A Multi-Criteria Framework for Sustainability Evaluation of Hydrogen-Based Multi-Microgrid Systems under Triangular Intuitionistic Fuzzy Environment

Abstract

Developing hydrogen-based multi-microgrid systems (HBMMSs) is vital to the low-carbon energy transition, which can promote the utilization of renewable energy and reduce carbon emissions. However, there have been no studies presenting a sustainability evaluation of HBMSSs. Multi-attribute decision-making (MADM) methods are widely used to perform a sustainability evaluation. This paper develops a triangular intuitionistic fuzzy framework to make a comprehensive evaluation of HBMMSs from the perspective of sustainability. Firstly, a sustainability evaluation criteria system including economic, social, environmental, technical, and coordination criteria is established. Secondly, the paper proposes a hybrid fuzzy decision-making method. A triangular intuitionistic fuzzy decision-making trial and evaluation laboratory technique is used to analyze the correlation between criteria and sub-criteria and provides a basis for determining their fuzzy densities. A ranking method combining the triangular intuitionistic fuzzy number, fuzzy measure, and Choquet integral is used to rank the alternatives and choose an optimal one. Moreover, a case study is performed to validate the practicability of the developed framework. Finally, sensitivity analysis, scenario analysis, and comparative analysis are conducted to verify the robustness and effectiveness of the framework. As such, this study provides a guide for evaluating the sustainability of HBMMSs.

1. Introduction

Hydrogen energy is one of the most promising forms of energy due to its high combustion heat, cleanness, sustainability, etc. Unlike coal, oil, and natural gas, hydrogen energy cannot be directly exploited but can be produced by using other energy sources. Using renewable energy to produce hydrogen is a prospective production method. With the technological development of electrolyzers, fuel cells, and others, the levelized cost of hydrogen will drop in the future. Moreover, there are more and more hydrogen refueling stations, and the number of hydrogen-powered cars is increasing. Therefore, the development of hydrogen energy is helpful to promote the low-carbon transition. However, the safety issue of hydrogen energy hinders the healthy development of the hydrogen industry to some degree. Scholars worldwide have performed numerous studies on hydrogen energy. Zhang et al. [1] assessed the economic and technical efficiencies of the hydrogen production industry and found that the energy efficiency and exergy efficiency from medical waste and biogas in the hydrogen production process were very high. Di Lullo et al. [2] conducted an economic, environmental, and technical evaluation of hydrogen transportation systems and pointed out that using a pipeline to transport hydrogen could reduce cost and emissions. Jahanbani Veshareh et al. [3] studied the feasibility of hydrogen storage and found that a depleted chalk reservoir could store significant amounts of hydrogen. Endo et al. [4] studied the design and operation of a hydrogen energy utilization system and found that constant power was important for hydrogen production. Kwon et al. [5] evaluated the risk of hydrogen refueling stations and pointed out that expanding location and separation distance was advantageous for safety improvement. Moreover, hydrogen-based multi-microgrid systems (HBMMS) have also received attention. Rezaei and Pezhmani [6] optimized the operation of an islanded multi-microgrid system based on power and hydrogen and found that demand response and unexpected outages could reduce and increase operating costs, respectively. However, we have still been lacking a comprehensive performance evaluation of HBMMSs’ sustainability. Therefore, this paper focuses on the sustainability evaluation of HBMMSs. The basic structure of the proposed HBMMS is displayed in Figure 1.

At present, few studies on the sustainability evaluation of HBMMSs have been carried out, and there have been some problems with the existing studies.

Firstly, although evaluation studies of off-grid microgrids, grid-connected microgrids, and multi-microgrid systems have been performed, the established multiple evaluation criteria systems have not been able to reflect the characteristics of HBMMSs comprehensively and accurately. Therefore, there is a lack of a sustainability evaluation criteria system for HBMMSs.

Secondly, the existing microgrid evaluation methods have not been suitable to thoroughly consider the uncertainties of decision-making information and reveal the interactions between criteria and cause-and-effect relationships at the same time.

In response to the above problems, a triangular intuitionistic fuzzy framework including an innovation evaluation criteria system and a hybrid decision-making method is proposed in the paper. More specifically, the framework consists of two parts: (i) an innovation evaluation criteria system is established for the sustainability evaluation of HBMMSs, which includes economy, society, environment, technology, and coordination; and (ii) a hybrid decision-making method combining triangular intuitionistic fuzzy numbers (TIFNs), the decision-making trial and evaluation laboratory (DEMATEL) technique, a fuzzy measure, and Choquet integral (CI) is proposed to select the best HBMMS, which considers the interactions between criteria and cause-and-effect relationships as well in an uncertain environment.

The remainder of this paper is organized as follows: Section 2 reviews influencing factors and decision-making methods. Section 3 establishes a comprehensive evaluation criteria system for the sustainability evaluation of HBMMSs. Section 4 introduces the methodology and materials. Section 5 presents a case study using the proposed method. Sensitivity analysis, scenario analysis, and comparative analysis are carried out in Section 6. Section 7 draws the main conclusions.

2. Literature Review

2.1. Influencing Factors

To comprehensively assess the sustainability of HBMMSs, influencing factors should be identified. Experts and scholars worldwide have carried out evaluation research on various hybrid systems, and wide-ranging factors have been considered. Some papers only focused on one aspect. Wang et al. [7] paid attention to the energy payback time of a standalone hybrid microgrid. Moreover, reliability has received attention [8]. Tahir et al. [9] conducted a microgrid evaluation from the aspect of efficiency. Karimi et al. [10], meanwhile, studied the demand-side flexibility of grid-connected multi-microgrid systems.

Some papers considered influencing factors from multiple aspects. Nawaz Khan and Ali Abbas Kazmi [11] assessed renewable-dominated standalone hybrid microgrids from the aspects of economy and technology. Ding et al. [12] studied the total energy cost and CO₂ emission rates of multi-energy microgrids. Economy and reliability were considered in a municipal solid-waste-based microgrid [13] and resilient microgrids [14]. Nagapurkar and Smith [15] studied the economy, technology, and environment of microgrids. Zhao et al. [16] assessed the performances of a combined cooling, heating, and power microgrid (CCHP-MG) system from the three aspects of the economy, environment, and energy. Javed et al. [17] considered cost, reliability, and curtailment in renewable-energy-based remote microgrids. Luo et al. [18] considered economics, reliability, and renewable energy penetration in a microgrid performance evaluation. Wang et al. [19] studied economy, reliability, generation penetration, and power exchange in multi-microgrid systems.

From the above literature review, it can be concluded that: ① the economy is one of the significant influencing factors, which has been explored in many studies; ② other aspects, such as technology, environment, society, and energy, were also considered, but the evaluation criteria systems were not comprehensive; ③ there are various evaluation objects, such as off-grid microgrids, grid-connected microgrids, and multi-microgrid systems, but few studies evaluated the sustainability of HBMMSs.

2.2. Decision-Making Methods

The sustainability of HBMMSs is influenced by many factors. Therefore, the sustainability evaluation of HBMMSs should be regarded as a multi-attribute decision-making (MADM) problem. To evaluate the sustainability of HBMMSs, the paper uses DEMATEL, fuzzy measure theory, and CI.

In the literature, there are some studies on DEMATEL. Zhao et al. [16] used grey DEMATEL to calculate the subjective weights for a CCHP-MG system evaluation. Chen et al. [20] used an interval-valued intuitionistic fuzzy DEMATEL method to obtain the weights. Meanwhile, Giri et al. [21] proposed a Pythagorean fuzzy DEMATEL method to analyze relationships between criteria in supplier selection. To analyze relationships between indicators in multi-energy transaction evaluation, Liu et al. [22] used an interval type-2 fuzzy DEMATEL method. In addition, Vardopoulos [23] employed a triangular fuzzy DEMATEL method to identify the critical sustainable development factors. Dong et al. [24] used hesitant interval-valued intuitionistic fuzzy DEMATEL to obtain critical factors of wind energy investments.

To avoid independent assumption and rank alternatives, fuzzy measure theory and CI have been used. Geng and Lin [25] used CI with respect to λ-fuzzy measure and linguistic CI with respect to λ-fuzzy measure to evaluate the responsibility for greenhouse gas emission reduction. Wu et al. [26] proposed a hybrid fuzzy decision-making method by integrating the λ-fuzzy measure, CI, and interval type-2 fuzzy numbers. Büyüközkan et al. [27] used an intuitionistic fuzzy Choquet integral operator under a group decision-making environment to select a sustainable urban transportation alternative. Wu et al. [28] proposed a cloud Choquet integral operator. Xing et al. [29] combined CI and interval type-2 trapezoidal fuzzy numbers to make an optimal sustainable supplier. Divsalar et al. [30] integrated a probabilistic hesitant fuzzy Choquet integral and an acronym in Portuguese of interactive and multiple attribute decision-making to choose the best alternative. Rahnamay Bonab et al. [31] combined CI and spherical fuzzy sets to evaluate logistic autonomous vehicles.

From the above literature, it can be seen that DEMATEL has been extended and plays an important role in weight determination, correlation analysis between factors, and selection of critical factors. CI operator has been extended in an interval type-2 fuzzy environment, intuitionistic fuzzy environment, etc., to aggregate decision-making information. However, few studies used DEMATEL, fuzzy measure theory, and CI under a triangular intuitionistic fuzzy (TIF) environment to conduct a performance evaluation of HBMMSs.

3. Sustainability Evaluation Criteria System for HBMMSs

To obtain accurate and scientific evaluation results of HBMMSs’ sustainability, it is essential to establish a sustainability evaluation criteria system for HBMMSs. To do so, firstly, a selection of potential influencing factors of the sustainable development of HBMMSs must be collated through a review of the literature and industry research reports. Then, critical influencing factors are selected by an evaluation team consisting of senior experts. Finally, the critical influencing factors are divided based on five criteria: economic, social, environmental, technical, and coordination criteria. The sustainability evaluation criteria system is established, as displayed in

Table 1. Criteria and sub-criteria for sustainability evaluation of HBMMSs.

Criteria	Sub-Criteria	Type
Economic criterion (C1)	Investment cost (C11)	Cost
	Operation cost (C12)	Cost
	Payback period (C13)	Cost
	Cost-saving benefit (C14)	Benefit
	Operation revenues (C15)	Benefit
	Policy subsidies (C16)	Benefit
Social criterion (C2)	Job creation (C21)	Benefit
	Promotion for the development of related industries (C22)	Benefit
	Public acceptance (C23)	Benefit
Environmental criterion (C3)	Reduction in sulfur and nitrogen oxides (C31)	Benefit
	Carbon emission reduction (C32)	Benefit
	Damage to ground vegetation (C33)	Cost
	Noise pollution (C34)	Cost
Technical criterion (C4)	Technical innovation (C41)	Benefit
	Technical maturity (C42)	Benefit
	Technical reliability (C43)	Benefit
Coordination criterion (C5)	Coordination with local power grid (C51)	Benefit
	Coordination with local gas, heating, and cooling networks (C52)	Benefit
	Coordination with other hydrogen energy industries (C53)	Benefit

.

3.1. Economic Criterion

• Investment cost [32] (C11) is relatively high currently in China. It mainly consists of procurement costs and installation costs of the fuel cell, hydrogen tank, etc. In addition, it occupies a certain land scale, and land cost is also included.
• Operation cost (C12) includes the purchased fuel cost, operation and maintenance cost of each device, and salaries of workers of HBMMSs.
• Payback period [33] (C13) is used to assess the solvency of the project itself. The smaller the payback period, the more profitable the HBMMSs.
• Cost-saving benefit (C14) is beneficial to cost reduction in the power grid and other related hydrogen industries.
• Operation revenues (C15) mainly comes from energy trading with external energy networks and other energy consumers.
• Policy subsidies (C16) are provided by the government to support the sustainable development of HBMMSs.

3.2. Social Criterion

• Job creation (C21): The construction and operation of the HBMMSs can create a large number of jobs and enhance the employment rate.
• Promotion for the development of related industries (C22): The emergence and development of HBMMSs will drive the development of power equipment manufacturing enterprises, hydrogen energy equipment manufacturing enterprises, fuel supply enterprises, etc.
• Public acceptance [34] (C23): The successful construction and operation of HBMMSs are depended on public acceptance to a certain degree.

3.3. Environmental Criterion

• Reduction in sulfur and nitrogen oxides (C31): Developing HBMMSs can help reduce the emissions of sulfur and nitrogen oxides such as sulfur dioxide, nitrogen dioxide, etc.
• Carbon emission reduction [35] (C32): Compared with conventional microgrids, HBMMSs are more environmentally friendly. The carbon emission will be reduced as HBMMSs are put into operation.
• Damage to ground vegetation (C33) is mainly produced during the construction period of HBMMSs.
• Noise pollution (C34) will be produced in both the construction stage and operation stage of HBMMSs.

3.4. Technical Criterion

• Technical innovation (C41) measures the technological breakthrough and leading position of HBMMSs.
• Technical maturity (C42) evaluates the comprehensive application level of a variety of techniques.
• Technical reliability (C43) denotes the level of safe and stable operation of HBMMSs and reflects the abilities to resist extreme weather, network attacks, etc.

3.5. Coordination Criterion

• Coordination with local power grid (C51): HBMMSs should be coordinated with the local power grid to promote the development of the economy and society.
• Coordination with local gas, heating, and cooling networks (C52): The site location of HBMMSs should consider the layout and planning of the gas, heating, and cooling networks.
• Coordination with other hydrogen energy industries (C53): The site location of HBMMSs should consider the development of other hydrogen energy industries. As a result, hydrogen fuel can be transported and used economically and conveniently.

4. Methodology and Materials

4.1. Triangular Intuitionistic Fuzzy Number

Compared with crisp numbers, TIFNs can provide more accurate information about evaluation criteria to decision-makers, which creates a maximum degree of membership and a minimum degree of non-membership (reflecting ambiguity and hesitation). Scholars have combined TIFNs and other methods to conduct performance evaluations, such as an extended VIKOR method with TIFNs [36], an extended TODIM method with TIFNs [37], an extended PROMETHEE method with TIFNs [38], etc. The paper uses TIFNs to represent uncertain information in the sustainability evaluation of HBMMSs. Basic definitions and properties of TIFNs are presented as follows:

Definition 1 

([39]). A TIFN $\tilde{a}=((\underset{\_}{a},a,\overline{a});u_{\tilde{a}},v_{\tilde{a}})$ is a special intuitionistic fuzzy set on a real number set R. Its membership function and non-membership function are defined, respectively, as follows:

$$u_{\tilde{a}}(x)=\{\begin{array}{cc}\frac{x-\underset{\_}{a}}{a-\underset{\_}{a}}{u}_{\tilde{a}},& \underset{\_}{a}\le x<a\\ u_{\tilde{a}},& x=a\\ \frac{\overline{a}-x}{\overline{a}-a}{u}_{\tilde{a}},& a<x\le \overline{a}\\ 0,& \begin{array}{ccc}x<\underset{\_}{a}& or& x>\overline{a}\end{array}\end{array}$$

(1)

and

$$v_{\tilde{a}}(x)=\{\begin{array}{cc}\frac{[a-x+v_{\tilde{a}}(x-\underset{\_}{a})]}{a-\underset{\_}{a}},& \underset{\_}{a}\le x<a\\ v_{\tilde{a}},& x=a\\ \frac{[x-a+v_{\tilde{a}}(\overline{a}-x)]}{\overline{a}-a},& a<x\le \overline{a}\\ 1,& \begin{array}{ccc}x<\underset{\_}{a}& or& x>\overline{a}\end{array}\end{array}$$

(2)

where$u_{\tilde{a}}$is the maximum degree of membership, and$v_{\tilde{a}}(x)$is the minimum degree of non-membership. Moreover, they satisfy the conditions:$0\le u_{\tilde{a}}\le 1$,$0\le v_{\tilde{a}}\le 1$, and$0\le u_{\tilde{a}}+v_{\tilde{a}}\le 1$. ${\begin{array}{l}\pi \hfill \end{array}}_{\tilde{a}}(x)=1-u_{\tilde{a}}-v_{\tilde{a}}$is called an intuitionistic fuzzy index of element$x$in$\tilde{a}$.

Definition 2 

([39,40]). Let $\tilde{a}=((\underset{\_}{a},a,\overline{a});u_{\tilde{a}},v_{\tilde{a}})$ and $\tilde{b}=((\underset{\_}{b},b,\overline{b});u_{\tilde{b}},v_{\tilde{b}})$ be two TIFNs, and $\beta$ be a real number. Then, the operations for TIFNs are defined as follows:

① $\tilde{a}+\tilde{b}=((\underset{\_}{a}+\underset{\_}{b},a+b,\overline{a}+\overline{b});\min (u_{\tilde{a}},u_{\tilde{b}}),\max (v_{\tilde{a}},v_{\tilde{b}}))$;

② $\tilde{a}-\tilde{b}=((\underset{\_}{a}-\overline{b},a-b,\overline{a}-\underset{\_}{b});\min (u_{\tilde{a}},u_{\tilde{b}}),\max (v_{\tilde{a}},v_{\tilde{b}}))$;

③ $\beta \tilde{a}=\{\begin{array}{cc}((\beta \underset{\_}{a},\beta a,\beta \overline{a});u_{\tilde{a}},v_{\tilde{a}}),& \beta \ge 0\\ ((\beta \overline{a},\beta a,\beta \underset{\_}{a});u_{\tilde{a}},v_{\tilde{a}}),& \beta <0\end{array}$.

Definition 3 

([41]). Let $\tilde{a}=((\underset{\_}{a},a,\overline{a});u_{\tilde{a}},v_{\tilde{a}})$ be a TIFN. Its score function $S(\tilde{a})$ and accuracy function $H(\tilde{a})$ can be defined as follows:

$$S(\tilde{a})=\frac{\underset{\_}{a}+2a+\overline{a}}{4}(u_{\tilde{a}}-v_{\tilde{a}})$$

(3)

$$H(\tilde{a})=\frac{\underset{\_}{a}+2a+\overline{a}}{4}(u_{\tilde{a}}+v_{\tilde{a}})$$

(4)

Definition 4 

([41]). For two TIFNs $\tilde{a}=((\underset{\_}{a},a,\overline{a});u_{\tilde{a}},v_{\tilde{a}})$ and $\tilde{b}=((\underset{\_}{b},b,\overline{b});u_{\tilde{b}},v_{\tilde{b}})$,

① if $S(\tilde{a})>S(\tilde{b})$, then $\tilde{a}>\tilde{b}$;

② if $S(\tilde{a})=S(\tilde{b})$, and $H(\tilde{a})>H(\tilde{b})$, then $\tilde{a}>\tilde{b}$;

③ if $S(\tilde{a})=S(\tilde{b})$, and $H(\tilde{a})=H(\tilde{b})$, then $\tilde{a}=\tilde{b}$.

Definition 5 

([36]). Let $\tilde{a}=((\underset{\_}{a},a,\overline{a});u_{\tilde{a}},v_{\tilde{a}})$ and $\tilde{b}=((\underset{\_}{b},b,\overline{b});u_{\tilde{b}},v_{\tilde{b}})$ be two TIFNs. The hamming distance between them is defined as follows:

$$d(\tilde{a},\tilde{b})=\frac{1}{3}(|\underset{\_}{a}-\underset{\_}{b}|+|a-b|+|\overline{a}-\overline{b}|)+\max (|u_{\tilde{a}}-u_{\tilde{b}}|,|v_{\tilde{a}}-v_{\tilde{b}}|)$$

(5)

4.2. Fuzzy Measure Theory and Choquet Integral

The fuzzy measure theory developed by Sugeno [42] has been widely used. It can make up for some deficiencies of conventional weighting methods: on the one hand, the additive property is replaced by the monotonic property; on the other hand, it is very flexible, and useful when decision-makers need to calculate the importance of the index combination set. In addition, the CI operator has been used to rank alternatives. Some basic definitions and properties of the λ-fuzzy measure and Cl operator are shown below:

Definition 6 

([42,43]). Let $X=(x_1,x_2,\dots ,x_n)$ be a universe of discourse. A λ-fuzzy measure $\phi$ on $X$ satisfies the following conditions:

$$\phi (AUB)=\phi (A)+\phi (B)+\lambda \phi (A)\phi (B)$$

(6)

where $-1<\lambda <\infty$, $\forall A,B\in \phi (X)$, and $A\cap B=\varphi$.

① If $\lambda >0$, then $\phi (AUB)>\phi (A)+\phi (B)$, which means a multiplicative effect exists between A and B;

② if $\lambda =0$, then $\phi (AUB)=\phi (A)+\phi (B)$, which means A and B are mutually independent;

③ if $\lambda <0$, then $\phi (AUB)<\phi (A)+\phi (B)$, which means a substitutive effect exists between A and B.

Let$X=(x_1,x_2,\dots ,x_n)$be a finite set. The λ-fuzzy measure$\phi$satisfies the following two cases:

① if $\lambda \ne 0$, then $\phi (X)=\frac{1}{\lambda }[{\displaystyle \prod _{i=1}^n}(1+\lambda \phi (x_i))-1]$;

② if $\lambda =0$, then $\phi (X)={\displaystyle \sum _{i=1}^n\phi (x_i)}$.

In the above-mentioned two cases, the unique$\lambda$value is obtained by solving the following formula:

$$\lambda +1=\prod _{i=1}^n(1+\lambda \phi (x_i))$$

(7)

Definition 7 

([44]). Let $X=(x_1,x_2,\dots ,x_n)$ be a no-empty classical set, $f$ be a nonnegative real function defined on $X$, and $\mu$ be a fuzzy measure on $X$. The Cl of function $f$ with respect to $\mu$ is defined by

$$C_{\mu }(f(x_{(1)}),f(x_{(2)}),\dots ,f(x_{(n)}))={\displaystyle \sum _{i=1}^{n}f(x_{(i)})}[\mu (A_{(i)})-\mu (A_{(i+1)})]$$

(8)

where $f(x_{(1)})\le f(x_{(2)})\le \dots f(x_{(n)})$, $A_{(i)}=\left\{x_{(i)},\dots ,x_{(n)}\right\}$, and $A_{(n+1)}=\varphi$.

4.3. A Hybrid Decision-Making Method for HBMMSs’ Sustainability Evaluation

This paper develops a hybrid decision-making method by combining TIFNs, the λ-fuzzy measure, Cl, and DEMATEL to assess the sustainability of HBMMSs, as shown in Figure 2. The proposed four-phase method considers the uncertainty of decision information and analyzes the correlation between indicators in cause-and-effect relationship analysis and aggregation of decision information.

Phase I. Conduct correlation analysis

Step 1. Construct a TIFN-based initial direct-relation matrix

$$F=\left[\begin{array}{cccc}{f}_{11}& f_{12}& \cdots & f_{1n}\\ f_{21}& f_{22}& \cdots & f_{2n}\\ ⋮& ⋮& ⋮& ⋮\\ f_{n1}& f_{n2}& \cdots & f_{nn}\end{array}\right]$$

(9)

where $f_j{}_k$ represents the influence degree of factor $j$ on factor $k$.

Step 2. Obtain a crisp number-based initial direct-relation matrix $G={[g_{jk}]}_{n\times n}$

Convert the TIFN-based initial direct-relation matrix into the crisp number-based initial direct-relation matrix $G={[g_{jk}]}_{n\times n}$ by employing the score function in Equation (3).

Step 3. Obtain a normalized direct-relation matrix $H={[h_{jk}]}_{n\times n}$

$$H=\frac{G}{x}$$

(10)

$$x=\max (\max {\displaystyle \sum _{k=1}^n{g}_{jk}},\max {\displaystyle \sum _{j=1}^n{g}_{jk}})$$

(11)

Step 4. Construct a total relation matrix $T={[t_{jk}]}_{n\times n}$

In addition to direct influences between the influencing factors, indirect influences between the influencing factors need to be considered. Therefore, the total relation matrix is constructed as follows:

$$T=H{(I-H)}^{-1}$$

(12)

where $I$ is an identity matrix.

Step 5. Obtain a cause group and an effect group

$$R_j={\displaystyle \sum _{k=1}^n{t}_{jk}}$$

(13)

$$D_j={\displaystyle \sum _{k=1}^n{t}_{kj}}$$

(14)

$$P_j=R_j+D_j$$

(15)

$$Q_j=R_j-D_j$$

(16)

where $R_j$ represents the influence produced by factor $j$ on other factors; $D_j$ represents the influence produced by other factors on factor $j$; $P_j$ is center degree of factor $j$; $Q_j$ is cause degree of factor $j$. If $Q_j>0$, factor $j$ belongs to the cause group; if $Q_j<0$, factor $j$ belongs to the effect group.

Phase II. Calculate the fuzzy density

Step 1. Obtain the fuzzy density of each indicator

According to the correlation between indicators, the center degree, and cause degree, the fuzzy density of each indicator is determined.

Step 2. Calculate the fuzzy density of each index combination set

Based on the fuzzy density of each indicator, coefficient λ is calculated and the fuzzy density of each index combination set is calculated.

Phase III. Construct a decision matrix and carry out normalization

Step 1. Construct a TIF decision matrix

$$A=\left[\begin{array}{cccc}{\tilde{a}}_{11}& {\tilde{a}}_{12}& \cdots & {\tilde{a}}_{1n}\\ {\tilde{a}}_{21}& {\tilde{a}}_{22}& \cdots & {\tilde{a}}_{2n}\\ ⋮& ⋮& ⋮& ⋮\\ {\tilde{a}}_{m1}& {\tilde{a}}_{m2}& \cdots & {\tilde{a}}_{mn}\end{array}\right]$$

(17)

where ${\tilde{a}}_{ij}$ denotes the TIF decision information of alternative $i$ on indicator $j$.

Step 2. Normalize the TIF decision matrix

To eliminate the impact of differences in indicator type and dimension, the initial decision information should be normalized. The normalization formula for benefit indicators is Equation (18), and the normalization formula for cost indicators is Equation (19).

$${\tilde{r}}_{ij}=((\frac{{\underset{\_}{a}}_{ij}-\underset{j}{\min }{\underset{\_}{a}}_{ij}}{\underset{j}{\max }{\overline{a}}_{ij}-\underset{j}{\min }{\underset{\_}{a}}_{ij}},\frac{a_{ij}-\underset{j}{\min }{\underset{\_}{a}}_{ij}}{\underset{j}{\max }{\overline{a}}_{ij}-\underset{j}{\min }{\underset{\_}{a}}_{ij}},\frac{{\overline{a}}_{ij}-\underset{j}{\min }{\underset{\_}{a}}_{ij}}{\underset{j}{\max }{\overline{a}}_{ij}-\underset{j}{\min }{\underset{\_}{a}}_{ij}});u_{{\tilde{a}}_{ij}},v_{\tilde{a}}{}_{{}_{ij}})$$

(18)

$${\tilde{r}}_{ij}=((\frac{\underset{j}{\max }{\overline{a}}_{ij}-{\overline{a}}_{ij}}{\underset{j}{\max }{\overline{a}}_{ij}-\underset{j}{\min }{\underset{\_}{a}}_{ij}},\frac{\underset{j}{\max }{\overline{a}}_{ij}-a_{ij}}{\underset{j}{\max }{\overline{a}}_{ij}-\underset{j}{\min }{\underset{\_}{a}}_{ij}},\frac{\underset{j}{\max }{\overline{a}}_{ij}-{\underset{\_}{a}}_{ij}}{\underset{j}{\max }{\overline{a}}_{ij}-\underset{j}{\min }{\underset{\_}{a}}_{ij}});u_{{\tilde{a}}_{ij}},v_{\tilde{a}}{}_{{}_{ij}})$$

(19)

Phase IV. Rank the HBMMSs

Step 1. Aggregate decision-making information

To obtain the performance of alternatives on the five criteria and the overall, the TIF decision-making information is aggregated through Equation (8).

Step 2. Obtain the positive/negative ideal solutions

$${\tilde{r}}_j{}^{+}=((\underset{i}{\max }{\underset{\_}{r}}_{ij},\underset{i}{\max }{r}_{ij},\underset{i}{\max }{\overline{r}}_{ij});\underset{i}{\max }{u}_{{\tilde{r}}_{ij}},\underset{i}{\min }{v}_{{\tilde{r}}_{ij}})$$

(20)

$${\tilde{r}}_j{}^{-}=((\underset{i}{\min }{\underset{\_}{r}}_{ij},\underset{i}{\min }{r}_{ij},\underset{i}{\min }{\overline{r}}_{ij});\underset{i}{\min }{u}_{{\tilde{r}}_{ij}},\underset{i}{\max }{v}_{{\tilde{r}}_{ij}})$$

(21)

where ${\tilde{r}}_j{}^{+}$ is the positive ideal solution under criterion $j$, and ${\tilde{r}}_j{}^{-}$ is the negative ideal solution under criterion $j$.

Step 3. Obtain the hamming distances between alternatives and the positive/negative ideal solutions

The hamming distances between the alternative $i$ and the positive/negative ideal solutions are obtained using Equation (5) and denoted as $d_i{}^{+}$ and $d_i{}^{-}$, respectively.

Step 4. Obtain the rankings of HBMMSs

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

(22)

Step 5. Select an optimal HBMMS

The larger $d_i$ is, the better the HBMMS.

5. Case Study

5.1. Case Background

A large integrated investment group is ready to develop hydrogen energy. After multi-round preliminary research and argumentation, the group makes a final decision to develop HBMMSs. Then, an expert evaluation committee is formed according to the practical requirements of decision-making. It includes ten leading experts in hydrogen energy industry investment, hydrogen technology, hydrogen economy, etc. Through field research and discussions with the government, four HBMMSs labeled A1, A2, A3, and A4 are selected by an expert evaluation committee.

5.2. Sustainability Evaluation of HBMMSs Using the Proposed Method

A TIFN-based initial direct-relation matrix is constructed by the expert evaluation committee, as shown in

Table 2. The TIFN-based initial direct-relation matrix.

Criteria	C1	C2	C3	C4	C5
C1	((0, 0, 0); 1, 0)	((0.6, 0.8, 0.9); 0.7, 02)	((0.4, 0.6, 0.8); 0.6, 0.2)	((0.7, 0.8, 01); 0.8, 0.1)	((0.5, 0.6, 0.7); 0.7, 0.2)
C2	((0.2, 0.3, 0.5); 0.7, 0.3)	((0, 0, 0); 1, 0)	((0.1, 0.2, 0.3); 0.5, 0.3)	((0.3, 0.4, 0.5); 0.6, 0.2)	((0.1, 0.2, 0.4); 0.7, 0.1)
C3	((0.1, 0.2, 0.3); 0.6, 0.2)	((0.2, 0.3, 0.5); 0.9, 0.1)	((0, 0, 0); 1, 0)	((0.1, 0.2, 0.3); 0.8, 0.1)	((0.2, 0.3, 0.5); 0.8, 0.2)
C4	((0.6, 0.7, 0.9); 0.8, 0.2)	((0.6, 0.8, 0.9); 0.9, 0.1)	((0.5, 0.7, 0.9); 0.7, 0.2)	((0, 0, 0); 1, 0)	((0.4, 0.5, 0.7); 0.6, 0.4)
C5	((0.4, 0.5, 0.6); 0.7, 0.2)	((0.5, 0.6, 0.8); 0.7, 0.2)	((0.3, 0.5, 0.6); 0.6, 0.4)	((0.6, 0.7, 0.8); 0.8, 0.2)	((0, 0, 0); 1, 0)

. Then, the TIFN-based initial direct-relation matrix is converted into the crisp number-based initial direct-relation matrix and normalized, as shown in

Table 3. The normalized direct-relation matrix.

Criteria	C1	C2	C3	C4	C5
C1	0	0.245	0.152	0.366	0.190
C2	0.082	0	0.025	0.101	0.085
C3	0.051	0.165	0	0.089	0.123
C4	0.275	0.392	0.222	0	0.066
C5	0.158	0.198	0.060	0.266	0

.

According to Table 3 and Equation (12), the total relation matrix is obtained, as shown in

Table 4. The total relation matrix.

Criteria	C1	C2	C3	C4	C5
C1	0.347	0.762	0.408	0.717	0.419
C2	0.203	0.205	0.128	0.254	0.174
C3	0.198	0.382	0.113	0.269	0.225
C4	0.521	0.807	0.427	0.393	0.313
C5	0.404	0.596	0.270	0.550	0.198

. Following this, $R_j$,$D_j$,$P_j$, and $Q_j$ are calculated using Equations (13)–(16), as shown in Figure 3.

In Figure 3, it can be concluded that the five criteria can be divided into a cause group and an effect group. The economic criterion (C1), technical criterion (C4), and coordination criterion (C5) belong to the cause group and easily influence the other factors because $Q_j$ is positive. Furthermore, the social criterion (C2) and environmental criterion (C3) belong to the effect group and are easily affected by the others because $Q_j$ is negative.

The fuzzy densities of criteria and sub-criteria are displayed in Figure 4 and Figure 5.

In Figure 4, it can be concluded that the fuzzy density of the technical criterion (C4) is the largest, which indicates that the technical criterion (C4) is the most important criterion. The economic criterion (C1) is then the second-most-important criterion. The social criterion (C2) and coordination criterion (C5) are equally important as they have the same fuzzy densities. The environmental criterion (C3) is the least important criterion as it has the smallest fuzzy density.

In Figure 5, the fuzzy densities of operation revenues (C15) and technical reliability (C43) rank first and second. So, these are the two most important sub-criteria. In terms of social aspects, public acceptance (C23) is less important than job creation (C21) and promotion for the development of related industries (C22). Then, concerning environmental aspects, carbon emission reduction (C32) is more important than the other three. In terms of coordination aspects, coordination with local power grid (C51) is the most important factor.

The performances of four alternatives with respect to sub-criteria are yielded by the expert evaluation committee, and the TIF decision matrix is shown in

Table 5. The TIF decision matrix.

	A1	A2	A3	A4
C11	((5.6, 6, 7.5); 0.7, 0.1)	((6.4, 7.5, 8.2); 0.8, 0.1)	((8, 8.6, 9.4); 0.6, 0.2)	((5.5, 6.5, 7.4); 0.8, 0.1)
C12	((5.2, 6.2, 7.6); 0.6, 0.3)	((6.1, 7.3, 8.4); 0.6, 0.4)	((5.6, 7.6, 8.5); 0.7, 0.2)	((6.5, 7.6, 8.4); 0.5, 0.3)
C13	((5.6, 7.5, 8.3); 0.5, 0.4)	((5.8, 6.8, 8.6); 0.5, 0.4)	((6.8, 7.5, 8.5); 0.8, 0.1)	((6.8, 7.5, 8.6); 0.6, 0.3)
C14	((5.4, 6.7, 7.8); 0.8, 0.1)	((6, 7.8, 8.8); 0.7, 0.2)	((8, 8.5, 9.2); 0.7, 0.1)	((7.2, 8.3, 9.4); 0.7, 0.2)
C15	((6.5, 7.2, 8.5); 0.6, 0.3)	((7, 8.2, 9); 0.7, 0.1)	((8.2, 8.8, 9.6); 0.6, 0.3)	((6.3, 7.7, 8.6); 0.6, 0.3)
C16	((7.3, 8.5, 9.6); 0.7, 0.2)	((7.5, 8.4, 8.9); 0.8, 0.1)	((7.5, 8.5, 9.3); 0.8, 0.2)	((7.2, 8.6, 9.3); 0.8, 0.1)
C21	((6.8, 7.5, 8.6); 0.6, 0.2)	((6.5, 7.6, 8.5); 0.6, 0.3)	((6.8, 7.2, 8.8); 0.7, 0.2)	((7.3, 8.5, 9.6); 0.7, 0.1)
C22	((7.2, 8.2, 9.5); 0.8, 0.1)	((6.7, 7.8, 9.2); 0.7, 0.2)	((6.8, 8.2, 9); 0.8, 0.1)	((6.8, 7.4, 9.2); 0.7, 0.2)
C23	((6.9, 8.3, 8.8); 0.8, 0.2)	((6.6, 7.5, 8.5); 0.8, 0.1)	((7.1, 8.5, 9.2); 0.7, 0.3)	((6.7, 7.6, 8.5); 0.5, 0.4)
C31	((5.8, 6.6, 7.8); 0.6, 0.3)	((6.3, 7.5, 8.8); 0.8, 0.2)	((7.2, 8.3, 9.2); 0.6, 0.2)	((7, 8.2, 9.1); 0.6, 0.3)
C32	((6, 7.3, 8.4); 0.7, 0.1)	((6.1, 7.8, 9.2); 0.8, 0.1)	((6.5, 7.5, 8.6); 0.8, 0.1)	((6.5, 7.3, 8.5); 0.6, 0.2)
C33	((5.6, 7.5, 8.5); 0.6, 0.2)	((6.2, 7.5, 8.9); 0.6, 0.3)	((7, 8.2, 9.1); 0.8, 0.2)	((7.5, 8, 9.2); 0.7, 0.2)
C34	((5.3, 6.6, 7.6); 0.8, 0.1)	((7.3, 8.5, 9.4); 0.6, 0.2)	((7, 7.6, 8.5); 0.6, 0.4)	((7.6, 8.6, 9.3); 0.8, 0.1)
C41	((6.8, 7.8, 8.9); 0.7, 0.3)	((6.8, 7.6, 9.1); 0.7, 0.3)	((6.8, 7.5, 8.4); 0.5, 0.4)	((7.1, 7.7, 8.6); 0.8, 0.1)
C42	((7.3, 8.6, 9.5); 0.7, 0.1)	((7.7, 8.6, 9.6); 0.8, 0.1)	((7.3, 8.5, 9.2); 0.6, 0.3)	((7.5, 8.4, 9.4); 0.5, 0.4)
C43	((7.9, 8.8, 9.4); 0.8, 0.1)	((7.5, 8.6, 9.5); 0.7, 0.1)	((6.5, 8, 9.2); 0.7, 0.2)	((7.6, 8.2, 9); 0.7, 0.1)
C51	((8.2, 9, 9.6); 0.7, 0.2)	((7.6, 8.6, 9.3); 0.8, 0.1)	((6.6, 7.5, 8.5); 0.6, 0.3)	((8, 8.6, 9.3); 0.7, 0.2)
C52	((8.5, 9.2, 9.8); 0.6, 0.3)	((8.3, 8.8, 9.6); 0.7, 0.2)	((6.7, 7.8, 8.6); 0.8, 0.1)	((7.8, 8.4, 9.6); 0.8, 0.1)
C53	((7.8, 8.6, 9.5); 0.5, 0.4)	((8.1, 8.9, 9.5); 0.6, 0.3)	((7, 8.2, 9); 0.7, 0.2)	((8.2, 8.8, 9.6); 0.8, 0.1)

.

The TIF decision matrix is normalized using Equations (18) and (19). Then, the decision-making information is obtained using Equation (8), as shown in

Table 6. Decision-making information on criteria and overall.

	A1	A2	A3	A4
C1	((0.271, 0.649, 0.879); 0.5, 0.4)	((0.251, 0.528, 0.791); 0.5, 0.4)	((0.489, 0.684, 0.9); 0.6, 0.3)	((0.049, 0.502, 0.78); 0.5, 0.3)
C2	((0.15, 0.529, 0.911); 0.6, 0.2)	((0, 0.363, 0.772); 0.6, 0.3)	((0.083, 0.532, 0.851); 0.7, 0.3)	((0.17, 0.519, 0.918); 0.5, 0.4)
C3	((0.121, 0.431, 0.803); 0.6, 0.3)	((0.066, 0.475, 0.862); 0.6, 0.3)	((0.214, 0.504, 0.793); 0.6, 0.4)	((0.168, 0.45, 0.731); 0.6, 0.3)
C4	((0.327, 0.694, 0.96); 0.7, 0.3)	((0.27, 0.64, 1); 0.7, 0.3)	((0, 0.487, 0.866); 0.5, 0.4)	((0.177, 0.498, 0.876); 0.5, 0.4)
C5	((0.49, 0.759, 0.991); 0.5, 0.4)	((0.385, 0.683, 0.92); 0.6, 0.3)	((0, 0.38, 0.681); 0.6, 0.3)	((0.446, 0.652, 0.929); 0.7, 0.2)
Overall	((0.289, 0.643, 0.931); 0.5, 0.4)	((0.239, 0.588, 0.923); 0.5, 0.4)	((0.229, 0.56, 0.842); 0.5, 0.4)	((0.223, 0.541, 0.851); 0.5, 0.4)

. For example, the fuzzy densities of C51, C52, and C53 are $\phi (c51)=0.6$, $\phi (\mathrm{C}52)=0.3$, and $\phi (\mathrm{C}53)=0.5$, respectively. As a result, $\lambda =-0.706$. The normalized TIF decision-making information of alternative A3 with respect to C51, C52, and C53 is ((0, 0.3, 0.633); 0.6, 0.3), ((0, 0.355, 0.613); 0.8, 0.1), and ((0, 0.462, 0.769); 0.7, 0.2), respectively. Since $S(\mathrm{C}51)<S(\mathrm{C}53)<S(\mathrm{C}52)$, the descending order is $\mathrm{C}51<\mathrm{C}53<\mathrm{C}52$. Then, the decision-making information of alternative A3 on criterion C5 is obtained, which is ((0, 0.38, 0.681); 0.6, 0.3).

Following this, $d_i{}^{+}$, $d_i{}^{-}$, and $d_i$ are calculated according to Equations (20)–(22), and rankings of alternatives on criteria and overall are obtained, as shown in

Table 7. The ranking of alternatives on criteria and overall.

Categories	Ranking
C1	$\mathrm{A}3>\mathrm{A}1>\mathrm{A}2>\mathrm{A}4$
C2	$\mathrm{A}1>\mathrm{A}3>\mathrm{A}4>\mathrm{A}2$
C3	$\mathrm{A}2>\mathrm{A}1>\mathrm{A}4>\mathrm{A}3$
C4	$\mathrm{A}1>\mathrm{A}2>\mathrm{A}4>\mathrm{A}3$
C5	$\mathrm{A}4>\mathrm{A}2>\mathrm{A}1>\mathrm{A}3$
Overall	$\mathrm{A}1>\mathrm{A}2>\mathrm{A}3>\mathrm{A}4$

.

In Table 7, A1 performs the best in terms of the social criterion (C2) and technical criterion (C4) and has the best overall performance; its ranking in the coordination criterion (C5) is worse than its rankings in the other criteria. Therefore, the performance of A1 with respect to coordination should be the subject of attention. The other three alternatives perform well in one aspect, but they perform poorly in the other aspects. Consequently, we can surmise that the proposed triangular intuitionistic fuzzy framework is feasible to evaluate the sustainability of HBMSSs, and A1 is the best HBMMS, which should be selected.

6. Discussion

6.1. Sensitivity Analysis

Sensitivity analysis is performed by exchanging fuzzy densities to test the robustness of the proposed method, and the results are displayed in

Table 8. Results of sensitivity analysis.

Tests	Fuzzy Densities	Rankings
1	$\phi (C1)=0.3$, $\phi (C2)=0.4$, $\phi (C3)=0.2$, $\phi (C4)=0.5$, $\phi (C5)=0.3$	$\mathrm{A}1>\mathrm{A}2>\mathrm{A}4>\mathrm{A}3$
2	$\phi (C1)=0.2$, $\phi (C2)=0.3$, $\phi (C3)=0.4$, $\phi (C4)=0.5$, $\phi (C5)=0.3$	$\mathrm{A}1>\mathrm{A}2>\mathrm{A}4>\mathrm{A}3$
3	$\phi (C1)=0.5$, $\phi (C2)=0.3$, $\phi (C3)=0.2$, $\phi (C4)=0.4$, $\phi (C5)=0.3$	$\mathrm{A}1>\mathrm{A}2>\mathrm{A}3>\mathrm{A}4$
4	$\phi (C1)=0.3$, $\phi (C2)=0.3$, $\phi (C3)=0.2$, $\phi (C4)=0.5$, $\phi (C5)=0.4$	$\mathrm{A}1>\mathrm{A}2>\mathrm{A}4>\mathrm{A}3$
5	$\phi (C1)=0.4$, $\phi (C2)=0.2$, $\phi (C3)=0.3$, $\phi (C4)=0.5$, $\phi (C5)=0.3$	$\mathrm{A}1>\mathrm{A}2>\mathrm{A}3>\mathrm{A}4$
6	$\phi (C1)=0.4$, $\phi (C2)=0.5$, $\phi (C3)=0.2$, $\phi (C4)=0.3$, $\phi (C5)=0.3$	$\mathrm{A}1>\mathrm{A}3>\mathrm{A}2>\mathrm{A}4$
7	$\phi (C1)=0.4$, $\phi (C2)=0.3$, $\phi (C3)=0.5$, $\phi (C4)=0.2$, $\phi (C5)=0.3$	$\mathrm{A}1>\mathrm{A}3>\mathrm{A}2>\mathrm{A}4$
8	$\phi (C1)=0.4$, $\phi (C2)=0.3$, $\phi (C3)=0.3$, $\phi (C4)=0.5$, $\phi (C5)=0.2$	$\mathrm{A}1>\mathrm{A}2>\mathrm{A}3>\mathrm{A}4$
9	$\phi (C1)=0.4$, $\phi (C2)=0.3$, $\phi (C3)=0.2$, $\phi (C4)=0.3$, $\phi (C5)=0.5$	$\mathrm{A}1>\mathrm{A}2>\mathrm{A}4>\mathrm{A}3$

.

In Table 8, A3 ranks last in tests 1, 2, 4, and 9, and A4 ranks last in tests 3 and 5–8. A2 ranks third in tests 6–7 and ranks second in the other tests. A1 is still the optimal HBMMS in the above tests. In other words, the performance of A1 is stable. This reveals that the sustainability evaluation results of HBMMSs obtained by using the proposed method are robust.

6.2. Scenario Analysis

To highlight the significance of the established sustainability evaluation criteria system, several different scenarios are set. One criterion is not considered in scenarios 1–5, while two criteria are not considered in scenarios 6 and 7. The results of the scenario analysis are shown in

Table 9. The results of scenario analysis.

	C1	C2	C3	C4	C5	Rankings
Scenario 0	√	√	√	√	√	$\mathrm{A}1>\mathrm{A}2>\mathrm{A}3>\mathrm{A}4$
Scenario 1		√	√	√	√	$\mathrm{A}2>\mathrm{A}1>\mathrm{A}4>\mathrm{A}3$
Scenario 2	√		√	√	√	$\mathrm{A}1>\mathrm{A}2>\mathrm{A}4>\mathrm{A}3$
Scenario 3	√	√		√	√	$\mathrm{A}1>\mathrm{A}2>\mathrm{A}4>\mathrm{A}3$
Scenario 4	√	√	√		√	$\mathrm{A}3>\mathrm{A}1>\mathrm{A}4>\mathrm{A}2$
Scenario 5	√	√	√	√		$\mathrm{A}1>\mathrm{A}3>\mathrm{A}2>\mathrm{A}4$
Scenario 6	√	√	√			$\mathrm{A}3>\mathrm{A}1>\mathrm{A}4>\mathrm{A}2$
Scenario 7	√			√	√	$\mathrm{A}1>\mathrm{A}2>\mathrm{A}4>\mathrm{A}3$

.

In Table 9, scenario 0 is the original scenario with a complete evaluation criteria system. A2 is the best under scenario 1, while A3 is the best under scenarios 4 and 6. Compared with scenario 0 and scenario 1, this suggests that the economic criterion (C1) is a critical factor. When observing scenarios 4–6, it can be seen that the technical criterion (C4) and coordination criterion (C5) have a large impact on the overall ranking. Under scenarios 2, 3, 5, and 7, A1 has the best overall performance. When comparing scenarios 2, 3, and 7 with scenario 0, it can be seen that the social criterion (C2) and environmental criterion (C3) influence the rankings of A3 and A4. Therefore, the established sustainability evaluation criteria system can comprehensively reflect HBMMSs’ sustainability, thus fulfilling a current need to ensure HBMMSs’ sustainability evaluation.

6.3. Comparative Analysis

The TIF-WA operator [36] and TIFN-WAA operator [45] are used for a comparison with the proposed method. The fuzzy densities of criteria and sub-criteria are normalized and used in the TIF-WA and TIFN-WAA operator environments, and the results of the comparative analysis are shown in

Table 10. Results of comparative analysis.

	Proposed Method	TIF-WA Operator	TIFN-WAA Operator
Rankings	$\mathrm{A}1>\mathrm{A}2>\mathrm{A}3>\mathrm{A}4$	$\mathrm{A}1>\mathrm{A}2>\mathrm{A}4>\mathrm{A}3$	$\mathrm{A}1>\mathrm{A}2>\mathrm{A}4>\mathrm{A}3$

.

In Table 10, it can be seen that A4 is the worst in the proposed method and A3 ranks last in the other two cases. This shows that when the correlations between the criteria and sub-criteria are considered in the proposed method, the rankings of alternatives change. Moreover, A1 ranks first and A2 ranks second in the above three cases. This indicates that the proposed method is accurate and the sustainability evaluation results of HBMMSs are believable.

7. Conclusions

To measure the comprehensive benefits of HBMMSs from the perspective of sustainability, the paper presented a comprehensive evaluation of the sustainable development of HBMMSs. The main conclusions are summarized as follows:

• To assess the HBMMSs’ sustainability, a comprehensive evaluation criteria system was established from the economic, social, environmental, technical, and coordination aspects, which includes five cost sub-criteria and fourteen benefit sub-criteria.
• An integrated fuzzy MADM method combining TIFNs, λ-fuzzy measure, Cl, and DEMATEL was proposed to rank the alternatives and select the best one, which simultaneously considers the uncertainty of decision information and correlation of indicators.
• Through a cause-and-effect relationship analysis and determination of fuzzy densities, economic, technical, and coordination criteria were determined to be cause factors, and social and environmental criteria were found to belong to the effect group. Technical and economic criteria were the two most important, rank first and second, respectively.
• Sensitivity analysis and comparative analysis were performed to validate the robustness and accuracy of the proposed method and highlight its advantages. Moreover, scenario analysis revealed the need for an established sustainability evaluation criteria system.

The paper has made contributions to the sustainability evaluation of HBMMSs, but there are still some limitations. Future research work should be carried out in these directions: (i) from the perspective of strategic development, portfolio selection is needed in this field; (ii) from the perspective of methodology, future work must consider the psychological behavior and risk preference of MDs by introducing cumulative prospect theory and other MADM methods.