Investment risk evaluation for new energy resources: An integrated decision support model based on regret theory and ELECTRE III

Energy Conversion and Management 183 (2019) 332–348

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Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman

Investment risk evaluation for new energy resources: An integrated decision support model based on regret theory and ELECTRE III Hong-gang Peng, Kai-wen Shen, Sang-sang He, Hong-yu Zhang, Jian-qiang Wang

T

⁎

School of Business, Central South University, Changsha 410083, PR China

A R T I C LE I N FO

A B S T R A C T

Keywords: Multi-criteria decision-making Z-numbers Regret theory ELECTRE III New energy investment

As conventional energy resources are limited and polluting, new energy resources, being renewable and environmentally friendly, have been receiving increasing attention in recent years. However, no study on new energy investment, which acts a significant role in promoting the development and use of new energy resources, has been conducted. To cover this gap, an applicable decision support model is established by integrating Znumbers, regret theory and elimination and choice translating reality III (ELECTRE III) to address new energy investment risk evaluation problems. In this way, Z-numbers are used to describe the decision-making information involved in the problems, a suggested method is combined with regret theory to determine the utility, rejoice and regret values of Z-information, and ELECTRE III is introduced to handle multiple criteria evaluation comprehensively. To elucidate and validate the application of the established model, a case study for new energy investment in Qingshuitang Industrial Zone is conducted and in-depth results analysis and discussion are implemented. The study shows that solar energy is the best investment project and environment is the most important investment factor. Moreover, the results demonstrate that the established model can effectively support new energy investment decision-making and it performs better than other existing methods.

1. Introduction China has become the second largest economy in the world in the over 30 years of rapid development following the reform and opening up. However, the extensive development mode in the past has led to a series of energy and environment problems that have seriously restricted the sustainable development of China’s economy and society [1]. Faced with the grim situation of tight resource constraint, serious environment pollution and degraded ecosystem in the development process, the 19th National Congress emphasised the importance of energy reform. China has a shortage of resources and limited traditional energy reserves, and the use of traditional energy pollutes the environment [2]. In response to the severe energy situation, it is urgent to establish a sustainable energy development strategy and to effectively develop and utilise new energy resources [3]. China possesses abundant new energy resources, and their development prospects are considerably broad. Contrary to traditional energy sources, new energy has the advantages of large reserves, no pollution, sustainability and great potential for development [4]. New energy resource can effectively solve the endless demand for energy and plays a pivotal role in sustainable development. In recent years, an increasing number of studies on new energy ⁎

Corresponding author. E-mail address: [email protected] (J.-q. Wang).

https://doi.org/10.1016/j.enconman.2019.01.015 Received 19 November 2018; Accepted 9 January 2019 0196-8904/ © 2019 Elsevier Ltd. All rights reserved.

industry have been conducted. Many scholars investigated the status quo, challenges and trend of China’s new energy industry. Wang et al. [5] discussed the factors underlying the export fluctuation of China’s new energy industry and presented various suggestions for the development of new energy. Zeng et al. [6] examined the sample data of new energy firms in China and assessed the investment efficiency of new energy industry. Xu and Lin [7] established a regress model to evaluate China’s new energy industry and recommended distinct policies for different development stages. Moreover, new energy vehicle, as a significant strategy for solving energy and environment problems, has received much attention [8]. Ren [9] investigated the success factors of sustainable development of new energy vehicles and proposed strategic implications for authority. Martinez et al. [10] surveyed the interactions of plug-in hybrid electric vehicle energy management strategies using intelligent transportation systems. Liu et al. [11] formulated a predictive energy management strategy for a parallel hybrid electric vehicle in light of reinforcement learning and velocity prediction. In addition, many studies focused on new energy systems and technologies. Lin et al. [12] investigated the risk elements of new energy power systems and discussed their internal interrelationships. Aklin et al. [13] examined the cost, access inequality and individuals’ acceptance of new energy technology in developing countries. Neij et al. [14] discussed

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selection problem under incomplete information. However, regret theory under Z-number environments has not been studied. Over the years, various MCDM approaches have been proposed to address real-world problems. In general, MCDM approaches can be categorised as aggregation operator-based methods [28], measurebased methods [29] and outranking methods [30]. Compared with aggregation operator-based and measure-based methods, outranking methods have prominent advantages in reflecting DMs’ willingness and identifying the non-compensation among criteria. Elimination and choice translating reality (ELECTRE) methods are representative of the outranking methods, and ELECTRE III is particularly the most popular among the family of ELECTRE [31]. ELECTRE III permits intransitivity and comparability of preferences, and its main advantage is its capability of dealing with imperfect information grounded in real-world problems [32]. Recently, the application of ELECTRE III in the energy industry elicited extensive attention. Wu et al. [33] proposed an intuitionistic fuzzy ELECTRE III method to address the site selection problem of offshore wind power stations. Neves et al. [34] used ELECTRE III to identify the best energy actions for sustainable development and formulated a municipal sustainable energy strategy. Martínez-García et al. [35] incorporated semantic criteria into ELECTRE III to assess energy generation technologies. However, no study has applied ELECTRE III to manage new energy investment problems. According to the preceding reviews, the motivations for subsequent work are summarised as follows. Firstly, to promote the development and use of new energy resources, new energy investment risk evaluation problems are investigated. Secondly, Z-numbers are introduced to reliably describe the decision-making information in the problems. Thirdly, regret theory is used to reflect the psychological behaviour of DMs in the decision-making process. Fourthly, ELECTRE III is used to identify the comprehensive criteria evaluation and risk classification in the problems. With the aforementioned motivations, an applicable decision support model is established by the integration of Z-numbers, regret theory and ELECTRE III to address new energy investment risk evaluation problems, focusing on the following significant gaps:

the local learning need in the deployment of new energy technologies and concluded policy implications. Existing research shows that new energy is a hot topic that has been extensively investigated in diverse fields. However, no study related to new energy investment is currently available. New energy investment plays an important role in promoting the development and use of new energy resources. Nevertheless, the investment process involves various risk uncertainties with complex factors, and it is difficult to make effective investment decisions without scientific tools. In essence, the risk evaluation of new energy investment is affected by multiple factors (criteria) and is a complicated decision activity under uncertain circumstances, and it is therefore identified as a multi-criteria decisionmaking (MCDM) problem. To reliably represent decision-making information under uncertain circumstances, Zadeh [15] proposed the fuzzy theoretic concept of Znumbers. A Z-number is an ordered pair of fuzzy numbers with a straightforward structure of fuzzy restriction and reliability and is typically described in natural languages. For example, an expert states that ‘it is certain that the social acceptability of solar energy is very good in Zhuzhou’. Then, the evaluation of ‘solar energy’ regarding the criterion ‘social acceptability’ can be expressed as a Z-number (very good, certain). The main advantages of Z-number are its consistency with people’s expression habits and its capability of comprehensively reflecting the reliability and uncertainties of information [16]. Although Z-number is effective for describing decision-making information, the processing of Z-information is difficult and complex because Z-number has a two-dimensional structure with fuzzy and probabilistic uncertainties [17]. Given this, many studies related to Zinformation processing have been conducted, among which direct processing [18] and transformation processing [19] are the primary methods. The direct processing method is complicated because there are many programming problems, convolution computations, fuzzy arithmetic and probabilistic arithmetic. Therefore, the application of this method to solve practical problems is difficult. The transformation processing method has low computation complexity. However, this method simply converts a Z-number into a fuzzy number. This strategy inevitably loses and distorts Z-information because Z-number is a bimodal distribution with fuzzy and probabilistic uncertainties. To balance computation complexity and accuracy, Peng and Wang [20] introduced cloud model to deal with Z-information. This method can simply and effectively address the bimodal distribution and uncertainties of Z-numbers and it has been successfully applied to handle game problems [21]. In general, people behave in bounded rationality in real-world decision activities because of incomplete information, cognition limitation and time pressure [22]. In this case, deviations between practical and expected decision results usually exist. Therefore, to appropriately solve decision-making problems, many methods have been developed in light of bounded rationality hypothesis. Regret theory [23] is a kind of behavioural decision theory and is also one of the most popular bounded rationality models. The primary characteristic of regret theory is that it compares the result of a given alternative with that of an optional alternative to measure the rejoice and regret levels of decision-makers (DMs) and to select the best alternative that DMs will not regret. In recent years, many scholars have introduced regret theory into fuzzy and uncertain decision-making environments. Zhang et al. [24] defined fuzzy regret/rejoice function, perceived utility formula and group consistency index based on regret theory and proposed a multi-criteria group decision-making (MCGDM) method based on multidimensional preference information. Peng and Yang [25] combined interval-valued fuzzy number with regret theory to propose a MCDM method. Ji et al. [26] defined the power, regret/rejoice and perceived utility functions of probability multivalued neutrosophic linguistic numbers and proposed a regret theory-based performance evaluation model. Chen et al. [27] proposed a bounded rationality model by combining triangular fuzzy axiomatic design and extended regret theory to solve a logistic provider

(1) The risk evaluation of new energy investment can be implemented in accordance with the comprehensive effects of economy, environment, society and technology, which are generally depicted in natural languages and are incomplete and partially reliable. In this case, the evaluation information needs to be described with the help of comprehensive qualitative tools. Z-numbers work towards incorporating subjective and objective information involved in natural language expressions into strengthening decision-making information understanding, and devote to exploring the reliability of information to support human decision activities. Therefore, Znumbers are introduced to describe the evaluation information of new energy investment whilst measuring information reliability. (2) The Z-number has a complicated two-dimensional structure and is difficult to defuzzify into real values for subsequent computations. Moreover, experts or DMs express their opinions to provide evaluation information in a bounded rationality way under practical decision environments because of various uncertain factors. Given this, the suggested method in [20] is incorporated into regret theory to effectively deal with the Z-information involved in new energy investment risk evaluation problems. This strategy can not only handle the fuzzy and probabilistic uncertainties in Z-numbers appropriately, but also identify the utility, rejoice and regret values of Z-information precisely by considering the psychological behaviour of DMs. (3) In new energy investment risk evaluation problems, the performances of decision alternatives are affected by diverse factors (criteria). Meanwhile, the evaluations under different criteria cannot compensate each other in the integration process. To handle the comprehensive criteria evaluations and conduct the new energy investment risk classification, ELECTRE III is utilised to construct 333

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In essence, the Z-number is a bimodal distribution: possibility and probability distributions. Peng and Wang [20] discussed the existence of a similar theoretical basis between cloud model and Z-number, and then used cloud model to determine the bimodal distribution in Znumbers as follows. For a Z-valuation (X , A, B ) , the possibility distribution of X can be presented using a normal membership function as

fuzzy outranking relations between alternatives and characteristic actions. In this way, the non-compensation principle among criteria is considered fully by modelling pseudo-criteria based on the indifference, preference and veto thresholds, and the interaction with DMs is implemented in the decision process. 2. Materials and methods In this section, the materials and methods necessary to establish the subsequent model are introduced. Firstly, the energy evaluation criteria are reviewed from the literature. Secondly, the method for Z-information processing is provided. Thirdly, a Z-number-based regret theory method is presented. Furthermore, an outranking assignment method is formulated.

R (X ): X = A → Poss (X = x ) = uA (x ) = e

−

(x − μ)2 2σ 2

,

where uA (x ) is the membership function of A . The probability distribution of X can be presented using a normal probability density function as

R (X ): X

pX → Prob (x ⩽ X ⩽ x + dx ) = pX (x ) dx ,

isp

2.1. Energy evaluation criteria hierarchy where pX (x ) =

1 (δ′)

e 2π

−

(x − ε )2 2(δ′)2

2

In this section, related studies are reviewed to construct the energy evaluation criteria hierarchy. In real-world decision-making environments, new energy investment risk evaluation is affected by many factors (criteria). These criteria can reflect the different aspects of new energy investment risk, and the identification of a general evaluation criteria hierarchy is crucial. In recent years, numerous studies were implemented to investigate energy evaluation criteria. Some related studies are briefly reviewed as follows. Liu [36] investigated the sustainability evaluation criteria of renewable energy from three aspects, namely, environment, economy and society, and presented a sustainability indicator framework for renewable energy system. Kabak and Dağdeviren [37] presented different types of criteria to analyse the energy status in Turkey and proposed a hybrid MCDM method to prioritise renewable energy sources. Arce et al. [38] grouped the criteria involved in energy field into four categories (technology, environment, economy and society) according to previous studies and discussed the weighting methods of energy criteria. Çelikbilek and Tüysüz [39] determined eleven evaluation criteria for renewable energy sources in light of the literature and developed a comprehensive energy evaluation MCDM method by integrating decision making trial and evaluation laboratory (DEMATEL), analytic network process (ANP) and visekriterijumska optimizacija i kompromisno resenje (VIKOR). Kumar et al. [40] reviewed different MCDM methods and the corresponding criteria applied in the development of sustainable renewable energy. Büyüközkan and Karabulut [41] comprehensively summarised the economic, societal and environmental factors on energy evaluation and combined analytic hierarchy process (AHP) with VIKOR to propose an energy project assessment approach. Lin et al. [12] designed a risk identification model for new energy power system, in which many risk criteria are examined and analysed through DEMATEL. Çolak and Kaya [42] identified the renewable energy evaluation criteria based on the existing studies and proposed a fuzzy AHP method to determine the weights of the criteria. Based on the preceding reviews, the energy evaluation criteria hierarchy are constructed in Table 1.

is the probability density function of X ,

η2 ) .

Obviously, p (x ) is a changeable funcx ∼ N (ε , δ′ ) and δ′ ∼ N (δ , tion in terms of ε , δ and η . The numerical characters μ and σ in the membership function, and ε , δ and η in the probability density function can be determined according to the uncertainty transformation method in [20]. 2.3. Z-number-based regret theory method In this section, a Z-number-based regret theory method is proposed to determine the utility, rejoice and regret values of Z-information. In general, regret theory method comprises the utility function, utility value and regret-rejoice function. The key step of this method is to calculate the utility value by combining the utility function with the probability density function of variables. However, the probability density function is unknown in many problems, and many studies assumed that the variables follow a specific distribution (e.g., uniform distribution) so that the probability density function can be obtained. To overcome this limitation, a Z-number-based regret theory method is proposed to integrate the probability density function pX (x ) with the utility function to calculate the utility value. The procedures of this method are as follows. Firstly, the utility function with experts’ risk preference is described. Let x ∈ X be the uncertain variable of Z = (A, B ) , then the utility function u (x ) is given as

u (x ) =

1 − e−λx , (0 < λ < 1), λ

(1)

where λ is the risk aversion coefficient of experts. The risk aversion degree of experts is great when the value of λ is small. Secondly, the utility value of Z = (A, B ) is given as

u (Z ) =

μ σ

ε + max δ

∫ε−max δ

where pX (x ) =

u (x )

1 e (δ′) 2π

δ + max η

∫δ−max η

(x − ε )2 − 2(δ′)2

pX (x ) dδ′ dx ,

(2)

is the probability density function of X ,

2

x ∼ N (ε , δ′ ) and δ′ ∼ N (δ , η2) . Thirdly, the rejoice function R+ (Z ) of Z = (A, B ) is given as

2.2. Z-information processing method In this section, a suggested method for Z-information processing is provided. To ensure the reliability of decision information, Zadeh [15] introduced Z-numbers as a new information description tool. A Z-number can be denoted as Z = (A, B ) and is an ordered pair of fuzzy numbers. Z = (A, B ) is associated with a real-valued uncertain variable X , and Zvaluation is defined as (X , A, B ) , in which A is a fuzzy restriction on the values that X can take, and B is a measure of the reliability of A . Typically, the two components of Z-numbers are expressed in natural language, such as (very good, sure). Decision information that consists of Z-numbers is called Z-information.

R+ (Z ) = 1 − e−λΔu (Z ),

(3)

where Δu (Z ) = u (Z ) − u (Z −) , and Z − is the negative ideal solution (NIS) of a set of Z-numbers. Evidently, R+ (Z ) ⩾ 0 , and Z = (A, B ) is large when the value of R+ (Z ) is large. Fourthly, the regret function R− (Z ) of Z = (A, B ) is given as

R− (Z ) = 1 − e−λΔu (Z ),

(4)

where Δu (Z ) = u (Z ) − u (Z+) , and Z+ is the positive ideal solution (PIS) of a set of Z-numbers. Evidently, R− (Z ) ⩽ 0 , and Z = (A, B ) is small when the value of |R− (Z )| is large. 334

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Table 1 Summary of energy evaluation criteria. Criteria

Sub-criteria

Description

Literature

Economy (c1)

Value creation (c11 ) Payback (c12 ) Business continuity (c13 ) Return on investment (c14 ) Costs (c15 ) Job creation (c21) Social benefits (c22 ) Social acceptance (c23 ) Human/technology influence (c31) Pollutant emission (c32 ) Ecology influence (c33 ) Land requirement (c34 ) Energy efficiency (c41) Energy safety (c42 ) Innovation (c43 ) Maturity (c44 )

Create value to facilitate local and regional economic development Measure the time of initial investment is offset by cash flows Represent the investment for future business and risk Represent the internal rate of return earned by investment project Contain capital, operation and maintenance costs Represent the capacity of creating direct and indirect job for residents Represent the contribution for the advancement of local society Represent the attitudes of users on a specific energy resource Indicate the influence on environment by energy production and consumption Indicate the emissions of greenhouse gases (carbon dioxide, nitrogen oxides, sulphur dioxide) and waste Represent the direct and indirect influences on ecosystem Represent the use and destroy of land for energy generation Indicate the ratio between the useful output and the input of energy conversion machines Represent the safety for the workers and the local society Indicate competitive advantage through innovation Include technology properties, technology parameters and energy reliability

[41,42] [12,41,42] [36,41] [36,37] [36,38,40] [12,37,40] [36,41] [12,38,42] [40,41] [36,38] [36,41] [39,41] [12,39,41] [40,41] [38,39,42] [36,37]

Society (c2 )

Environment (c3 )

Technology (c4 )

In the new energy investment risk evaluation problem, suppose that ai (i = 1, 2, ...,n) be an alternative, cj (j = 1, 2, ...,m) be a criterion with weight wj , bk (k = 1, 2, ...,g ) be the characteristic action of risk category hk , and Zij = (Aij , Bij ) and Pkj = (Akj , Bkj ) be respectively the Z-number evaluations of ai and bk under cj . Then, the comprehensive concordance index CC (ai , bk ) of ai over bk is presented as

2.4. Outranking assignment method In this section, an outranking assignment method is proposed according to the rules of ELECTRE III. Firstly, the concordance and discordance indices for Z-numbers are given based on the preceding rejoice and regret functions. Subsequently, several outranking indices are provided to implement the comparisons between alternatives and characteristic actions. Finally, a sorting rule is formulated for alternative assignment. Let Z1 = (A1 , B1) and Z2 = (A2 , B2) be two Z-numbers, R+ (Zi ) and − R (Zi ) be respectively the rejoice and regret functions of Zi (i = 1, 2) , and qj , pj and vj be respectively the indifference, preference and veto thresholds with 0 ⩽ qj < pj < vj < 1. Then, the rejoice concordance index CO (Z1, Z2) of Z1 over Z2 is presented as

m

CC (ai , bk ) =

=

⎨ ⎪1, ⎩

pj − qj

where Cj (Zij, Pkj ) is the concordance index of ai over bk under cj . CC (ai , bk ) becomes the rejoice comprehensive concordance index CCO (ai , bk ) when Cj (Zij, Pkj ) is the rejoice concordance index COj (Zij, Pkj ) , whereas CC (ai , bk ) becomes the regret comprehensive concordance index CCG (ai , bk ) when Cj (Zij, Pkj ) is the regret concordance index CGj (Zij, Pkj ) . Let CC (ai , bk ) be the comprehensive concordance index, and Dj (Zij, Pkj ) be the discordance index of ai over bk under cj . Then, the credibility index R (ai , bk ) of ai over bk is presented as

if R+ (Z1) + pj ⩽ R+ (Z2), ,

if R+ (Z1) + qj < R+ (Z2) < R+ (Z1) + pj , if R+ (Z1) + qj ⩾ R+ (Z2).

(9)

j=1

CO (Z1, Z2) ⎧ 0, ⎪ R+ (Z1) − R+ (Z2) + pj

∑ wj Cj (Zij, Pkj),

R (ai , bk ) (5)

=

The regret concordance index CG (Z1, Z2) of Z1 over Z2 is presented as

⎧CC (ai , bk ), ⎨CC (ai , bk ) ∏j ∈ J ⎩

if ∀ j, Dj (Zij, Pkj ) ⩽ CC (ai , bk ); 1 − Dj (Zij, Pkj ) 1 − CC (ai, bk )

,

otherwise ; (10)

CG (Z1, Z2) ⎧ 0, ⎪ |R− (Z2)| − |R− (Z1)| + pj , ⎪ pj − qj = ⎨ ⎪ ⎪1, ⎩

where J = {j Dj (Zij, Pkj ) > CC (ai , bk )} . Similarly, R (ai , bk ) becomes the rejoice or regret credibility index when CC (ai , bk ) and Dj (Zij, Pkj ) are the rejoice or regret indices. The credibility index R (ai , bk ) represents the power for supporting alternative ai outranks characteristic action bk . The larger the value of R (ai , bk ) , the more superior ai is to bk . To integrate the rejoice and regret credibility indices, the sorting index for identifying the outrank degree between ai and bk is described as follows. Let RO (ai , bk ) and RG (ai , bk ) be respectively the rejoice and regret credibility indices of ai over bk , and RO (bk , ai ) and RG (bk , ai ) be respectively the rejoice and regret credibility indices of bk over ai . Then, the sorting index ψ (ai , bk ) of ai over bk is presented as

if |R− (Z2)| + pj ⩽ |R− (Z1)|, if |R− (Z2)| + qj < |R− (Z1)| < |R− (Z2)| + pj , if

|R− (Z

2 )|

+ qj ⩾ |R− (Z1)|.

(6)

The rejoice discordance index DO (Z1, Z2) of Z1 over Z2 is presented as

DO (Z1, Z2) =

⎧ 0, ⎪ R+ (Z2) − R+ (Z1) − pj ⎨ ⎪1, ⎩

vj − pj

if R+ (Z2) − R+ (Z1) ⩽ pj , , if pj < R+ (Z2) − R+ (Z1) < vj, if R+ (Z2) − R+ (Z1) ⩾ vj.

ψ (ai , bk ) =

(7)

The regret discordance index DG (Z1, Z2) of Z1 over Z2 is presented

DG (Z1, Z2) =

⎨ ⎪1, ⎩

vj − pj

(11)

The assignment of new energy alternatives to the given risk categories can be implemented by comparing the sorting indices as follows:

as

⎧ 0, ⎪ |R− (Z1)| − |R− (Z2)| − pj

RO (ai , bk ) + RG (ai , bk ) . RO (ai , bk ) + RG (ai , bk ) + RO (bk , ai ) + RG (bk , ai )

if |R− (Z1)| − |R− (Z2)| ⩽ pj , ,

(1) If ψ (ai , b1) > ψ (b1, ai ) , then ai is assigned to h1 (ai → h1); (2) If ψ (ai , bk ) > ψ (bk , ai ) and ψ (ai , bk + 1) ⩽ ψ (bk + 1, ai ) , then ai is assigned to hk + 1 (ai → hk + 1); (3) If ψ (ai , bg − 1) > ψ (bg − 1, ai ) , then ai is assigned to hg (ai → hg ).

if pj < |R− (Z1)| − |R− (Z2)| < vj, if |R− (Z1)| − |R− (Z2)| ⩾ vj. (8) 335

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Identify alternatives, criteria, categories and characteristic actions

Information module

Criteria module

Obtain the evaluation information

Construct the direct-relation

Determine the numerical characters

Calculate the utility value Normalise the utility value

Regret module Obtain the comprehensive relation matrix

Calculate the utility value

Analyse the importance and relationship

Calculate the rejoice value

Calculate the weights of criteria

Calculate the regret value

Outranking module Assignment module

Calculate the rejoice/regret concordance index

Calculate the sorting index Calculate the rejoice/regret discordance index

Determine the assignment of alternatives

Calculate the rejoice/regret comprehensive concordance index Assignment result

Calculate the rejoice/regret credibility index

Fig. 1. Framework of the established model.

3. Model establishment

Pkj = (Akj , Bkj )(k = 1, 2, ...,g − 1; j = 1, 2, ...,m) . Step 1.2: Determine the numerical characters of Z-numbers. According to the uncertainty transformation method in [20], the numerical characters of the membership and probability density functions in Z-numbers can be obtained. Step 2: Z-information value calculation. Step 2.1: Calculate the utility value of Z-information.

In this section, the preceding presented methods and a straightforward criteria analysis method are integrated to establish a comprehensive support decision model to address new energy investment risk evaluation problems. Fig. 1 presents the framework of the established model. In general, this framework consists of five primary modules, namely, information module, regret module, criteria module, outranking module and assignment module. The main procedures of the established model are summarised in the following steps. During initialisation, the new energy investment risk evaluation problem is analysed to identify the new energy alternatives, criteria, risk categories and characteristic actions.

The utility value of the obtained Z-information in Step 1.1 can be calculated using Eq. (2) by integrating the numerical characters and probability density function of Z-numbers with the utility function. Step 2.2: Calculate the rejoice value of Z-information.

Step 1: Information description and processing. Step 1.1: Obtain the evaluation information of alternatives and characteristic actions.

Firstly, the NIS Z − of Z-numbers is determined as = (min Aij , min Bij ) . Then, the rejoice value of Z-information can be calculated by the rejoice function R+ (Z ) given in Eq. (3).

Z−

All the new energy alternatives and characteristic actions are evaluated by experts in terms of the criteria according to related investigations and information gathering. Z-number Zij = (Aij , Bij ) is used to describe the evaluation information of ai (i = 1, 2, ...,n) with regard to cj (j = 1, 2, ...,m) , where Aij signifies the fuzzy restriction of ai under cj , and Bij signifies experts’ reliability for the provided fuzzy restriction. Similarly, the evaluation information of bk is characterised by Z-number

Step 2.3: Calculate the regret value of Z-information. Firstly, the PIS Z+ of Z-numbers is determined as Z+ = (max Aij , max Bij ) . Then, the regret value of Z-information can be calculated by the regret function R− (Z ) described in Eq. (4).

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Step 3: Criteria analysis and weight determination.

Prominence x j1 represents the importance of c j1, and relation y j1 reflects the net effect of c j1. The bigger value of x j1 indicates criterion c j1 is more important. y j1 ⩾ 0 demonstrates that c j1 is a cause factor, whereas y j1 < 0 indicates that c j1 is an effect factor. According to the obtained prominence and relation indices, the importance and relationship among the criteria can be visually presented in a causal diagram.

In real-world MCDM problems, there are complex relationships among different criteria. For example, some criteria are the influencing factors, whereas some criteria are the influenced factors; some criteria can directly affect the performance of others, and some criteria play more significant role in the decision process than others. DEMATEL, as a straightforward technique for visualising the complicated relationships among criteria, has been successfully applied to solve diverse problems, such as water security sustainability evaluation [43] and nuclear power plant development [44]. This method can effectively detect the essential causality among criteria rely on relationship matrix and diagram. Based on the relationship analysis of criteria, appropriate measures can be made to manage different criteria factors. Considering the applicability and effectiveness of DEMATEL in analysing criteria, the following steps are formulated to identify criteria relationships and weights.

Step 3.6: Calculate the weights of the criteria. Based on the obtained prominence indices, the criterion weight of c j1 can be calculated as follows:

w j1 =

x j1 m

∑j

1 =1

x j1

. (16)

Step 4: Outranking aggregation and exploitation. Step 4.1: Calculate the rejoice/regret concordance index.

Step 3.1: Construct the direct-relation between different criteria. Based on the obtained rejoice/regret value of Z-information, the rejoice/regret concordance index CO (Zij, Pkj ) /CG (Zij, Pkj ) between alternative ai and characteristic action bk under criterion cj can be calculated using Eq. (5)/(6).

The expert team is invited to conduct the pairwise comparison between different criteria to identify the relative influence and influence degree of a criterion over another. The comparison evaluations are presented using Z-numbers. Then, the direct-relation of mutual influence between criteria c j1 and c j2 can be obtained and is denoted by Z j1 j2 = (A j1 j2 , B j1 j2)(j1 , j2 = 1, 2, ...,m) .

Step 4.2: Calculate the rejoice/regret discordance index. Based on the obtained rejoice/regret value of Z-information, the rejoice/regret discordance index DO (Zij, Pkj ) /DG (Zij, Pkj ) between ai and bk under each criterion can be calculated using Eq. (7)/(8).

Step 3.2: Calculate the utility value of Z j1 j2 . Similar to Step 2.1, the utility value u (Z j1 j2) of Z j1 j2 can be calculated using Eq. (2).

Step 4.3: Calculate the rejoice/regret comprehensive concordance index.

Step 3.3: Normalise the utility value u (Z j1 j2) .

According to the obtained criteria weights and concordance indices, the rejoice/regret comprehensive concordance index CCO (ai , bk ) /CCG (ai , bk ) between ai and bk can be calculated using Eq. (9).

The obtained utility value u (Z j1 j2) can be normalised according to the following formula:

u (Z j1 j2) = u (Z j1 j2) ξ,

(12)

Step 4.4: Calculate the rejoice/regret credibility index.

m m m where ξ = max ⎧max ∑ j = 1 u (Z j1 j2), max ∑ j = 1 u (Z j1 j2) ⎫. ∑ j = 1 u (Z j1 j2) 2 2 1 ⎬ ⎨ j1 j2 ⎭ ⎩ signifies the total influence degree c j1 exerts on other criteria, and m ∑ j = 1 u (Z j1 j2) signifies the total influence degree received by c j2 from 1 others.

According to the obtained discordance and comprehensive concordance indices, the rejoice/regret credibility index RO (ai , bk ) /RG (ai , bk ) between ai and bk can be calculated using Eq. (10).

Step 3.4: Obtain the comprehensive relation matrix.

Step 5: Alternative assignment. Step 5.1: Calculate the sorting index.

Matrix U = (u (Z j1 j2))m × m can be constructed based on the normalised utility value u (Z j1 j2) . Then, the comprehensive relation matrix

According to the obtained credibility indices, the sorting index ψ (ai , bk ) between ai and bk can be calculated using Eq. (11).

P = ⎜⎛p j1 j2 ⎟⎞ can be obtained according to the following formula: ⎝ ⎠m × m P = U (1 − U )−1. (13)

Step 5.2: Determine the assignment of the alternatives.

Step 3.5: Analyse the importance and relationship among the criteria.

According to the sorting rules described in Section 2.4, the obtained sorting indices are used to determine the risk categories of all the new energy alternatives.

, the Based on the comprehensive relation matrix P = ⎜⎛p j1 j2 ⎟⎞ ⎝ ⎠m × m prominence x j1 and relation y j1 of criterion c j1 can be obtained as follows:

y j1 =

∑

p j1 j2 +

∑

j2 = 1

j2 = 1

m

m

∑ j2 = 1

In this section, an empirical case regarding new energy investment risk evaluation is provided to highlight the application of the established model.

m

m

x j1 =

4. Case study

p j1 j2 −

∑ j2 = 1

p j2 j1 ,

(14) 4.1. Background information

p j2 j1 .

(15)

In this section, the background information for new energy 337

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Table 2 Evaluation information of the new energy alternatives under the sub-criteria.

a1 a2 a3 a4 a5 a6

c11

c12

c13

c14

c15

c21

c22

c23

c31

c32

c33

c34

c41

c42

c43

c44

7,6 3,5 5,4 7,9 6,8 8,7

5,5 6,4 4,6 7,6 5,8 7,7

5,7 5,5 4,6 6,7 4,7 3,9

6,6 4,5 5,6 6,6 6,4 7,8

6,6 5,7 4,5 7,9 5,6 8,7

5,6 4,7 7,4 7,6 5,8 4,6

4,7 7,4 5,6 6,5 6,8 5,5

5,4 4,7 5,6 6,7 7,6 4,8

4,7 3,8 5,4 7,6 6,4 5,9

4,8 5,5 7,3 8,5 5,6 6,7

3,7 4,5 7,5 5,8 8,6 4,4

4,8 6,4 3,7 5,6 5,7 7,4

7,4 4,5 5,6 6,5 5,7 6,5

5,7 6,5 5,4 9,5 6,5 7,6

7,4 6,5 5,3 6,5 7,8 5,6

6,6 5,7 6,5 7,5 8,6 5,9

(h1), medium risk (h2 ) and low risk (h3 ). Then, the characteristic actions b1 and b2 need to be determined to distinguish h1 and h2 , and h2 and h3 , respectively.

investment and development in Qingshuitang Industrial Zone is described. Zhuzhou is included in the first batch of key industrial cities built after the founding of New China, and it has been playing a pivotal role in the industrial system in Central China. With the continuous advancement of industrialisation, Zhuzhou’s economy has achieved breakthrough development. However, the rapid development resulted in many unsustainable problems with high investment, consumption and pollution, and low efficiency. Qingshuitang Industrial Zone is an old industrial base invested and constructed during the First Five-Year Plan and the Second Five-Year Plan in Zhuzhou, and more than 200 heavy industrial enterprises are gathered here. Due to industrial structure and historical reasons, the sulphur dioxide emissions in Qingshuitang Industrial Zone account for more than 90% of the city’s industry, the discharge of heavy metal pollutants has been at a high level for a long time, and the water pollution is relatively serious. Qingshuitang Industrial Zone is always the main obstacle for the improvements of urban air quality in Zhuzhou City and water environment quality in Zhuzhou section of the Xiangjiang River. Furthermore, it is the top priority of environment pollution control in the city. To prevent environment deterioration, the government officially decided to relocate and rebuild Qingshuitang Industrial Zone in 2014. At present, most enterprises in Qingshuitang Industrial Zone are shut down and relocated, and the reconstruction work is being carried out gradually. In 2015, Zhuzhou Economic and Information Committee invited the current study’s team to implement ‘The 13th Five-Year Plan for New Industrialisation Development in Zhuzhou’. The local government is conducting this plan step by step. The completed report suggested developing new energy resources in Qingshuitang Industrial Zone to facilitate industry green development. Now, the established model is used to evaluate the investment risk of new energy and to select suitable new energy resource(s) for development in Qingshuitang Industrial Zone.

Step 1: Information description and processing. A professional team that included several experts in diverse fields was formed to assist decision. Related data need to be acquired to conduct alternative evaluation. The experts need to go to Qingshuitang Industrial Zone for field investigation. Interview and questionnaire surveys should be implemented to collect local residents’ views about new energy resources. In addition, some useful information can be found from research papers and government websites. Then, the experts conduct overall evaluation for new energy investment risk based on the acquired data. The experts use linguistic terms in S = {s1=extremely poor, s2 =very poor, s3 =poor, s4 =slightly poor, s5 =fair, s6 =slightly good, s7 =good, s8 =very good, s9 =extremely good} to present the fuzzy restriction on the new energy alternatives, and use linguistic terms in r3=uncertain, r2=very uncertain, uncertain, R = {r1=strongly r4=somewhat uncertain, r5=neutral, r6=somewhat certain, r7=certain, r8=very certain, r9=strongly certain} to evaluate the reliability of the given fuzzy restriction. The evaluation value of new energy alternative ai under criterion cj is displayed in the form of Z-number in Table 2. For example, the experts provide the evaluation (good, somewhat certain) = (s7 , r6 ) for a1 with respect to c11; this evaluation is denoted as ‘7,6’ for brevity. In addition, after a heated discussion of the experts, the characteristic actions b1 and b2 under all the sub-criteria are determined and exhibited in Table 3. Normalising the obtained evaluation information is unnecessary, given that Z-numbers can consistently describe information under different types of criteria. For example, suppose that a1 has high carbon emissions, then the experts will evaluate (very poor, certain) for a1 with respect to pollutant emission (c32 ). According to the uncertainty transformation method in [20], the numerical characters and probability density function of Z-information described in Tables 2 and 3 can be obtained. For example, the numerical characters of the evaluation (slightly poor, very certain) are obtained as μ = 0.3750 , σ = 0.2083, ε = 0.8750 , δ = 0.2917 and η = 0.0139.

4.2. Decision-making procedures In this section, the main procedures for evaluating new energy investment risk using the established model are summarised in the following steps. Generated results are provided in detail in the supplementary material for brevity. Through the comprehensive investigation of resource base, geographical location, market space and development potential, biomass energy (a1), hydrogen energy (a2 ), nuclear energy (a3 ), solar energy (a4 ), hydro energy (a5 ) and wind energy (a6 ) are selected as the new energy alternative(s) for investment and development in Qingshuitang Industrial Zone. Many factors affect the investment of new energy resources, and the reviewed criteria in Table 1 are considered here. The investment risks are divided into three categories, namely, high risk

Step 2: Z-information value calculation. Based on the obtained numerical characters, Eq. (2) is used to calculate the utility value of the Z-number evaluation information. The calculated utility values of alternatives are shown in Table 4. From Table 2, the NIS is determined as Z −=(poor, uncertain). Then, the rejoice values of alternatives can be calculated using Eq. (3), as shown in

Table 3 Evaluation information of the characteristic actions under the sub-criteria.

b1 b2

c11

c12

c13

c14

c15

c21

c22

c23

c31

c32

c33

c34

c41

c42

c43

c44

4,5 6,5

5,5 6,6

4,5 6,5

6,4 6,5

5,6 5,7

5,6 6,7

5,7 6,7

5,5 6,6

5,6 5,7

5,4 6,6

4,5 5,6

4,6 5,6

4,4 6,5

5,4 6,5

5,4 6,5

5,4 6,5

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Table 4 Utility values of the alternatives under the sub-criteria.

a1 a2 a3 a4 a5 a6

c11

c12

c13

c14

c15

c21

c22

c23

c31

c32

c33

c34

c41

c42

c43

c44

0.13 0.04 0.07 0.15 0.14 0.14

0.09 0.08 0.08 0.13 0.12 0.14

0.12 0.09 0.08 0.14 0.08 0.05

0.13 0.07 0.11 0.13 0.08 0.14

0.13 0.12 0.07 0.15 0.11 0.14

0.11 0.08 0.08 0.13 0.12 0.08

0.08 0.08 0.11 0.11 0.14 0.09

0.07 0.08 0.11 0.14 0.13 0.08

0.08 0.05 0.07 0.13 0.08 0.13

0.08 0.09 0.05 0.11 0.11 0.14

0.05 0.07 0.11 0.12 0.13 0.05

0.08 0.08 0.05 0.11 0.12 0.08

0.08 0.07 0.11 0.11 0.12 0.11

0.12 0.11 0.07 0.12 0.11 0.13

0.08 0.11 0.04 0.11 0.14 0.11

0.13 0.12 0.11 0.11 0.13 0.13

Table 5. Similarly, the PIS is determined as Z+=(extremely good, strongly certain), and the regret values of alternatives can be calculated using Eq. (4).

Table 6 Direct-relation of mutual influence between different criteria.

Step 3: Criteria analysis and weight determination.

c1 c2 c3 c4

The comparison evaluation between different criteria is conducted by the experts using Z-numbers. Linguistic terms in S = {s1=no influence, s2 =low influence, s3 =medium influence, s4 =high influence, s5 =very high influence} are used to describe the fuzzy restriction of influence relations, and linguistic terms in R = {r1=very uncertain, r2=uncertain, r3=neutral, r4=certain, r5=very certain} are used to evaluate the reliability of the former. For example, through information search and heated discussion, the expert team considers that economy (c1) has high influence to society (c2 ) and provides the reliability ‘certain’ for this comparison. Then, the Z-number (s4 , r4 ) is determined as the influence degree between the two criteria. In this way, the directrelation Z j1 j2 (j1 , j2 = 1, 2, 3, 4) of mutual influence between different criteria is obtained and shown in Table 6. Using Eq. (2), the utility value u (Z j1 j2) of Z j1 j2 can be calculated, as shown in Table 7. And the normalised utility value can be obtained using Eq. (12), as shown in Table 8. Then, the comprehensive relation matrix P = ⎜⎛p j1 j2 ⎟⎞ ⎝ ⎠4 × 4 ⎡ 0.4745 1.0348 0.4114 0.4837 P=⎢ ⎢ 0.6893 1.0202 ⎢ ⎣ 0.3597 0.5221

c2

c3

c4

– 3,2 4,3 3,2

4,4 – 4,4 2,4

3,4 3,3 – 3,3

3,5 4,3 3,4 –

Table 7 Utility value u (Z j1 j2) of Z j1 j2 .

c1 c2 c3 c4

c1

c2

c3

c4

– 0.0290 0.0790 0.0290

0.1045 – 0.1045 0.0348

0.0784 0.0592 – 0.0592

0.0893 0.0790 0.0784 –

c1

c2

c3

c4

– 0.1065 0.2901 0.1065

0.3840 – 0.3840 0.1280

0.2880 0.2176 – 0.2176

0.3281 0.2901 0.2880 –

Table 8 Normalised utility value.

can be obtained using Eq. (13) as

0.8752 0.6021 0.6367 0.5264

c1

c1 c2 c3 c4

1.0360 ⎤ 0.7388⎥ . 0.9935⎥ 0.4211⎥ ⎦

According to Eq. (5), the comparison between the rejoice values of alternatives and characteristic actions can be implemented with the thresholds under each criterion. For simplicity, qj = 0.005, pj = 0.02 and vj = 0.04 are used under all the sub-criteria. Then, the rejoice concordance index CO (Zij, Pkj ) between ai and bk under all the sub-criteria can be obtained, as shown in Table 9. Similarly, using Eqs. (6)–(8), the regret concordance, rejoice discordance, and regret discordance indices between ai and bk can be obtained, respectively. According to the obtained criteria weights and concordance indices, the rejoice and regret comprehensive concordance indices between ai and bk can be obtained using Eq. (9), as shown in Table 10. Then, using Eq. (10), the rejoice and regret credibility indices between ai and bk can be calculated, as shown in Table 11.

Based on P = ⎜⎛p j1 j2 ⎟⎞ , Eq. (14) is used to calculate the prominence ⎝ ⎠4 × 4 indices as x1 = 5.3553, x2 = 5.2968, x3 = 5.9801 and x 4 = 5.0187 , and Eq. (15) is used to calculate the relation indices as y1 = 1.4855, y2 = −0.8248, y3 = 0.6993 and y4 = −1.3601. Then, using Eq. (16), the criteria weights are calculated as w1 = 0.2473, w2 = 0.2446, w3 = 0.2762 and w4 = 0.2318. Therefore, the influence analysis and weight determination of the four main criteria are completed. Similar procedures can be conducted to analyse the sixteen sub-criteria, and the sub-criteria weights are obtained as w11 = 0.0564 , w12 = 0.0454,w13 = 0.0508,w14 = 0.0485, w15 = 0.0462,w21 = 0.0866, w22 = 0.0815, w23 = 0.0765, w31 = 0.0683, w32 = 0.0731, w33 = 0.0700 , w34 = 0.0647 , w41 = 0.0563, w42 = 0.0626, w43 = 0.0481 and w44 = 0.0648.

Step 5: Alternative assignment.

Step 4: Outranking aggregation and exploitation. Table 5 Rejoice values of the alternatives under the sub-criteria. (10−1).

a1 a2 a3 a4 a5 a6

c11

c12

c13

c14

c15

c21

c22

c23

c31

c32

c33

c34

c41

c42

c43

c44

0.54 0.10 0.26 0.64 0.60 0.58

0.37 0.32 0.30 0.54 0.51 0.58

0.49 0.37 0.30 0.58 0.32 0.16

0.54 0.24 0.45 0.54 0.32 0.60

0.54 0.49 0.24 0.64 0.45 0.58

0.45 0.32 0.32 0.54 0.51 0.30

0.32 0.32 0.45 0.45 0.60 0.37

0.26 0.32 0.45 0.58 0.54 0.33

0.32 0.15 0.26 0.54 0.32 0.54

0.33 0.37 0.17 0.45 0.45 0.58

0.14 0.24 0.45 0.51 0.54 0.16

0.33 0.32 0.14 0.45 0.49 0.32

0.32 0.24 0.45 0.45 0.49 0.45

0.49 0.45 0.26 0.48 0.45 0.54

0.32 0.45 0.13 0.45 0.60 0.45

0.54 0.49 0.45 0.45 0.54 0.54

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Table 9 Rejoice concordance index between alternatives and characteristic actions. CO (Zij, P1j )

a1 a2 a3 a4 a5 a6

c11

c12

c13

c14

c15

c21

c22

c23

c31

c32

c33

c34

c41

c42

c43

c44

1 0.39 1 1 1 1

1 0.95 0.82 1 1 1

1 1 1 1 1 0.83

1 0.81 1 1 1 1

1 1 0 1 1 1

1 0.44 0.41 1 1 0.28

0.21 0.19 1 1 1 0.57

0.58 0.98 1 1 1 1

0.44 0 0.04 1 0.41 1

1 1 0.71 1 1 1

0.69 1 1 1 1 0.80

1 1 0.31 1 1 1

1 1 1 1 1 1

1 1 1 1 1 1

1 1 0.47 1 1 1

1 1 1 1 1 1

c11

c12

c13

c14

c15

c21

c22

c23

c31

c32

c33

c34

c41

c42

c43

c44

1 0 0.09 1 1 1

0.21 0 0 1 1 1

1 0.84 0.32 1 0.48 0

1 0 1 1 0.46 1

1 1 0 1 1 1

0.50 0 0 1 0.83 0

0 0 0.50 0.45 1 0

0 0 0.75 1 1 0

0.21 0 0 1 0.19 1

0 0.21 0 0.71 0.75 1

0 0 1 1 1 0

0.52 0.41 0 1 1 0.41

0.46 0 1 1 1 1

1 1 0.09 1 1 1

0.46 1 0 1 1 1

1 1 1 1 1 1

CO (Zij, P2j )

a1 a2 a3 a4 a5 a6

[45]. However, it is difficult for experts to provide precise values for these thresholds without scientific tools under complex decisionmaking environments, especially the environments with lots of factors. In Section 4.2, the thresholds qj , pj and vj are presented as constant real numbers under all the sub-criteria for simplicity. To verify the influences of different values of qj , pj and vj on the decision results, the following investigations are conducted. Different values of qj′, pj′ and v′j with respect to different criteria are determined (as shown in Table 13) and are used to address the described problem. The same procedures in Section 4.2 are applied to classify the alternatives, and then the sorting indices and assignment results can be obtained. The sorting indices ψ (ai , b1) and ψ (ai , b2) obtained using constant thresholds in comparison with the sorting indices ψ′ (ai , b1) and ψ′ (ai , b2) obtained using modified thresholds are shown in Fig. 2, where ψ (ai , b1) , ψ (ai , b2), ψ′ (ai , b1) and ψ′ (ai , b2) are labelled as ‘c1’, ‘c2’, ‘d1’ and ‘d2 ’, respectively. Then, the assignment results are identified as a1 → h2 , a2 → h1, a3 → h2 , a4 → h3, a5 → h3 and a6 → h2 . Obviously, the sorting indices change with the modified thresholds, and the assignment of a2 changes from h2 to h1, that of a3 changes from h1 to h2 , and that of a5 changes from h2 to h3 . These changes can attribute to the different values of thresholds in regard to different criteria. In the following, how the thresholds affect the assignment results is explained specifically. The proposed outranking assignment method in Section 2.4 indicates that the concordance and discordance indices between alternatives and characteristic actions will change first when the threshold values are modified. The rejoice concordance index CO (Z2j, P1j ) of a2 over b1 under the sixteen sub-criteria obtained using constant thresholds, the rejoice concordance index CO′ (Z2j, P1j ) obtained using modified thresholds, and the difference CO′ (Z2j, P1j ) − CO (Z2j, P1j ) are shown in Fig. 3(a), where CO (Z2j, P1j ) , CO′ (Z2j, P1j ) and CO′ (Z2j, P1j ) − CO (Z2j, P1j ) are labelled as ‘C21’, ‘M21’ and ‘D21’, respectively; and CO (P1j, Z2j ), CO′ (P1j, Z2j ) and CO′ (P1j, Z2j ) − CO (P1j, Z2j ) are respectively labelled as ‘C12 ’, ‘M12 ’ and ‘D12 ’ in Fig. 3(b). Similarly,

Using Eq. (11), the sorting index ψ (ai , bk ) between ai and bk can be obtained, as shown in Table 12. Then, the assignment of all the alternatives can be determined according to the formulated sorting rules. For example, and ψ (a1, b1) = 0.5632 > ψ (b1, a1) = 0.4368 ψ (a1, b2) = 0.2543 < ψ (b2 , a1) = 0.7457 , then a1 is assigned to h2 . Similarly, the assignment results of other alternatives are obtained as a2 → h2 , a3 → h1, a4 → h3, a5 → h2 and a6 → h2 . Therefore, solar energy (a4 ) has the lowest investment risk, whereas nuclear energy (a3 ) has the highest investment risk. The prospect for vigorously investing and developing solar energy in Qingshuitang Industrial Zone is bright because in Zhuzhou, many streets have begun to use solar street lamps, and a large number of charging stations need to be built rapidly to drive the application of new energy vehicles. Moreover, the investment risk ranking of the new energy alternatives can be identified according to the obtained sorting indices. From Table 12, both ψ (a4 , b1) > ψ (a5, b1) > and ψ (a6, b1) > ψ (a1, b1) > ψ (a2 , b1) > ψ (a3, b1) ψ (a4 , b2) > ψ (a5, b2) > ψ (a6, b2) > ψ (a1, b2) > ψ (a2 , b2) > ψ (a3, b2) can be determined. This finding demonstrates the validity and stability of the established model. Therefore, the risk ranking of the alternatives is identified as a4 ≻a5 ≻a6 ≻a1 ≻a2 ≻a3 . 4.3. Results analysis and discussion In this section, the obtained results in Section 4.2 are analysed further to demonstrate the validity and feasibility of the established model for solving new energy investment risk evaluation problems. 4.3.1. Influence analysis of modified thresholds In this section, the influences of modified thresholds on the decision results are investigated. In general, the thresholds qj , pj and vj are defined as affine functions with respect to the evaluations of alternatives under each criterion Table 10 Rejoice and regret comprehensive concordance indices.

a1 a2 a3 a4 a5 a6

CCO (ai , b1)

CCO (ai , b2)

CCO (b1, ai )

CCO (b2, ai )

CCG (ai , b1)

CCG (ai , b2)

CCG (b1, ai )

CCG (b2, ai )

0.8437 0.7693 0.7376 1 0.9600 0.8797

0.4780 0.3068 0.3643 0.9338 0.8597 0.5965

0.6523 0.7630 0.7674 0.2464 0.3862 0.5076

0.9494 1 1 0.8717 0.8927 0.8862

0.8249 0.7477 0.7161 1 0.9554 0.8637

0.4527 0.2945 0.3422 0.9252 0.8413 0.5922

0.6420 0.7440 0.7542 0.2111 0.3567 0.5000

0.9404 1 1 0.8560 0.8790 0.8694

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Table 11 Rejoice and regret credibility indices.

a1 a2 a3 a4 a5 a6

RO (ai , b1)

RO (ai , b2)

RO (b1, ai )

RO (b2, ai )

RG (ai , b1)

RG (ai , b2)

RG (b1, ai )

RG (b2, ai )

0.8437 0.7693 0.7376 1 0.9600 0.8797

0.4029 0.0471 0.0328 0.9338 0.8597 0.5965

0.6523 0.7630 0.7674 0 0.0264 0.2449

0.9494 1 1 0.8717 0.8927 0.8862

0.8249 0.7477 0.7161 1 0.9554 0.8637

0.2416 0.0088 0 0.9252 0.8413 0.5922

0.6420 0.7440 0.7542 0 0.0015 0.0794

0.9404 1 1 0.8560 0.8790 0.8694

a3 over b1 increases from 0.4886 to 0.5148, as shown in Fig. 2. Therefore, b1 outranks a3 becomes a3 outranks b1, and then the assignment of a3 upgrades from h1 to h2 . Similar to Fig. 4, Fig. 5 presents analogous changes causing the assignment upgradation of a5 from h2 to h3 . The discussions above demonstrate that the thresholds can influence the power of criteria towards outranking degrees between alternatives and characteristic actions leading to the change of assignment results.

Table 12 Sorting index.

ψ (ai , b1) ψ (ai , b2) ψ (b1, ai ) ψ (b2, ai )

a1

a2

a3

a4

a5

a6

0.5632 0.2543 0.4368 0.7457

0.5017 0.0272 0.4983 0.9728

0.4886 0.0161 0.5114 0.9839

1 0.5183 0 0.4817

0.9857 0.4898 0.0143 0.5102

0.8432 0.4037 0.1568 0.5963

4.3.2. Sensitivity analysis of varying thresholds In this section, the sensitivity of the obtained results with respect to the varying threshold values is analysed. In Section 4.3.1, the influences of different thresholds concerning different criteria on the decision results are investigated. In this section, the sensitivity of the obtained results to the varying thresholds is discussed further. The values of qj , pj and vj are modified from 0 to 0.01, 0.015 to 0.025 and 0.035 to 0.045 with the increase of 0.001, respectively. In each experiment, only one threshold is modified and the others retain their original values (qj = 0.005, pj = 0.020 and vj = 0.040 ). The same procedures in Section 4.2 are conducted, and then the sorting indices between alternatives and characteristic actions can be obtained according to the varying thresholds. The sorting index ψ (ai , b1) between alternative ai and characteristic action b1 obtained using the varying values of qj are shown in Fig. 6(a), and the obtained sorting index ψ (ai , b2) between ai and b2 are shown in Fig. 6(b), where ψ (ai , b1) , and ψ (ai , b2) are labelled as ‘ xi ’ and ‘ yi ’, respectively. In the same way, the obtained sorting indices with the varying values of pj and vj are shown in Figs. 7 and 8, respectively. Fig. 6 shows that the sorting indices change slightly with the variation of qj , whereas the sorting indices change obviously with pj and vj in Figs. 7 and 8. The reason is that the preference threshold pj plays an important role in distinguishing preferences between different objects to determine the concordance and discordance indices, and the veto threshold vj acts as the veto function in determining the discordance index to enhance the non-compensation effect for outranking comparison, while the indifference threshold qj merely characterises the indifference degree between different objects to present their concordance index [46]. Moreover, Figs. 6–8 show that many sorting indices remain basically consistent in several adjacent threshold values, however, once the thresholds reach a certain value, the sorting indices will change obviously. The reason is that the concordance and discordance indices only change when the thresholds reach a certain value. For example, Fig. 7(a) shows that ψ (a5, b1) remains basically consistent when pj is modified from 0.015 to 0.019, but it decreases evidently when pj is bigger than 0.02. This is because the concordance index of a5 over b1 under c31 increases and the discordance index of a5 over b1 under c31

the rejoice concordance indices between a3 and b1 under the sixteen sub-criteria obtained using constant and different thresholds are shown in Fig. 4, and the rejoice concordance indices between a5 and b2 obtained using constant and modified thresholds are shown in Fig. 5. Evidently, the rejoice concordance indices obtained using the modified thresholds are not less than those obtained using the constant thresholds in Figs. 3–5. This is because the modified thresholds are bigger than the constant thresholds under most of the sub-criteria. For example, CO (Z211, P111) = 0.3868 increases to CO′ (Z211, P111) = 0.5802 ′ = 0.01 and p11 = 0.02 remains when q11 = 0.005 is modified into q11 unchanged under c11. Eq. (5) demonstrates that the increase of CO (Z211, P111) = 0.3868 to CO′ (Z211, P111) = 0.5802 is because the difference pj − qj decreases. Many similar phenomena appear in Figs. 3–5. Moreover, the rejoice concordance index will increase to 1 when qj is modified to larger values. The differences are small and gather in the centre in Fig. 3(a), whereas the differences are relatively bigger and scattered in Fig. 3(b). CO (Z2j, P1j ) represents the outranking degree of a2 over b1, while CO (P1j, Z2j ) represents the outranking degree of b1 over a2 . Therefore, Fig. 3 demonstrates that the increases of the outranking degrees of b1 over a2 are larger than those of a2 over b1 under all the sub-criteria. Moreover, the analyses for the regret concordance, rejoice discordance and regret discordance indices between a2 and b1 can obtain similar results. The varying concordance and discordance indices make the rejoice credibility index of a2 over b1 increases from 0.7693 to 0.8368 and that of b1 over a2 increases from 0.7630 to 0.8611, and the regret credibility index of a2 over b1 increases from 0.7477 to 0.8180 and that of b1 over a2 increases from 0.7440 to 0.8392. Finally, the sorting index of a2 over b1 decreases from 0.5017 to 0.4932, as shown in Fig. 2. Hence, a2 outranks b1 becomes b1 outranks a2 , and then the assignment of a2 degrades from h2 to h1. The differences are large and scattered in Fig. 4(a), whereas the differences are small and concentrated in Fig. 4(b). This finding indicates that the increases of outranking degrees of a3 over b1 are bigger than those of b1 over a3 under all the sub-criteria. All the varying concordance, discordance and credibility indices make the sorting index of

Table 13 Thresholds with respect to each criterion. (10−1). c13

c15

c22

c34

q′j

0.1

0.15

0.05

0.1

0.15

0.1

0.05

0.05

0.15

0.05

0.1

0.05

0.1

0.15

0.1

0.05

p′j

0.2

0.3

0.25

0.3

0.3

0.25

0.25

0.2

0.3

0.35

0.25

0.2

0.3

0.25

0.3

0.25

v′j

0.55

0.55

0.5

0.55

0.55

0.45

0.45

0.5

0.5

0.55

0.5

0.5

0.5

0.45

0.5

0.45

341

c31

c32

c33

c41

c42

c43

c12

c14

c21

c23

c11

c44

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Fig. 2. Sorting indices with constant and modified thresholds.

research.

decreases obviously when pj is bigger than 0.02. Notably, although the sorting indices constantly change, the assignment results are always a1 → h1, a4 → h3, a5 → h2 and a6 → h2 with the modifications of the three thresholds. However, a2 and a3 are assigned to h1 or h2 with the varying values of the three thresholds. On the one hand, this finding validates the stability and effectiveness of the established model for solving practical problems. On the other hand, this finding is different from the discussions in Section 4.3.1. Fig. 2 shows that the changes of sorting indices are evident with the modifications of the three thresholds, whereas the changes of sorting indices in Figs. 6–8 are slighter than those in Fig. 2 with the variation of one threshold. In general, the sorting indices and assignment results evidently change when more thresholds are modified. The discussions in Sections 4.3.1 and 4.3.2 indicate that the indifference, preference and veto thresholds have a significant influence on the decision results. In general, the three thresholds can be determined by subjective and objective methods. On the one hand, experts can provide values for different thresholds according to their experiences and judgments based on the acquired criteria information. The discussions in Sections 4.3.1 and 4.3.2 demonstrate that minor threshold modifications and the modifications of one threshold have a slight effect on the decision results. Therefore, certain errors are allowed for experts to subjectively provide threshold values. On the other hand, the threshold values can be objectively calculated according to the evaluations of alternatives in regard to the criteria. However, no study currently conducts this work. In fact, the three thresholds are closely related to the evaluations under the criteria. Therefore, objective models, such as goal programming, can be constructed based on the evaluations to determine these thresholds. This finding directs future

4.3.3. Sensitivity analysis of risk coefficient In this section, the sensitivity analysis of risk coefficient in terms of the obtained results is conducted. In the calculation process in Section 4.2, the risk aversion coefficient λ = 0.5 is used by the established model to obtain the assignment results. The impacts of different values of λ on the obtained results should be discussed. The sorting index ψ (ai , b1) between alternative ai and characteristic action b1 obtained according to the varying values of λ are shown in Fig. 9(a), and the obtained sorting index ψ (ai , b2) between ai and b2 are shown in Fig. 9(b), where ψ (ai , b1) and ψ (ai , b2) are labelled as ‘ xi ’ and ‘ yi ’, respectively. As shown in Fig. 9, most of the sorting indices change prominently with the varying values of λ , whereas ψ (a4 , b2) and ψ (a5, b2) remain relatively stable. Moreover, the sorting indices increase or decrease steadily with the increase of λ when λ < 0.5, whereas these indices change sharply when λ ⩾ 0.5. In general, λ can reflect the risk attitude of DMs. DMs, who are optimistic and prefer pursuing high return with high risk, will select large values of λ . Furthermore, DMs, who are pessimistic and prefer pursuing low return for reducing risk, will select small values of λ . This finding is consistent with the changes of sorting indices in Fig. 9, where the changes are dramatic, and the differences among different sorting indices are conspicuous when λ is large, whereas the changes and differences are slight when λ is small. Fig. 9(a) shows that ψ (a1, b1) , ψ (a3, b1) , ψ (a4 , b1) , ψ (a5, b1) and ψ (a6, b1) increase continuously, whereas ψ (a2 , b1) decreases constantly. Fig. 9(b) shows that ψ (a1, b2) , ψ (a3, b2) , ψ (a3, b2) and ψ (a6, b2) diminish dramatically, ψ (a4 , b2) raises gradually, and ψ (a5, b2) slightly increases

Fig. 3. Rejoice concordance indices between a2 and b1 with constant and modified thresholds. 342

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Fig. 4. Rejoice concordance indices between a3 and b1 with constant and modified thresholds.

Fig. 5. Rejoice concordance indices between a5 and b2 with constant and modified thresholds.

when λ ⩽ 0.4 and decreases when λ > 0.4 . According to the obtained sorting indices in Fig. 9, the assignment results of all alternatives can be determined, as shown in Table 14. The assignment results of a2 , a3, a4 and a5 change with the varying of λ , whereas those of a1 and a6 always remain consistent under different values of λ . Notably, these changes occur when λ is relatively small or large. Specifically, the assignment of

a2 changes when λ ⩽ 0.3, the assignments of a3 and a4 change when λ = 0.1, and the assignment of a5 changes when λ ⩽ 0.2 and λ ⩾ 0.7 . This finding demonstrates that the established model is more sensitive to the variation of small and large risk coefficient values than that of medium risk coefficient values. The preceding discussions demonstrate that the established model is

Fig. 6. Sorting indices with the varying values of indifference threshold qj . 343

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Fig. 7. Sorting indices with the varying values of preference threshold pj .

very flexible for evaluating the investment risk of new energy resources, which allows DMs to select suitable values for λ according to their risk preferences to obtain satisfactory and accurate results. Because there is abundant evaluation information with multiple criteria and the experts in new energy investment risk evaluation problems have diverse backgrounds, it is essential and rational to take this factor into consideration.

Table 15 shows that the rankings obtained by the three existing methods [17,20,47] are different from that obtained by the established model. Especially, the ranking obtained by method [47] is greatly different from that obtained by the established model, whereas slight difference between the ranking obtained by method [20] and that obtained by the established model is observed. Both method [8] and method [9] determine solar energy (a4 ) as the best new energy source for investment and development in Qingshuitang Industrial Zone, which is identical to the result obtained by the established model. However, method [47] selects wind energy (a6 ) as the best new energy investment project. The current number of photovoltaic power stations is larger than that of wind power stations in Zhuzhou, and many photovoltaic power generation projects are being prepared for investment and construction. Moreover, in November 2018, the government planned to install photovoltaic street lamps in rural areas to promote clean energy and facilitate people’s safe travel [48]. Therefore, solar energy has a better investment prospect than wind energy in Qingshuitang Industrial Zone. Hydro energy is also a good choice because Qingshuitang Industrial Zone is located on the side of the Xiangjiang River. However, nuclear energy (a3 ) should be identified as the worst new energy investment project because its radioactive waste and thermal pollution are not conducive to the ecological restoration in Qingshuitang Industrial Zone. Thus, the new energy investment alternative ranking obtained by the established model is more reasonable than that by the existing methods. In addition, the investment risk of new energy projects can be detected by the established model whereas

4.3.4. Comparison discussion In this section, the differences and advantages of the established model over other existing methods are investigated. Considering that no sorting method under Z-number environments currently exists, three ranking methods in Chatterjee and Kar [47], Shen and Wang [17] and Peng and Wang [20] are used here. Chatterjee and Kar [47] proposed a complex proportional assessment (COPRAS) method based on Z-numbers to solve renewable energy selection problems under uncertain environments. Shen and Wang [17] defined the weighted distance of Z-numbers and combined it with VIKOR to propose a MCDM method. Peng and Wang [20] introduced cloud model to deal with Z-numbers and developed a MCGDM method by combining aggregation operators and multi-objective optimization by ratio analysis plus the full multiplicative form (MULTIMOORA). These existing methods can be used to address the described new energy investment risk evaluation problem based on the evaluation information of alternatives in Table 2. The ranking results obtained by different methods are shown in Table 15.

Fig. 8. Sorting indices with the varying values of veto threshold vj . 344

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Fig. 9. Sorting indices with varying risk coefficient values.

not only effectively handle Z-information but also consider the risk preferences of DMs based on their provided evaluation information. Secondly, essential differences in fusing information between methods [20,47] and the established model are observed. The existing methods [20,47] used weighted aggregation operators with fuzzy operations to fuse evaluation information under different criteria. Whereas the established model devotes to exploiting the outranking integration among different criteria values based on their outranking relations instead of directly aggregating the evaluation values. This strategy completely abandons the fuzzy operations and can address complex problems, which require the processing of large amounts of data, more easier and effectively than the existing methods [20,47] by systematically comparing different criteria values and establishing the corresponding outranking relations. Thirdly, different ranking approaches are used by the three existing methods [17,20,47] and the established model. Method [47] uses COPRAS to identify the ranking, method [17] combines weighted distance with VIKOR to identify the ranking, and method [20] incorporates distance measure into MULTIMOORA to identify the ranking. In fact, these existing methods [17,20,47] are function models, and they assume the final ranking to be subject to complete compensation among different criteria. This strategy inevitably leads to information loss and ignores the actual will of DMs. On the contrary, the outranking exploitation used in the established model sufficiently considers the noncompensation principle among criteria. In this way, pseudo-criteria are modelled by introducing three thresholds to implement the multi-criteria comparison of different alternatives, and interaction with DMs is considered in the decision process. The aforementioned comparisons demonstrate that the established model exhibits the following advantages over the existing methods. Firstly, the established model incorporates the suggested method in [20] into regret theory to effectively deal with Z-information, thereby avoiding inappropriate information conversion and complicated computations whilst reflecting the psychological behaviour of DMs. Secondly, the established model conducts the outranking integration for different criteria values so that many complicated problems, especially problems with lots of factors, can be easily solved. Thirdly, the established model implements the outranking exploitation to sufficiently identify alternative ranking and assignment considering the non-compensation principle among criteria and the interaction with DMs. Because of these qualities, the established model performs better in the decision process and it can identify more reasonable and appropriate results than other existing methods.

Table 14 Assignment results with varying risk coefficient values. ai λ

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

a1 a2 a3 a4 a5 a6

h2 h2 h1 h2 h2 h2

h2 h2 h2 h3 h2 h2

h2 h2 h2 h3 h3 h2

h2 h1 h2 h3 h3 h2

h2 h1 h2 h3 h3 h2

h2 h1 h2 h3 h3 h2

h2 h1 h2 h3 h2 h2

h2 h1 h2 h3 h2 h2

h2 h1 h2 h3 h2 h2

Table 15 Ranking results obtained by different methods. Method

Alternative ranking

COPRAS method [47] VIKOR method [17] MULTIMOORA method [20] Established model

a6 ≻a4 ≻a1 ≻a3 ≻a5 ≻a2 a4 ≻a6 ≻a5 ≻a2 ≻a1 ≻a3 a4 ≻a5 ≻a6 ≻a1 ≻a3 ≻a2 a4 ≻a5 ≻a6 ≻a1 ≻a2 ≻a3

the existing methods cannot. The reasons for the ranking differences are summarised as follows. Firstly, the processing approaches of Z-information are distinct. Method [47] represents the fuzzy restriction and reliability of Z-numbers as trapezoidal and triangular fuzzy numbers, respectively, and converts the Z-number into a trapezoidal fuzzy number according to the fuzzy expectation rules. This strategy is the simplest way to deal with Z-information, however, it treats Z-numbers as fuzzy numbers essentially. Undoubtedly, method [47] fails to handle the intrinsic uncertainties in Z-numbers and loses and distorts the original information because it ignores the randomness and probability distribution of Z-numbers. To improve the effectiveness of Z-number processing, Shen and Wang [17] simultaneously dealt with the fuzzy components and probability distributions of Z-numbers. However, many complex procedures, such as linear programming and probabilistic arithmetic, need to be implemented to calculate the underlying probability distributions. To handle Z-information simply and effectively, Peng and Wang [20] used cloud model to identify the possibility and probability distributions of Z-numbers. In this way, the uncertainties involved in Z-numbers are addressed appropriately, and there merely need some simple computations because the numerical characters of functions in Z-numbers are extracted and calculated. Given this, the information processing strategy in [20] is adopted in the established model, and then the probability density function of Z-numbers is incorporated into regret theory to propose a comprehensive method. The proposed method can

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society, environment and technology factors are presented in Fig. 11(a)–(d), respectively. Fig. 11(a) shows that the importance order of the five economy subcriteria is identified as c11 ≻c13 ≻c14 ≻c15 ≻c12 , and their weights are calculated as w11 = 0.2282 , w12 = 0.1834 , w13 = 0.2053, w14 = 0.1961 and w15 = 0.1870 according to the prominence indices. Moreover, the relation indices show that c11, c14 and c15 have larger influence degrees than c12 and c13 , and categorise c11, c14 and c15 into the cause group and categorise c12 and c13 into the effect group. Fig. 11(a) shows that return on investment is the primary causal factor for new energy investment and development in Qingshuitang Industrial Zone. The reason is that return on investment represents the profitability of a new energy investment project and can evaluate the project’s financial worth and economic success for investment and development. Hence, this factor has the largest impact on other economic factors. Moreover, the prominence indices illustrate that value creation is the most important economy factor for new energy investment and development in Qingshuitang Industrial Zone. The reason is that many deserted buildings exist after the relocation of the old industry enterprises, and the top priority of local government is to attract investment and create value to facilitate economic development. Fig. 11(b) shows that the importance order of the three society subcriteria is identified as c21 ≻c22 ≻c23 , and their weights are calculated as w21 = 0.3541, w22 = 0.3331 and w23 = 0.3128 according to the prominence indices. Moreover, the relation indices categorise c21 into the cause group and categorise c22 and c23 into the effect group. Evidently, job creation has the biggest prominence and relation indices. This finding indicates that job creation is the most important factor and the primary causal factor in the aspect of society for new energy investment and development in Qingshuitang Industrial Zone. In practice, many local residents lose their jobs due to the relocation of old industry enterprises. In this case, the resettlement and employment of local residents must be appropriately solved to maintain and facilitate societal stability and development. Job creation is a significant objective for new energy investment and development in Qingshuitang Industrial Zone. Undoubtedly, the new energy projects that can create considerable amount of local jobs can essentially enhance social benefits and

Fig. 10. Causal diagram for the main criteria.

4.4. Factor analysis for new energy investment In this section, the importance and relationship analyses for new energy investment factors are conducted according to the obtained results in Step 3 in Section 4.2. The influence relationships among the main factors: economy (c1), society (c2 ), environment (c3 ) and technology (c4 ), are visually presented in Fig. 10. The prominence indices demonstrate that the importance order of the four main criteria is c3 ≻c1 ≻c2 ≻c4 , and their weights are w1 = 0.2473, w2 = 0.2446, w3 = 0.2762 and w4 = 0.2319. Moreover, the relation indices divide c1 and c3 into the cause group and divide c2 and c4 into the effect group. Fig. 10 shows that environment is the most important factor for new energy investment and development in Qingshuitang Industrial Zone. The reason is that the environment in Qingshuitang Industrial Zone has been severely damaged after decades of industrial production, and environment protection is the most remarkable concern in the development of new energy resources. Economy (c1) has the highest relation index, indicating that the fluctuation of economy has significant influence on the environment, society and technology. The influence relationships among the sub-criteria under economy,

Fig. 11. Causal diagram for the economy, society, environment and technology sub-criteria. 346

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of decision-making information, but also ensure the reliability of final results. Secondly, a simple computation method is proposed by combining the uncertainty transformation technique in [20] with regret theory to effectively deal with Z-information. On the one hand, the fuzzy and probabilistic uncertainties in Z-numbers are appropriately addressed without losing and distorting original information. On the other hand, the intrinsic psychological behaviour of DMs in real-world decision activities is perfectly reflected through utility, regret and rejoice values. Thirdly, DEMATEL is used to manage multiple criteria in new energy investment risk evaluation problems. In this way, the complicated relationships among diverse factors can be visualised, the importance and causality of criteria can be identified, and the criteria weights, which are significant parameters for decision-making results, can be acquired. This approach is simple and intuitive and can provide helpful suggestions to manage complex factors in new energy investment. Fourthly, an effective sorting method is proposed to implement investment risk identification. This method utilises pseudo-criteria modelling to explore the outranking relations between alternatives and characteristic actions and sufficiently considers the non-compensation principle among criteria. Then, the outranking aggregation and exploitation are conducted to identify the final assignment. By this means, the established model can address practical problems that involve large amounts of data and multiple criteria by systematically comparing different objects and establishing their outranking relations, and it is therefore more applicable than existing methods. Many problems are currently encountered in the development of new energy in China, among which technical problem is the most prominent. China’s new energy technology development is still in its infancy, and the development level lags far behind that of developed countries. Vigorously developing new energy technologies can expand production scales, reduce production costs, enhance market competitiveness and promote the development and use of new energy sources. In general, the future development of China’s new energy can be divided into two phases: commercialisation of new energy technologies and commercialisation of new energy sources. The first stage is the foundation of the second stage and will continue for several years or even up to ten years in China. In future study, it will be interesting to establish appropriate decision support models to address problems, such as new energy material selection, in the first stage to accelerate the commercialisation of new energy technologies.

acceptance. Fig. 11(c) shows that the importance order of the four environment sub-criteria is identified as c32 ≻c33 ≻c31 ≻c34 , and their weights are calculated as w31 = 0.2472 , w32 = 0.2648, w33 = 0.2536 and w34 = 0.2344 according to the prominence indices. Moreover, human/technology influence and pollutant emission are identified as cause factors, and ecology influence and land requirement are identified as effect factors according to the relation indices. Human/technology influence has the highest relation index among all the environmental factors because environmental pollution is often caused by human/technology activities. Pollutant emission is identified as the most important environment factor, and therefore acts a significant role for new energy investment and development in Qingshuitang Industrial Zone. Environmental governance, restoration and protection are major concerns in the subsequent development because the environment in Qingshuitang Industrial Zone was severely damaged in the past decades. Therefore, pollutant emission should be considered the most environment factor for evaluating the investment and development of new energy projects. Fig. 11(d) shows that the importance order of the four technology sub-criteria is identified as c44 ≻c42 ≻c41 ≻c43 , and their weights are calculated as w41 = 0.2430 , w42 = 0.2699, w43 = 0.2074 and w44 = 0.2797 according to the prominence indices. Moreover, innovation and maturity are identified as cause factors, and energy efficiency and energy safety are identified as effect factors according to the relation indices. The biggest prominence and relation indices indicate that maturity is the most important factor and the primary causal factor in the aspect of technology for new energy investment and development in Qingshuitang Industrial Zone. Maturity reflects the level of a new energy technology being widespread internationally and locally and contains many technological parameters, such as technology properties, technology regulation, technology control and technology reliability. Therefore, a new energy investment project with high maturity can ensure energy safety, improve energy efficiency and facilitate energy technology innovation. Although energy safety is an effect factor with low relation index, it is identified as the second most important technology factor, and indispensable attention should be paid to it. 5. Conclusions, novelties and future studies The investment and exploitation of new energy resources have important strategic significance for national development and have a vital impact on the sustainable progress of human society. New energy investment risk evaluation problems involve various factors with uncertainties. After a review of the existing studies, an energy evaluation criteria hierarchy is constructed to identify such factors. Then, an applicable decision support model is established and used to evaluate the investment risk of new energy and to select suitable new energy resource(s) for development in Qingshuitang Industrial Zone. The obtained results show that solar energy has the lowest investment risk, and environment is the most important factor for new energy investment and development in Qingshuitang Industrial Zone. These results have significant implications and can provide valuable suggestions for governments and enterprises. The result analyses indicate that the used parameters have different impacts on the decision results and enable the established model to flexibly support real-world decision activities. The comparison discussions demonstrate that the established model can identify more reasonable outcomes than the existing methods. The outstanding novelties of the established model are summarised as follows. Firstly, Z-numbers are introduced to address situations in which experts present evaluation information for new energy investment in uncertain environments and the reliability of the information needs to be ensured. Z-number expression considerably conforms with human perception and exhibits adequate description capability in identifying fuzzy and partially reliable information in practical problems. Therefore, this expression can not only facilitate the description

Conflict of interest The authors declare that there is no conflict of interest. Acknowledgements The authors are very grateful to the anonymous reviewers for their valuable comments and suggestions to help improve the overall quality of this paper. This work was supported by the National Natural Science Foundation of China (No. 71871228) and Research Project of Graduate Student of Central South University (No. 2018dcyj028). References [1] Xu J, Wang F, Lv C, Xie H. Carbon emission reduction and reliable power supply equilibrium based daily scheduling towards hydro-thermal-wind generation system: a perspective from China. Energy Convers Manage 2018;164:1–14. [2] Hu XS, Wang H, Tang XL. Cyber-physical control for energy-saving vehicle following with connectivity. IEEE Trans Ind Elec 2017;64(11):8578–87. [3] Wu XH, Hu XS, Teng YQ, Qian SD, Cheng R. Optimal integration of a hybrid solarbattery power source into smart home nanogrid with plug-in electric vehicle. J Power Sources 2017;363:277–83. [4] Wang Y, Kuckelkorn J, Li D, Du J. Evaluation on distributed renewable energy system integrated with a Passive House building using a new energy performance index. Energy 2018;161:81–9. [5] Wang ZX, Zheng HH, Pei LL, Jin T. Decomposition of the factors influencing export fluctuation in China's new energy industry based on a constant market share model. Energy Policy 2017;109:22–35.

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