\\ a_2\\ ⋮\\ a_n\end{array}\right)$$

(7)

Here, $r$ denotes the fuzzy assessment value; $a$ denotes the degree of importance.

Further, we need to process the inference unit. The evaluation object is fuzzified using the above method. Here, firstly, an exact number is converted into a triangular fuzzy number by the affiliation function, and then the fuzzy output of TA, HS, MS, LS, and PS will be generated according to fuzzy rules.

The $E{S}_1={\left(s_{11},s_{21},\dots ,s_{m1}\right)}^T$ denotes the initial evaluation results of each enterprise given by $E{S}_1$. A new fuzzy matrix is formed by associating linguistic terms with rating levels through an affiliation function, as expressed in Equation (8).

Next, the “product-sum” fuzzy operator ($R\left(•,\oplus \right)$) is used to assemble the fuzzy matrix, and this paper uses the affiliation function to represent the importance preference of the evaluation subject. The assessment results ($E{S}_1$) are presented in Equation (9).

$$F_1=\left[\begin{array}{cccc}\left(s_{11},u_{PS}\left(s_{11}\right)\right)& \left(s_{11},u_{LS}\left(s_{11}\right)\right)& \cdots & \left(s_{11},u_{TS}\left(s_{11}\right)\right)\\ \left(s_{21},u_{PS}\left(s_{21}\right)\right)& \left(s_{21},u_{LS}\left(s_{21}\right)\right)& \cdots & \left(s_{21},u_{TS}\left(s_{21}\right)\right)\\ ⋮& ⋮& \cdots & ⋮\\ \left(s_{m1},u_{PS}\left(s_{m1}\right)\right)& \left(s_{m1},u_{LS}\left(s_{m1}\right)\right)& \cdots & \left(s_{m1},u_{TS}\left(s_{m1}\right)\right)\end{array}\right]$$

(8)

$$E{S}_1^{*}=\left(u_{PS}\left(s_{11}\right)\times \frac{u_{PS}\left(s_{11}\right)}{s_{11}}\right)+\left(u_{LS}\left(s_{11}\right)\times \frac{u_{LS}\left(s_{11}\right)}{s_{11}}\right)+\dots +\left(u_{TS}\left(s_{m1}\right)\times \frac{u_{TS}\left(s_{11}\right)}{s_{m1}}\right)$$

(9)

The initial group decision-making is modified based on the fuzzy evaluation values derived from Equations (8) and (9). The new fuzzy group decision-making matrix with preference information is shown below.

$$S_{m\times 6}^{\prime }=\left[\begin{array}{cccc}{s}_{11}^{\prime }& s_{12}^{\prime }& \cdots & s_{16}^{\prime }\\ s_{21}^{\prime }& s_{22}^{\prime }& \cdots & s_{26}^{\prime }\\ ⋮& ⋮& \cdots & ⋮\\ s_{m1}^{\prime }& s_{m2}^{\prime }& \cdots & s_{m6}^{\prime }\end{array}\right]$$

(10)

where, $s_{ip}^{\prime }$ denotes the modified fuzzy value of $C_i$, $s_{ip}^{\prime }=E{S}_{ip}^{*}\times u\left(s_{ip}\right)$.

Finally, the fuzzy numbers are defuzzified. By utilizing the defuzzification process, the fuzzy values are transformed and output. In this paper, the fuzzy values are defuzzified using Equation (11) and the group decision matrix is modified in a close step [33].

$$s_{ip}^{″}=\frac{{s^{\prime }}_{ip}^l+{s^{\prime }}_{ip}^m+{s^{\prime }}_{ip}^b}{3}$$

(11)

$$S_{m\times 6}^{″}=\left[\begin{array}{cccc}{s}_{11}^{″}& s_{12}^{″}& \cdots & s_{16}^{″}\\ s_{21}^{″}& s_{22}^{″}& \cdots & s_{26}^{″}\\ ⋮& ⋮& \cdots & ⋮\\ s_{m1}^{″}& s_{m2}^{″}& \cdots & s_{m6}^{″}\end{array}\right]$$

(12)

3.3. Evaluation Information Integration

A fuzzy inference system is used to revise the initial group decision-making matrix, which results in a new group decision matrix with complete preference information, $S^{″}={\left[s_{ip}^{″}\right]}_{m\times 6}$. In this section, TOPSIS is used to aggregate the group decision-making information. The ESG evaluation obtained here is the closest to the positive ideal solution and the farthest from the negative ideal solution.

$$\mathrm{PIS}: {\widehat{s}}_p^{Max}=\max \left(s_{1p}^{″},s_{2p}^{″},\dots ,s_{mp}^{″}\right)$$

(13)

$$\mathrm{NIS}: {\widehat{s}}_p^{Min}=\min \left(s_{1p}^{″},s_{2p}^{″},\dots ,s_{mp}^{″}\right)$$

(14)

where ${\widehat{s}}_p^{Max}$ denotes the bigger ESG value given by $E{S}_p$; ${\widehat{s}}_p^{Min}$ denotes the smallest ESG value given by $E{S}_p$.

Based on Equations (13) and (14), the distance from $C_i$ to the positive ideal solution and the negative ideal solution can be expressed in Equations (15) and (16).

$$B_i^{+}=\sqrt{{\displaystyle \sum _{p=1}^6{\left(s_{ip}^{″}-{\widehat{s}}_p^{Max}\right)}^2}}$$

(15)

$$B_i^{-}=\sqrt{{\displaystyle \sum _{p=1}^6{\left(s_{ip}^{″}-{\widehat{s}}_p^{Min}\right)}^2}}$$

(16)

where, $B_i^{+}$ and $B_i^{-}$ denote the distances $C_i$ to the positive and negative ideal solutions, respectively. Nearly, Equation (17) is applied to calculate the relative proximity coefficient, which is the final evaluation value of the ESG.

$$B_i=\frac{B_i^{-}}{B_i^{-}+B_i^{+}}$$

(17)

The use of $B_i$ integrated multi-subject preference information is more appropriate to the actual evaluation situation so that the results can be accepted by the majority or all subjects and thus reach a group consensus.

3.4. Methodological Steps

In this paper, we propose an ESG assessment method that considers the preferences of multiple subjects based on group decision-making and fuzzy inference methods. This method fully considers the preferences of heterogeneous subjects for ESG assessment and the problem of information integrity, which adopts group decision-making for ESG assessment, so that the final ranking results can maximize the differential demands of heterogeneous subjects and thus reach group consensus. Fuzzy inference can reflect the hidden preferences of the subjects by fuzzifying the evaluation information, which makes the results more consistent with the real assessment results. The specific steps of the method are as follows:

Step 1: The initial group decision-making matrix is established. The decision-makers with different preferences are identified by a specific judgment of the important order among E, S, and G. There are six scenarios of preference decision-makers. Based on this, an initial group decision-making matrix with preference information is developed in this paper, $S_{i\times 6}=\left(s_{i1},s_{i2},\dots ,s_{i6}\right)$, $i=1,2,\dots ,m$.

Step 2: Heterogeneous subject preference information is analyzed. Due to the complexity and diversity of ESG evaluation indexes, as well as the attribute characteristics of the precise value itself, some preferences of analysts and investors are hidden. In this regard, this paper proposes a method to fuzzify the initial assessment values by using a fuzzy inference system to derive the following distribution of linguistic preference relations among subjects.

$$U_i^p=\frac{u_{PS}\left(s_{ip}\right)}{s_{ip}}+\frac{u_{LS}\left(s_{ip}\right)}{s_{ip}}+\frac{u_{MS}\left(s_{ip}\right)}{s_{ip}}+\frac{u_{HS}\left(s_{ip}\right)}{s_{ip}}+\frac{u_{TS}\left(s_{ip}\right)}{s_{ip}}$$

Next, a fuzzy group decision-making matrix with preferences is obtained by using the “product-sum” fuzzy operator to assemble the preferences, $S_{i\times 6}^{\prime }=\left(s_{i1}^{\prime },s_{i2}^{\prime },\dots ,s_{i6}^{\prime }\right)$. Further, the fuzzy group decision-making matrix is modified by using the defuzzification operator, and the new group evaluation matrix is $S_{i\times 6}^{″}=\left(s_{i1}^{″},s_{i2}^{″},\dots ,s_{i6}^{″}\right)$.

Step 3: ESG evaluation value and ranking are calculated. The TOPSIS method is selected to aggregate the preference evaluation information of six heterogeneous subjects to obtain the final ESG evaluation value of each evaluation subject. Based on the final ESG scores of the companies, they are ranked according to the idea of descending order.

The higher the final ESG score, the higher the ranking, and the more outstanding the comprehensive performance of the company in terms of society, environment, and corporate governance.

4. Case Study

4.1. Application Analysis

This paper uses the ESG scores of 30 companies from Harvest fund’s statistics as of May 2021 as a sample. The report assesses the ESG performance of each company in three aspects {($d_1$, environmental); ($d_2$, social); ($d_3$, governance)}, and the relevant information is shown in

Table 2. Initial data.

Company	Score	E	S	G
C1	11.622	67.182	20.213	38.316
C2	64.345	62.885	64.883	71.630
C3	76.067	82.820	57.463	75.853
C4	89.099	63.798	63.429	85.325
C5	43.114	57.830	47.829	60.820
C6	28.571	32.919	40.495	59.461
C7	61.174	62.710	78.887	61.908
C8	77.447	66.410	62.467	74.941
C9	89.745	62.063	82.821	81.995
C10	54.849	74.833	49.582	67.368
C11	90.149	84.623	76.976	81.164
C12	58.934	48.347	48.755	73.803
C13	79.242	44.821	58.206	83.388
C14	48.001	66.524	44.126	66.316
C15	84.757	59.862	76.840	79.293
C16	50.104	89.120	20.611	81.642
C17	75.207	81.911	52.717	79.589
C18	33.575	64.772	49.836	27.927
C19	67.259	63.490	45.051	78.846
C20	52.413	50.774	33.255	79.832
C21	83.585	55.453	60.201	82.684
C22	73.691	42.211	51.199	82.555
C23	80.037	60.714	55.880	82.734
C24	30.394	49.841	30.705	66.527
C25	69.169	61.495	64.755	70.210
C26	66.517	62.597	44.970	77.894
C27	5.548	51.732	16.757	8.917
C28	46.731	65.458	29.100	76.471
C29	66.743	42.395	53.408	75.491
C30	66.502	76.104	49.189	73.824

.

Due to the different environments faced by ESG assessment subjects (e.g., investors, analysts, etc.) or differences in their knowledge structures, there is significant heterogeneity among ESG assessment subjects, and they may present different assessment preferences for corporate ESG performance. For the problem of preference differences among heterogeneous subjects, the ESG assessment problem was investigated using the method proposed in this paper, and the specific steps are as follows:

Step 1: Using Song’s (2017) study [28], the preferences of subjects in six scenarios were analyzed. The initial group decision-making matrix is built based on Table 2, which is shown in

Table 3. Initial group decision matrix.

	ES1	ES2	ES3	ES4	ES5	ES6
C1	0.6096	0.6096	0.3489	0.3489	0.4972	0.3848
C2	0.6941	0.6941	0.7285	0.7746	0.8208	0.8208
C3	0.8879	0.8879	0.7934	0.7934	0.8820	0.8760
C4	0.7520	0.7747	0.7520	0.8532	1.0000	1.0000
C5	0.5310	0.5613	0.5310	0.5748	0.6793	0.6793
C6	0.3403	0.3403	0.3593	0.5104	0.6615	0.6615
C7	0.7353	0.7214	0.9405	0.9405	0.7214	0.8170
C8	0.7173	0.7300	0.7173	0.7780	0.8641	0.8641
C9	0.8250	0.8250	1.0000	1.0000	0.9564	0.9782
C10	0.7458	0.7554	0.6692	0.6692	0.7650	0.7650
C11	0.9257	0.9328	0.9257	0.9285	0.9455	0.9455
C12	0.5360	0.5619	0.5360	0.6668	0.8492	0.8492
C13	0.6046	0.6046	0.6274	0.8010	0.9746	0.9746
C14	0.5979	0.6746	0.5878	0.5878	0.7512	0.7512
C15	0.7700	0.7700	0.9095	0.9153	0.9210	0.9210
C16	1.0000	1.0000	0.6700	0.6700	0.9759	0.9518
C17	0.8717	0.8983	0.7803	0.7803	0.9249	0.9249
C18	0.5668	0.5668	0.5337	0.5007	0.4388	0.4388
C19	0.6291	0.7296	0.6291	0.6717	0.9152	0.9152
C20	0.4985	0.6229	0.4985	0.5889	0.9281	0.9281
C21	0.6747	0.6832	0.6747	0.8115	0.9654	0.9654
C22	0.5501	0.5645	0.5501	0.7425	0.9637	0.9637
C23	0.6843	0.7303	0.6843	0.7791	0.9661	0.9661
C24	0.4221	0.5275	0.4221	0.4826	0.7540	0.7540
C25	0.6791	0.6791	0.7265	0.7644	0.8022	0.8022
C26	0.6193	0.7154	0.6193	0.6649	0.9027	0.9027
C27	0.3347	0.3347	0.1674	0.1116	0.1674	0.1116
C28	0.5790	0.7315	0.5500	0.5500	0.8841	0.8841
C29	0.5316	0.5316	0.5548	0.7130	0.8713	0.8713
C30	0.7684	0.8089	0.7029	0.7029	0.8495	0.8495

.

Step 2: ① Fuzzification. According to Table 1 and Equations (4) and (5), the exact numbers in Table 3 are transformed into the corresponding linguistic evaluations and affiliation degrees. Due to the large amount of calculated data and similar calculation process, ES₁ is used as an example for the data presentation of this step (

Table 4. Preferences distribution and membership.

	PS	LS	MS	HS	TS
C1	0.0000	0.0000	0.5614	0.4386	0.0000
C2	0.0000	0.0000	0.2234	0.7766	0.0000
C3	0.0000	0.0000	0.0000	0.4484	0.5516
C4	0.0000	0.0000	0.0000	0.9921	0.0079
C5	0.0000	0.0000	0.8762	0.1238	0.0000
C6	0.0000	0.6389	0.3611	0.0000	0.0000
C7	0.0000	0.0000	0.0589	0.9411	0.0000
C8	0.0000	0.0000	0.1308	0.8692	0.0000
C9	0.0000	0.0000	0.0000	0.7000	0.3000
C10	0.0000	0.0000	0.0169	0.9831	0.0000
C11	0.0000	0.0000	0.0000	0.2973	0.7027
C12	0.0000	0.0000	0.8559	0.1441	0.0000
C13	0.0000	0.0000	0.5816	0.4184	0.0000
C14	0.0000	0.0000	0.6082	0.3918	0.0000
C15	0.0000	0.0000	0.0000	0.9201	0.0799
C16	0.0000	0.0000	0.0000	0.0000	1.0000
C17	0.0000	0.0000	0.0000	0.5131	0.4869
C18	0.0000	0.0000	0.7329	0.2671	0.0000
C19	0.0000	0.0000	0.4834	0.5166	0.0000
C20	0.0000	0.0059	0.9941	0.0000	0.0000
C21	0.0000	0.0000	0.3013	0.6987	0.0000
C22	0.0000	0.0000	0.7994	0.2006	0.0000
C23	0.0000	0.0000	0.2629	0.7371	0.0000
C24	0.0000	0.3117	0.6883	0.0000	0.0000
C25	0.0000	0.0000	0.2838	0.7162	0.0000
C26	0.0000	0.0000	0.5228	0.4772	0.0000
C27	0.0000	0.6610	0.3390	0.0000	0.0000
C28	0.0000	0.0000	0.6841	0.3159	0.0000
C29	0.0000	0.0000	0.8737	0.1263	0.0000
C30	0.0000	0.0000	0.0000	0.9264	0.0736

).

② Fuzzy rule. The “if-then” inference rules are used, and then the linguistic preference information and affiliation are aggregated using the product-sum operator.

③ Reasoning units. The ESG performance of 30 companies was analyzed based on the fuzzification results and the fuzzy rule. The relevant information of the revised group decision-making matrix is shown in

Table 5. Revised group evaluation fuzzy score.

	ES1	ES2	ES3	ES4	ES5	ES6
C1	(0.3596,0.6096,0.8596)	(0.3596,0.6096,0.8596)	(0.0989,0.3489,0.5989)	(0.0989,0.3489,0.5989)	(0.2472,0.4972,0.7472)	(0.1348,0.3848,0.6348)
C2	(0.4441,0.6941,0.9441)	(0.4441,0.6941,0.9441)	(0.4785,0.7285,0.9485)	(0.5246,0.7746,1.0000)	(0.5728,0.8208,1.0000)	(0.5708,0.8208,1.0000)
C3	(0.6379,0.8879,1.0000)	(0.6379,0.8879,1.0000)	(0.5434,0.7934,1.0000)	(0.5434,0.7934,1.0000)	(0.6320,0.8820,1.0000)	(0.6260,0.8760,1.0000)
C4	(0.5020,0.7520,1.0000)	(0.5247,0.7747,1.0000)	(0.5020,0.7520,1.0000)	(0.6032,0.8532,1.0000)	(0.7500,1.0000,1.0000)	(0.7500,1.0000,1.0000)
C5	(0.2810,0.5310,0.7810)	(0.3113,0.5613,0.8113)	(0.2810,0.5310,0.7810)	(0.3248,0.5748,0.8248)	(0.4293,0.6793,0.9293)	(0.4293,0.6793,0.9293)
C6	(0.0903,0.3403,0.5903)	(0.0903,0.3403,0.5903)	(0.1093,0.3593,0.6093)	(0.2604,0.5104,0.7604)	(0.4115,0.6615,0.9115)	(0.4115,0.6615,0.9115)
C7	(0.4853,0.7353,0.9853)	(0.4714,0.7214,0.9714)	(0.6905,0.9405,1.0000)	(0.6905,0.9405,1.0000)	(0.4714,0.7214,0.9714)	(0.5670,0.8170,1.0000)
C8	(0.4673,0.7173,0.9673)	(0.4800,0.7300,0.9800)	(0.4673,0.7173,0.9673)	(0.5280,0.7780,1.0000)	(0.6141,0.8641,1.0000)	(0.6141,0.8641,1.0000)
C9	(0.5750,0.8250,1.0000)	(0.5750,0.8250,1.0000)	(0.7500,1.0000,1.0000)	(0.7500,1.0000,1.0000)	(0.7064,0.9564,1.0000)	(0.7282,0.9782,1.0000)
C10	(0.4958,0.7458,0.9958)	(0.5054,0.7554,1.0000)	(0.4192,0.6692,0.9192)	(0.4192,0.6692,0.9192)	(0.5150,0.7650,1.0000)	(0.5150,0.7650,1.0000)
C11	(0.6757,0.9257,1.0000)	(0.6828,0.9328,1.0000)	(0.6757,0.9257,1.0000)	(0.6785,0.9285,1.0000)	(0.6955,0.9455,1.0000)	(0.6599,0.9455,1.0000)
C12	(0.2860,0.5360,0.7560)	(0.3119,0.5619,0.8119)	(0.2860,0.5360,0.7560)	(0.4168,0.6668,0.9168)	(0.5992,0.8492,1.0000)	(0.5992,0.8492,1.0000)
C13	(0.3546,0.6046,0.8546)	(0.3546,0.6046,0.8546)	(0.3774,0.6274,0.9774)	(0.5510,0.8010,1.0000)	(0.7246,0.9746,1.0000)	(0.7246,0.9746,1.0000)
C14	(0.3479,0.5979,0.8479)	(0.4246,0.6746,0.9246)	(0.3378,0.5878,0.8378)	(0.3378,0.5878,0.8378)	(0.5012,0.7512,1.0000)	(0.5012,0.7512,1.0000)
C15	(0.5200,0.7700,1.0000)	(0.5200,0.7700,1.0000)	(0.6895,0.9095,1.0000)	(0.6653,0.9153,1.0000)	(0.6710,0.9210,1.0000)	(0.6710,0.9210,1.0000)
C16	(0.7500,1.0000,1.0000)	(0.7500,1.0000,1.0000)	(0.4200,0.6700,0.9200)	(0.4200,0.6700,0.9200)	(0.7259,0.9759,1.0000)	(0.7018,0.9518,1.0000)
C17	(0.6217,0.8717,1.0000)	(0.6483,0.8983,1.0000)	(0.5303,0.7803,1.0000)	(0.5303,0.7803,1.0000)	(0.6749,0.9249,1.0000)	(0.6749,0.9249,1.0000)
C18	(0.3168,0.5668,0.8168)	(0.3168,0.5668,0.8168)	(0.2837,0.5337,0.7837)	(0.2507,0.5007,0.7507)	(0.1888,0.4388,0.6888)	(0.1888,0.4388,0.6888)
C19	(0.3791,0.6291,0.8791)	(0.4796,0.7296,0.9796)	(0.3791,0.6291,0.8791)	(0.4217,0.6717,0.9217)	(0.6652,0.9152,1.0000)	(0.6652,0.9152,1.0000)
C20	(0.2485,0.4985,0.7485)	(0.3729,0.6229,0.8729)	(0.2485,0.4985,0.7485)	(0.3389,0.5889,0.8389)	(0.6781,0.9281,1.0000)	(0.6781,0.9281,1.0000)
C21	(0.4247,0.6747,0.9247)	(0.4332,0.6832,0.9332)	(0.4247,0.6747,0.9247)	(0.5615,0.8115,1.0000)	(0.7154,0.9654,1.0000)	(0.7154,0.9654,1.0000)
C22	(0.3001,0.5501,0.8001)	(0.3145,0.5645,0.8145)	(0.3001,0.5501,0.8001)	(0.4915,0.7425,0.9925)	(0.7137,0.9637,1.0000)	(0.7137,0.9637,1.0000)
C23	(0.4343,0.6843,0.9343)	(0.4803,0.7303,0.9803)	(0.4343,0.6843,0.9343)	(0.5291,0.7791,1.0000)	(0.7161,0.9661,1.0000)	(0.7161,0.9661,1.0000)
C24	(0.1721,0.4221,0.6721)	(0.2775,0.5275,0.7775)	(0.1721,0.4221,0.6721)	(0.2326,0.4826,0.7326)	(0.5040,0.7540,1.0000)	(0.5040,0.7540,1.0000)
C25	(0.4291,0.6791,0.9291)	(0.4291,0.6791,0.9291)	(0.4765,0.7265,0.9765)	(0.5144,0.7644,1.0000)	(0.5522,0.8022,1.0000)	(0.5522,0.8022,1.0000)
C26	(0.3693,0.6193,0.8693)	(0.4654,0.7154,0.9654)	(0.3693,0.6193,0.8693)	(0.4149,0.6649,0.9149)	(0.6527,0.9027,1.0000)	(0.6527,0.9027,1.0000)
C27	(0.0847,0.3347,0.5847)	(0.0847,0.3347,0.5847)	(0.0000,0.1674,0.3347)	(0.0000,0.1116,0.2232)	(0.0000,0.1674,0.3347)	(0.0000,0.1116,0.2232)
C28	(0.3290,0.5790,0.8290)	(0.4815,0.7315,0.9815)	(0.3000,0.5500,0.8000)	(0.3000,0.5500,0.8000)	(0.6341,0.8841,1.0000)	(0.6341,0.8841,1.0000)
C29	(0.2816,0.5316,0.7816)	(0.2816,0.5316,0.7816)	(0.3048,0.5548,0.8048)	(0.4630,0.7130,0.9630)	(0.6213,0.8713,1.0000)	(0.6213,0.8713,1.0000)
C30	(0.5184,0.7684,1.0000)	(0.5589,0.8089,1.0000)	(0.4529,0.7209,0.9529)	(0.4529,0.7209,0.9529)	(0.5995,0.8495,1.0000)	(0.5995,0.8495,1.0000)

. Taking ES₁ as an example to demonstrate the calculation process. Combining with the fuzzy rule base, the resulting fuzzy evaluation value of ES₁.

$$F_1=\left[\begin{array}{cccc}PS& \cdots & HS& TS\\ ⋮& \cdots & ⋮& ⋮\\ PS& \cdots & HS& TS\\ PS& \cdots & HS& TS\end{array}\right]\times \left[\begin{array}{cccc}0& \cdots & 0& 0\\ ⋮& \cdots & ⋮& ⋮\\ 0.6096& \cdots & 0.5316& 0.7684\\ 0& \cdots & 0& 0.7684\end{array}\right]$$

$$E{S}_1^{*}\left(s_{i1}\right)=\left(PS\times u_{PS}\left(s_{i1}\right)\right)+\dots +\left(HS\times u_{HS}\left(s_{i1}\right)\right)+\left(TS\times u_{TS}\left(s_{i1}\right)\right)$$

$$\begin{array}{l}E{S}_1^{*}\left(s_{1,1}\right)=\left(PS\times 0\right)+\dots +\left(HS\times 0.6096\right)+\left(TS\times 0\right)\\ ⋮\\ E{S}_1^{*}\left(s_{30,1}\right)=\left(PS\times 0\right)+\dots +\left(HS\times 0.7684\right)+\left(TS\times 0.7684\right)\end{array}$$

④ Defuzzification. A new group decision-making matrix with complete preference information is obtained by defuzzifying the fuzzy numbers shown in Table 5 according to Equation (10), as shown in

Table 6. Revised group evaluation score.

	ES1	ES2	ES3	ES4	ES5	ES6
C1	0.6096	0.6096	0.3489	0.3489	0.4972	0.3848
C2	0.6941	0.6941	0.7285	0.7664	0.7972	0.7972
C3	0.8419	0.8419	0.7789	0.7789	0.8380	0.8340
C4	0.7513	0.7665	0.7513	0.8188	0.9167	0.9167
C5	0.5310	0.5613	0.5310	0.5748	0.6793	0.6793
C6	0.3403	0.3403	0.3593	0.5104	0.6615	0.6615
C7	0.7353	0.7214	0.8770	0.8770	0.7214	0.7947
C8	0.7173	0.7300	0.7173	0.7687	0.8261	0.8261
C9	0.8000	0.8000	0.9167	0.9167	0.8876	0.9021
C10	0.7458	0.7536	0.6692	0.6692	0.7600	0.7600
C11	0.8671	0.8718	0.8671	0.8690	0.8804	0.8804
C12	0.5360	0.5619	0.5360	0.6668	0.8161	0.8161
C13	0.6046	0.6046	0.6274	0.7840	0.8998	0.8998
C14	0.5979	0.6746	0.5878	0.5878	0.7508	0.7508
C15	0.7633	0.7633	0.8563	0.8602	0.8640	0.8640
C16	0.9167	0.9167	0.6700	0.6700	0.9006	0.8845
C17	0.8312	0.8489	0.7702	0.7702	0.8666	0.8666
C18	0.5668	0.5668	0.5337	0.5007	0.4388	0.4388
C19	0.6291	0.7296	0.6291	0.6717	0.8601	0.8601
C20	0.4985	0.6229	0.4985	0.5889	0.8687	0.8687
C21	0.6747	0.6832	0.6747	0.7910	0.8936	0.8936
C22	0.5501	0.5645	0.5501	0.7425	0.8925	0.8925
C23	0.6843	0.7303	0.6843	0.7694	0.8941	0.8941
C24	0.4221	0.5275	0.4221	0.4826	0.7527	0.7527
C25	0.6791	0.6791	0.7265	0.7596	0.7848	0.7848
C26	0.6193	0.7154	0.6193	0.6649	0.8518	0.8518
C27	0.3347	0.3347	0.1674	0.1116	0.1674	0.1116
C28	0.5790	0.7315	0.5500	0.5500	0.8394	0.8394
C29	0.5316	0.5316	0.5548	0.7130	0.8309	0.8309
C30	0.7623	0.7893	0.7029	0.7029	0.8163	0.8163

.

Step 3: Determine the positive and negative ideal solutions, which are known from the above table.

$${\widehat{s}}_p^{Max}=\left(0.9167,0.9167,0.9167,0.9167,0.9167,0.9167\right)$$

$${\widehat{s}}_p^{Min}=\left(0.4394,0.4394,0.4600,0.3245,0.4587,0.3245\right)$$

The ESG evaluation values of 30 companies can be calculated based on the positive and negative ideal solutions, which is shown in

Table 7. The ESG scores of 30 companies.

	Score		Score		Score
C1	0.3642	C11	0.9383	C21	0.7693
C2	0.7604	C12	0.6307	C22	0.6719
C3	0.859	C13	0.7203	C23	0.7816
C4	0.8405	C14	0.6377	C24	0.5157
C5	0.5556	C15	0.8654	C25	0.7463
C6	0.4333	C16	0.8147	C26	0.7111
C7	0.8052	C17	0.8628	C27	0
C8	0.7827	C18	0.4285	C28	0.6543
C9	0.9085	C19	0.7226	C29	0.6413
C10	0.731	C20	0.6243	C30	0.7817

.

To verify the validity and scientific accuracy of the proposed method, the Pearson correlation coefficient was used to analyze the correlation between the final ESG score and the group evaluation, which is calculated as follows: Pearson’s correlation coefficient is a common statistical method for bivariate correlation coefficient analysis. $\rho \in [0,0.2]$ indicates a very weak or no correlation, $\rho \in (0.2,0.4]$ indicates a weak correlation, $\rho \in (0.4,0.6]$ indicates a moderate correlation, $\rho \in (0.6,0.8]$ indicates a strong correlation, $\rho \in (0.8,1]$ indicates a very strong correlation.

$${\rho }_{xy}=\frac{\mathrm{cov}\left(x,y\right)}{{\sigma }_x{\sigma }_y}$$

where the numerator is the covariance of the two variables and the denominator is the product of the standard deviations. In this paper, the final ESG rating values are selected for correlation analysis with the modified population matrix. The results are calculated as shown in

Table 8. Pearson correlation coefficient.

	ES1	ES2	ES3	ES4	ES5	ES6
ρ	0.8394	0.8620	0.9692	0.9810	0.9189	0.9535

and plotted in Figure 2.

In Figure 2, the x-axis represents the group score with different preferences, namely ES1, ES2, ES3, ES4, ES5, and ES6, and the y-axis represents the final ESG score. As known from Table 8 and Figure 2, the ESG assessment values obtained by using the proposed method form a strong correlation with ES₁–ES₆, among which, ES₃ and ES₄ have the strongest correlation. It can be observed that the final ranking obtained by using the proposed method can satisfy the preference selection behavior of all subjects and better meet the requirements of heterogeneous subjects.

4.2. Discussion

4.2.1. Method Comparison

To further illustrate the advanced method proposed in this paper, the ESG assessment values calculated are compared with the initial data (Harvest) and the general group decision-making. The ESG assessment values and rankings obtained by the three methods are shown in Table 8. To facilitate more visual observation of data changes, the data information in

Table 9. The ESG scores of different methods.

	Harvest		GDM		Proposed Method
	Score	Ranking	Score	Ranking	Score	Ranking
C1	11.6221	29	0.3277	29	0.3642	29
C2	64.3446	17	0.6945	13	0.7604	13
C3	76.0671	9	0.8107	5	0.8590	5
C4	89.0987	3	0.7893	6	0.8405	6
C5	43.1143	25	0.5002	25	0.5556	25
C6	28.5712	28	0.3945	27	0.4333	27
C7	61.1738	18	0.7502	8	0.8052	8
C8	77.4468	8	0.7196	12	0.7827	9
C9	89.7447	2	0.8787	2	0.9085	2
C10	54.8492	20	0.6589	18	0.7310	15
C11	90.1492	1	0.9170	1	0.9383	1
C12	58.9338	19	0.5848	23	0.6307	23
C13	79.2421	7	0.6803	14	0.7203	17
C14	48.0010	23	0.5750	24	0.6377	22
C15	84.7571	4	0.8207	3	0.8654	3
C16	50.1037	22	0.7811	7	0.8147	7
C17	75.2072	10	0.8165	4	0.8628	4
C18	33.5746	26	0.3844	28	0.4285	28
C19	67.2590	13	0.6720	16	0.7226	16
C20	52.4131	21	0.5890	22	0.6243	24
C21	83.5851	5	0.7216	10	0.7693	12
C22	73.6912	11	0.6348	19	0.6719	19
C23	80.0374	6	0.7299	9	0.7816	11
C24	30.3935	27	0.4697	26	0.5157	26
C25	69.1694	12	0.6790	15	0.7463	14
C26	66.5166	15	0.6607	17	0.7111	18
C27	5.5477	30	0.0000	30	0.0000	30
C28	46.7309	24	0.6100	20	0.6543	20
C29	66.7434	14	0.5978	21	0.6413	21
C30	66.5023	16	0.7198	11	0.7817	10

is plotted in Figure 3.

In a recent step, this paper uses Spearman’s rank correlation coefficient to analyze the ESG assessment values obtained by the three methods, and the results of the analysis are shown in

Table 10. Spearman’s rank correlation coefficient.

	Environment	Social	Governance	Average	Improve
Harvest	0.0905	0.8033	0.7864	0.5601
GDM	0.4154	0.7241	0.6013	0.5802	+2.01%
Proposed method	0.4790	0.7237	0.6080	0.6036	+4.35%	+2.33%

. Spearman’s rank correlation coefficient can solve the problem of correlation between the ranking of two variables, which is a common method in statistics. The more inconsistent the ranking of two variables is, the smaller the Spearman’s rank correlation coefficient is, which is calculated as follows:

$$\varpi =1-\frac{6{\displaystyle \sum _{i=1}^m{\left(b_i\right)}^2}}{m\left(m^2-1\right)}$$

Here, $b_i$ denote the ranking difference of ith company ($C_i$).

From Table 9, it is noticed that the proposed method is superior to the other two methods, with an increase of 4.35% compared to the ranking of Harvest data and an increase of 2.33% compared to general group decision-making.

4.2.2. Others Analysis

In Section 4.2.1, the ranking obtained by the proposed method is compared with those obtained by the other two methods, taking 30 companies as a sample, to illustrate the superiority of the proposed method. We’d like to explore the impact of sample size on the proposed method. Spearman’s rank correlation coefficient is employed to calculate the correlation between each dimension score and the final score under different sample sizes, as shown in

Table 11. Correlation obtained by three methods under different samples.

	Samples	Environment	Social	Governance	Average	Improve
Harvest	10	0.4191	0.5652	0.5369	0.5071
GDM		0.5042	0.4558	0.5726	0.5109	+0.38%
Proposed method		0.4373	0.5827	0.5471	0.5224	+1.53%	+1.15%
Harvest	30	0.0905	0.8033	0.7864	0.5601
GDM		0.4154	0.7241	0.6013	0.5802	+2.01%
Proposed method		0.479	0.7237	0.608	0.6036	+4.35%	+2.33%
Harvest	50	0.1272	0.6513	0.4420	0.4069
GDM		0.1052	0.6091	0.5799	0.4314	+2.45%
Proposed method		0.1330	0.6069	0.6246	0.4548	+4.80%	+2.34%
Harvest	70	0.4493	0.4827	0.5865	0.5062
GDM		0.4948	0.5010	0.6076	0.5345	+2.83%
Proposed method		0.4823	0.5614	0.6329	0.5589	+5.27%	+2.44%

. The specific process is consistent with Section 4.1 and is not explained further. This only displayed the correlation between each dimension score and the final score at different samples.

From the table above, the final ESG score obtained by the proposed method has a higher correlation with each dimension. It can be shown that the proposed method is not affected by the sample size. It outperforms the method of harvest and the classical GDM under different samples.

5. Conclusions and Implications

5.1. Conclusions

In this paper, we propose an ESG assessment method that combines GDM and FIS to address the problem of preference differences among heterogeneous subjects for environment, society, and governance. To better integrate the preference information of heterogeneous subjects, the method firstly establishes an initial group decision-making matrix based on the importance of the three dimensions; secondly, the fuzzy inference system is used to mine the hidden preference information of the subjects; next, TOPSIS is used to aggregate the group decision-making information and obtain the ESG score and ranking; finally, the Pearson correlation coefficient and Spearman rank correlation coefficient are used to verify the effectiveness and advancement of the proposed method.

The results of this paper have important reference value for other ESG assessment agencies, such as investment agencies and analysts: ① Integrating the differences in preferences of heterogeneous subjects for environmental, social, and governance aspects, adopting group decision-making, and improving the recognition and attractiveness of financial market investment evaluation results. ② Due to the complexity of the evaluation environment, subjects may not be able to provide complete preference information, which leads to incomplete expression of preference relations among evaluation subjects. Further, there is a phenomenon of offsetting the scores of the indicators of equal-weighted evaluation when performing the integration of evaluation information, which reduces the correctness of the comprehensive evaluation results. In this paper, we use FIS to fuzzify the clear values and mine the hidden preference information to derive the complete preference relations and linguistic evaluation information of decision-makers, which improves the validity of the evaluation results.

There are also limitations in this study. When group decision-making information is assembled, different group weights can be given according to the needs of actual ESG evaluation institutions or organizations, thus helping companies attract the appropriate type of investors. In addition, this paper tries to mine the possible hidden preference information to increase the interpretation of the information contained in the original ESG data, but it still does not solve the problem that the ESG data does not fully reflect the violation behavior of the company. Finding better methods to address this issue of the unobserved ability of the majority of ESG factors will become the next main research problem.

5.2. Implications

For a company, having an excellent ESG rating represents market recognition of the company’s investment and performance in social responsibility, effectively helping the company establish a good brand image and attract investment. Many investment institutions have incorporated the company’s ESG rating into their investment decision-making considerations in their investment screening processes. Therefore, only by establishing reasonable methods to evaluate the ESG performance of companies can the goal of effectively guiding investment be achieved. The proposed method fully considers the individual investment preferences of investors and adds an additional layer of information extraction by mining that possibly hidden preference information, which could supposedly help institutions tailor the proposed measure of ESG to the needs and interests of a specific group of investors.