Partner selection for state-owned power grid enterprises in China based on an extended TODIM method: A case study in Inner Mongolia

Abstract

With the implementation of the electric power reform in China, an increasing number of state-owned power grid enterprises are encouraged to introduce social capital and develop mixed ownership in some businesses and therefore selecting suitable partners becomes a pressing issue. This study proposes an extended TODIM method to deal with the partner selection problem for state-owned power grid enterprises in the process of developing mixed ownership. First, 14 criteria are identified by Delphi method and classified into three categories including enterprise capacities, compatibility and risks. Then, specific decision-making steps of the proposed method are presented and in this method, intuitionistic fuzzy theory is introduced to handle the linguistic evaluation information and entropy weight method is applied to obtain the criteria weights. Next, the proposed method is implemented in a case study where Inner Mongolia Power Company plans to select the best new energy partner from four candidates. Finally, the influence of different attenuation factor of losses is discussed and a comparison analysis of different methods is performed to illustrate the robustness of the decision-making result and the feasibility of the proposed method.

Keywords

Partner selection power grid enterprises extended TODIM method Inner Mongolia

1. Introduction

Since 1980s, the electric power reform has been carried out in many countries all over the world to explore an effective approach to allocate the power resources in the market and establish market-oriented operation rules of the power industry. In China, the National Development and Reform Commission issued the document of opinions on further deepening the reform of the electric power system in March 2015, in which the general idea of a competitive power market was put forward [1]. It also means that the monopolistic power system will be broken and a large amount of social capital will be introduced into the power sale market in China. Meanwhile, state-owned power grid enterprises in China are actively encouraged to develop mixed ownership in some business areas including power sale, power distribution network and EV chargers, etc. In this situation, it is a major issue for state-owned power grid enterprises to select the most appropriate partners in the process of developing mixed ownership.

Partner selection refers to the process of making decisions among qualified candidates and has been recognized as a critical problem for strategic cooperation in the academic field. Meuleman et al. [2] proposed a theoretical framework drawing on relational network theory and agency theory to investigate how companies choose their partners considering relational embeddedness. Zhou et al. [3] proposed a genetic algorithm based model to solve the problem of the partner selection. He et al. [4] proposed a privacy-preserving ride matching scheme for selecting feasible ride-share partners in ride sharing services. Kang and Nie [5] studied to choose a suitable provider by building a multi-objective optimization model which was solved by genetic algorithm. Nikghadam et al. [6] integrated goal programming and fuzzy analytic hierarchy process (AHP) in order to evaluate the performance of partners and then enable the dynamic collaboration. Sung et al. [7] devised a partner selection algorithm based on the criteria and the resource allocation. Hong and Gao [8] developed a Markov chain based method to determine cloud computing alliance. These research studied partner selection problem under some certain circumstances but there is little literature related to the process for the power grid enterprises developing mixed ownership. Partner selection is a complex problem with multiple attributes to be considered and unlike the above research, environmental and social factors should also be taken into account for power grid companies.

Table 1
The decision-making criteria of partner selection for state-owned power grid enterprises

Goal	Criteria category	Criteria	Criteria type
Partner selection for	Enterprise capacities	Financial capability	Benefit
state-owned power		Technical level	Benefit
grid enterprises		Marketing capability	Benefit
		Management level	Benefit
		Enterprise scale	Benefit
		Environmental efficiency	Benefit
		Customer loyalty	Benefit
	Compatibility	Enterprise culture	Benefit
		Willingness to share information	Benefit
		Reputation	Benefit
		Reliability	Benefit
		Social benefits	Benefit
	Risks	Financial risk	Cost
		Market fluctuations	Cost

In the partner selection problem, it is necessary to consider appropriate attributes and therefore as an effective tool, multi-criteria decision-making methods (MCDM) are developed by many researchers to address this problem. Salah et al. [9] pointed out that the key issue of the collaborative network is the selection of the right partners based on several conflicting, quantitative, and qualitative criteria which was also considered as a MCDM problem. Wu and Barnes [10] developed Dempster-Shafer theory and formulated criteria in partner selection in agile supply chain. Dong and Wan [11] proposed a partner selection decision-making method for virtual enterprises by integrating Linear Programming Technique for Multidimensional Analysis of Preference (LINMAP) and Technique for Order Preference by Similarity to Ideal Solution (TOPSIS). Cao and Zhao [12] put forward a TOPSIS-based multi-attribute decisions method to help enterprises select the partner and support the decision. Chen et al. [13] built a mechanism for partner selection for strategic alliance by using analytic network process (ANP) approach based on interrelated criteria. Ye and Li [14] extended TOPSIS method for group decisions based on deviation degree and risk factors respectively to solve partner selection problem under imprecise information. Sarkis et al. [15] introduced ANP method to partner selection decisions for agile virtual enterprises with a comprehensive criteria system determined from literature. Wu and Barnes [16] proposed a model for green partner selection by integrating ANP and multi-objective programming methodologies. Guo and Lu [17] constructed an evaluation index system based on the characteristics of agricultural supply chain and employed a heuristic method to make partner selection decisions on this supply chain. It can be seen that MCDM methods are considered as an effective technique to deal with the partner selection problem. However, most existing MCDM methods are based on the assumption that the decision makers (DM) are completely rational [18]. Therefore, in order to deal with the uncertainty and vagueness in the DM’s experience and behaviors, prospect theory was proposed and combined with various MCDM problems. Based on prospect theory, TODIM method was proposed by Gomes and Lima [19] considering DM’s behaviors and data correlation between utilities and alternatives. Therefore, this paper will employ TODIM method to help power grid enterprises to select the best partners in the process of developing mixed ownership. In this method, a value function was built to determine the dominance degree of each alternative over other alternatives. However, the classic TODIM can only handle the problem in which the criteria values are crisp numbers and this characteristic makes it limited in practical situations.

In practical problems, it is critical to deal with the imprecise information and knowledge deficiency for partner selection because the DM’ opinions are subjective in most cases. Therefore, some academic research has focused on handling uncertainty in partner selection problem by using fuzzy set theory. Wu and Barnes [20] studied partner selection problem in agile supply chains by proposing a fuzzy intelligent approach in which fuzzy set theory was introduced to handle intangible factors. Yue [21] transformed the linguistic variables into intuitionistic fuzzy numbers to measure the uncertainty in partner selection for virtual enterprises under a group decision-making environment. Dong and Wan [11] dealt with the partner problem by an integrated MCDM method under the trapezoidal fuzzy environment. From the abovementioned literature, it is obvious that MCDM methods can be developed by introducing fuzzy set theory to handle the vagueness and uncertainty in the partner selection problem. Therefore, this paper will extend the TODIM method by applying intuitionistic fuzzy theory to quantify the linguistic information in the partner selection process.

Partner selection for state-owned power grid enterprises developing mixed ownership is a complex problem with multiple criteria and candidates under fuzzy and imprecise environment. Therefore this paper extends TODIM method by using intuitionistic fuzzy theory and entropy weight method based on a comprehensive criteria system to select the optimal partner for state-owned power grid enterprises in the process of developing mixed ownership. The main contributions of this paper are presented as follows.

(1) (1)

Fourteen criteria are identified from three perspectives of enterprise capacity, compatibility and risks. Based on these criteria, an evaluation index system is established.

(2)

An extended TODIM method is proposed to establish a priority order among candidate partners for state-owned power grid enterprises. In this method, intuitionistic fuzzy theory is employed to deal with the fuzzy information in this problem and the entropy weight method is applied to determine the weights of each criterion.

(3)

The proposed method is implemented in a case of Inner Mongolia Power Company in which four candidate partners are evaluated and the optimal is determined.

(4)

The influence of the attenuation factor of losses is discussed to prove the robustness of the decision-making result. Then the proposed met-hod is compared with PROMETHEE and TOPSIS to verify the superiority.

The remainder of this paper is organized as follows. Section 2 identifies the decision-making criteria from the perspectives of enterprise capacities, compatibility and risks. In Section 3, some preliminary concepts related to fuzzy theory, TODIM method and entropy weight method are presented. Section 4 establishes the framework of the extended TODIM method and described the specific decision-making steps. Section 5 studies an illustrative example in which the Inner Mongolia Power Company determines the best partner to set up a power sale company. Finally, the concluding remarks of the paper are presented in Section 6.

2. The decision-making criteria system

It is necessary to build a comprehensive criteria system in order to determine the best partner for state-owned power grid companies developing mixed ownership. In this paper, Delphi method is employed to identify the decision-making criteria. Delphi method is considered as a survey technique for achieving consensus among participants and has been widely used in the selection of criteria [22]. Accordingly, the criteria are determined by the following steps. First, 40 experts are selected including 20 professors in the field of electricity markets and 20 project management personnel of state-owned power grid enterprises. Then, after reviewing related literature and reports, these experts establish an initial index system. Finally, a questionnaire is designed and distributed to the experts. After analyzing the survey results and checking the consistency, a final criteria system is obtained. There are 14 criteria categorized into enterprise capacities, compatibility and risks, as shown in Table 1. These criteria are divided into two types including benefit type which means the larger the better and cost type which means the smaller the better. The specific descriptions of the decision-making criteria are presented as follows.

2.1 Enterprise capacities

(1) (1)
Financial capability (C1) [13]: Refers to the profitability of the enterprises which is related to ownership interest, operating revenue and market prospect, etc.
(2)
Technical level (C2) [8]: Refers to the technical resources of the candidate partners regarding some businesses such as energy storage, power sale and electric vehicles.
(3)
Marketing capability (C3) [20]: Refers to the marketing competitiveness which is an ability to achieve the sustainable development by meeting the needs of target customers.
(4)
Management level (C4) [23]: Refers to the coordination and management of the human resource, materials and finance, etc., which can increase the operation efficiency of the company.
(5)
Enterprise scale (C5) [24]: Refers to the size of the workforce, sales volume and total assets.
(6)
Environmental efficiency (C6) [17]: High dissipative enterprises should be avoid to cooperate with in order to achieve more environmental benefits. Therefore, the high-tech enterprises and the clean energy enterprises are potential partners.
(7)
Customer loyalty (C7): Refers to number of the electric power users, and the ability to maintain the existing customers and develop potential customers.

2.2 Compatibility

(1) (1)
Enterprise culture (C8) [24]: Refers to the core values and organizational culture of the company. Similar enterprise culture will promote the cooperation between companies.
(2)
Willingness to share information (C9) [25]: Refers to intention of the information resource cooperation such as power network planning, the user load, the power generation configuration and other technical information.
(3)
Reputation (C10) [26]: Refers to the social acceptance degree which can help the company explore opportunities and support.
(4)
Reliability (C11) [6]: Includes product reliability, human reliability, technical reliability and financial reliability, etc.
(5)
Social benefits (C12): Refers to the potential contributions to the whole society after the cooperation including the job opportunities, personnel training, public welfare establishments and scientific achievements.

2.3 Risks

(1) (1)
Financial risk (C13) [3]: Refers to the possibility of financial losses due to some unexpected factors in the financial activities.
(2)
Market fluctuations (C14) [11]: Refers to aperiodic changes of the market environment that the candidate partners are faced to.

3. Preliminary concepts

Suppose that there are $m$ alternatives $A_{i}(i=1,2,$ $\ldots,m)$ and $n$ criteria $C_{j}(j=1,2,\ldots,n)$ in the partner selection problem. The criteria weights are denoted as $W=(w_{1},\ldots,w_{j},\ldots,w_{n})$ which will be calculated by entropy weight method. The initial criteria values are represented by $x_{ij}$ and in order to obtain these values, $p$ decision makers $D_{s}(s=1,2,\ldots,p)$ are invited. In this section, some preliminary concepts including intuitionistic fuzzy sets, entropy weight method and the classical TODIM method will be introduced as follows.

3.1 Intuitionistic fuzzy sets

The criteria identified in Section 2 are all qualitative and the performance of these criteria is always determined by linguistic variables whose values are natural language phrases such as very good, good, medium, poor, etc. In order to deal with this ill-defined situation, fuzzy logic theory, proposed by Zadeh in 1965 is employed to grasp the vagueness in the criteria performance. In this paper, an intuitionistic fuzzy set is introduced to measure these linguistic terms [27]. The concepts and related definitions are presented as follows.

Definition 1 [28]. Let $X$ be the universe of discourse and then the intuitionistic fuzzy set (IFS) on $X$ is defined as

$\displaystyle A=\{(x,\mu_{A}(x),v_{A}(x))|x\in X\}$

where $\mu_{A}(x)$ and $v_{A}(x)$ are the membership and non-membership degrees represented as $\mu_{A}:X\to[0,1],x\in X\to\mu_{A}(x)\in[0,1]$ and $v_{A}:X\to[0,1],x\in X\to v_{A}(x)\in[0,1]$ respectively. They both satisfy the condition that $0\leqslant\mu_{A}(x)+v_{A}(x)\leqslant 1$ for $x\in X$ . The hesitancy degree of $x\in X$ belonging to $A$ is defined as $\pi_{A}(x)=1-\mu_{A}(x)-v_{A}(x)$ which satisfies ${\rm 0}\leqslant\pi_{A}(x)\leqslant 1$ .

Definition 2. In particular, $\alpha=(\mu_{\alpha},v_{\alpha},\pi_{\alpha})$ is called an intuitionistic fuzzy number (IFN) which satisfies $\mu_{\alpha}\in[0,1]$ , $v_{\alpha}\in[0,1]$ and $\mu_{\alpha}+v_{\alpha}\leqslant 1$ .

Definition 3. Let $\alpha=(\mu_{\alpha},v_{\alpha},\pi_{\alpha})$ and $\beta=(\mu_{\beta},v_{\beta},$ $\pi_{\beta})$ be two IFNs. $S(\alpha)=\mu_{\alpha}-v_{\alpha}$ is the score function and $H(\alpha)=\mu_{\alpha}+v_{\alpha}$ is the accuracy function [29]. Then $\alpha$ and $\beta$ can be compared by the following rules.

(1) (1)
If $S(\alpha)>S(\beta)$ , then $\alpha>\beta$ .
(2)
If $S(\alpha)=S(\beta)$ and $H(\alpha)>H(\beta)$ , then $\alpha>\beta$ .
(3)
If $S(\alpha)=S(\beta)$ and $H(\alpha)=H(\beta)$ , then $\alpha=\beta$ .

Definition 4. Let $\alpha=(\mu_{\alpha},v_{\alpha},\pi_{\alpha})$ and $\beta=(\mu_{\beta},v_{\beta},$ $\pi_{\beta})$ be two IFNs and the distance between them is defined as

$\displaystyle\hskip-8.535827ptd(\alpha,\beta)=$ $\displaystyle\hskip-8.535827pt\sqrt{\frac{1}{2}((\mu_{\alpha}-\mu_{\beta})^{2}% +(v_{\alpha}-v_{\beta})^{2}+(\pi_{\alpha}-\pi_{\beta})^{2})}$ (1)

Definition 5 [30]. Let $\alpha=(\mu_{\alpha},v_{\alpha},\pi_{\alpha})$ be an IFN. Then the entropy measure is defined as

$\displaystyle E(\alpha)=\bigg{\{}\sin\frac{\pi\times[1+\mu_{\alpha}(x)-v_{% \alpha}(x)]}{4}+\sin\frac{\pi\times[1-\mu_{\alpha}(x)+v_{\alpha}(x)]}{4}-1% \bigg{\}}\times\frac{1}{\sqrt{2}-1}$ (2)
3.2 The classical TODIM method

TODIM was proposed by Gomes and Lima [19] based on the concepts of prospect theory which can deal with cases of bounded rationality. In this method, the ranking order is determined by computing the dominance degree of each alternative over other alternatives. It is worth mentioning that the criteria values are in form of crisp numbers in the classical TODIM method. To extend this method, it is necessary to probe into the procedure of the algorithm described as follows.

Figure 1.

The framework of the extended TODIM method for optimal partner selection.

Step 1. Step 1.

Collect the data related to each criterion and build the decision matrix $X=\{x_{ij}\}_{m\times n}$ . According to a certain normalization meth-od, normalize the decision matrix into $R=\{r_{ij}\}_{m\times n}$ .

Step 2.

Calculate the relative weight $w_{jr}$ of criterion $C_{j}$ to the reference criterion $C_{r}$ according to Eq. (3).

$\displaystyle w_{jr}=w_{j}/w_{r},\quad j,r\in N$ (3)

where $w_{r}=\max\{w_{j}|j\in N\}$ .

Step 3.

Calculate the dominance degree of alternative $A_{i}$ over $A_{k}$ according to Eq. (4).

$\displaystyle\delta(A_{i},A_{k})=\sum\limits_{j=1}^{n}{\Phi_{j}(A_{i},A_{k})},% i,k\in M$ (4)

where

$\displaystyle\Phi_{j}(A_{i},A_{k})=$ $\displaystyle\left\{\!\!\begin{array}[]{c}\sqrt{\left(r_{ij}-r_{kj}\right)w_{% jr}/\left(\sum\limits_{j=1}^{n}{w_{jr}}\right)}\\ \qquad r_{ij}-r_{kj}>0\\ 0\\ \qquad r_{ij}-r_{ik}=0\\ -\frac{1}{\theta}\sqrt{\left(r_{ij}-r_{kj}\right)\left(\sum\limits_{j=1}^{n}{w% _{jr}}\right)/w_{jr}}\\ \qquad r_{ij}-r_{kj}<0\\ \end{array}\right.$ (5)

$\Phi_{j}(A_{i},A_{k})$ refers to the dominance degree alternative $A_{i}$ over $A_{k}$ with respect to criterion $C_{j}$ and the parameter $\theta$ represents the attenuation factor of the losses. In Eq. (Step 3.), there are three cases in which $r_{ij}-r_{kj}>0$ denotes a gain and $r_{ij}-r_{kj}<0$ represents a loss.

Step 4.

Calculate the final prospect value of alternative $A_{i}$ according to Eq. (Step 4.).

$\displaystyle\xi_{i}=$ $\displaystyle\frac{\makecell{\sum\limits_{k=1}^{m}{\delta(A_{i},A_{k})}-\min% \limits_{i}}{\makecell{\max\limits_{i}\left\{\sum\limits_{k=1}^{m}{\delta(A_{i% },A_{k})}\right\}-\min\limits_{i}}}}$ (6)

Step 5.

Rank alternatives according to $\xi_{i}$ . The best alternative is the one which has highest prospect value.

3.3 Entropy weight method

The entropy concept was proposed by Shannon and used to measure the uncertainty in information. In the decision-making process, the entropy is applied to analyze the quantity of information provided by data. Therefore the entropy weight method can evaluate the importance of criteria objectively according to the information entropy. The principle of this method is that the criteria with larger information entropies should be given higher weights. Based on the intuitionistic fuzzy entropy defined by [30], the weight of criterion $C_{j}$ is defined as Eq. (7) [31].

$\displaystyle w_{j}=\frac{1-E_{j}}{n-\sum\limits_{j=n}^{n}{E_{j}}}$ (7)

where

$\displaystyle E_{j}=\frac{1}{m}\sum\limits_{i=1}^{m}{E(r_{ij})}$ (8)

4. The framework of proposed method

In the optimal partner selection problem for state-owned power grid enterprises, an extended TODIM will be employed to select the best alternative. This method is an extension of classical TODIM method under intuitionistic fuzzy environment and can deal with imprecise information in the decision-making process. In this section, the specific steps of the extended TODIM method will be described as follows based on the preliminaries in the previous section. The framework of the proposed method is illustrated in Fig. 1.

Step 1. Step 1.
Process the evaluation information.

First, identify the alternatives and the criteria. Then invite several decision makers and build the expert panel. The performance of the alternatives regarding to each criterion should be evaluated by the experts according to their experience. In the evaluation process, the experts will use linguistic variables (shown in Table 2) which will be transformed into IFNs. This paper will employ the transformation rules of [27], given in Table 2.
Step 2.
Build and normalize the decision matrix.

The performance of criteria can be calculated by aggregating the weights of decision makers and evaluation information. Let $x_{ij}^{s}=(u_{ij}^{s},v_{ij}^{s},\pi_{ij}^{s})$ be the IFN of alternative $A_{i}$ with respect to criterion $C_{j}$ given by decision maker $D_{s}$ . The criteria values can be aggregated by the IFWA operator [32] according to Eq. (9).

$\displaystyle x_{ij}=\lambda_{1}x_{ij}^{1}\oplus\lambda_{2}x_{ij}^{2}\oplus% \cdots\oplus\lambda_{s}x_{ij}^{s}\oplus\cdots\oplus\lambda_{p}x_{ij}^{p}=\Bigg% {(}1-\prod\limits_{s=1}^{p}{(1-u_{ij}^{s})^{\lambda_{s}}},\prod\limits_{s=1}^{% p}{(v_{ij}^{s})^{\lambda_{s}}},\prod\limits_{s=1}^{p}{(1-u_{ij}^{s})^{\lambda_% {s}}}-\prod\limits_{s=1}^{p}{(v_{ij}^{s})^{\lambda_{s}}}\Bigg{)}$ (9)

where $\lambda_{s}$ is the weight of decision maker $D_{s}$ and can be computed according to Eqs (Step 2.) and (11).

$\displaystyle b_{s}(\pi)=$ $\displaystyle-\frac{1}{\left(\sum\limits_{i=1}^{m}{\sum\limits_{j=1}^{n}{\pi_{% ij}^{s}}}\right)\ln\left(\sum\limits_{i=1}^{m}{\sum\limits_{j=1}^{n}{\pi_{ij}^% {s}}}\right)}$ (10) $\displaystyle\lambda_{s}=\frac{b_{s}(\pi)}{\sum\limits_{s=1}^{p}{b_{s}(\pi)}}$ (11)

The aggregated criteria values $x_{ij}=(\mu_{ij},$ $v_{ij},\pi_{ij})$ can be obtained and the decision matrix $X\!=\!\{x_{ij}\}_{m\times n}$ can be built. Since the criteria are divided into benefit type and cost type, the criteria values should be transformed into the same type according to Eq. (12) [33]. Therefore the normalized decision matrix $R=$ $\{r_{ij}\}_{m\times n}$ can be obtained.

$\displaystyle r_{ij}=(\mu_{ij}^{\prime},v_{ij}^{\prime},\pi_{ij}^{\prime})=% \left\{\begin{array}[]{ll}x_{ij}&{\textit{for benefit type criteria}}\\ \bar{x}_{ij}&{\textit{for cost type criteria}}\\ \end{array}\right.$ (12)

where ${\bar{x}_{ij}}=(v_{ij},u_{ij},\pi_{ij})$ is the complement of $x_{ij}$ .
Step 3.
Determine the criteria weights.

In this step, the criteria weights will be determined by entropy weight method. First, calculate the entropy of criterion values $r_{ij}$ according to Eq. (2). Then obtain the weights of criteria according to Eqs (7) and (8).
Step 4.
Calculate the dominance degree of each alternative over other alternatives.

In this step, the relative criteria weights are used in classical TODIM method in cases of gains and losses but there is a question that the losses of more important criteria are reduced ( $w_{j}$ is larger but $\sum{w_{jr}}/w_{jr}$ becomes smaller) compared with less important criteria and vice versa [34]. Therefore the modification is proposed in $\Phi_{j}$ , shown in Eq. (Step 4.). Since the criteria values are in form of IFNs, the dominance degree of alternative $A_{i}$ over $A_{k}$ should be calculated according to Eq. (13).

$\displaystyle\delta(A_{i},A_{k})\!=\!\sum\limits_{j=1}^{n}{\Phi_{j}(A_{i},A_{k% })},∼{}∼{}i,k{\in}M$ (13)

where

$\displaystyle\Phi_{j}(A_{i},A_{k})=$ $\displaystyle\left\{\begin{array}[]{ll}\sqrt{d(r_{ij},r_{kj})w_{j}}&r_{ij}-r_{% kj}>0\\ 0&r_{ij}-r_{ik}=0\\ -\frac{1}{\theta}\sqrt{d(r_{ij},r_{kj})w_{j}}&r_{ij}-r_{kj}<0\\ \end{array}\right.$ (14)
Step 5.
Compute the final prospect values and rank the alternatives.

According to Eq. (Step 4.), the final prospect value $\xi_{i}$ of each alternative can be obtained. Then rank the alternatives according to the decreasing order of $\xi_{i}$ . The best alternative can be determined with the highest score.

Table 2
The transformation rules of linguistic variables provided by decision makers

Linguistic variables Corresponding IFNs

Extremely poor (EP) (0.05, 0.95, 0.00)

Very poor (VP) (0.15, 0.80, 0.05)

Poor (P) (0.25, 0.65, 0.10)

Medium poor (MP) (0.35, 0.55, 0.10)

Medium (M) (0.50, 0.40, 0.10)

Medium good (MG) (0.65, 0.25, 0.10)

Good (G) (0.75, 0.15, 0.10)

Very good (VG) (0.85, 0.10, 0.05)

Extremely good (EG) (0.95, 0.05, 0.00)

Table 3
The initial evaluation information

A1 A2 A3 A4

D1 D2 D3 D4 D1 D2 D3 D4 D1 D2 D3 D4 D1 D2 D3 D4

C1 MG VG M G G M G M VG EG G MG EG EG VG EG

C2 VG G VG EG G M G G G G M M G VG G G

C3 G M EG M G VG VG EG VG G P P EG MG M MG

C4 MG G G VG G M M G G MP G VG VG MG G M

C5 G G M P VG VG G M EG G M G MG G VG G

C6 VG G P VG VG G P G G M EG M MG G M P

C7 G VG P EG M MG VG P G VG VG P VG MG M MG

C8 VG MG G M G P EG G G M M VG G M G VG

C9 VP M VG G G P G VG G G P G VG EG G M

C10 MG M M M G M M M MG VG G MG G P G VG

C11 M P MP P G G G VG G G VG G G MP VG M

C12 EG G G VG VG EG VG G VG M G M G M M VG

C13 M MG P VP MP P P MP M MP M P MG M VP EG

C14 MP P VP M M MP M P M VP G M M G M M

Table 4
The processed criteria values

A1 A2 A3 A4

C1 (0.71, 0.20, 0.09) (0.65, 0.24, 0.11) (0.84, 0.12, 0.04) (0.93, 0.06, 0.01)

C2 (0.87, 0.09, 0.04) (0.70, 0.19, 0.11) (0.65, 0.25, 0.10) (0.78, 0.14, 0.08)

C3 (0.76, 0.19, 0.05) (0.87, 0.09, 0.04) (0.62, 0.18, 0.10) (0.77, 0.18, 0.05)

C4 (0.76, 0.15, 0.09) (0.65, 0.24, 0.11) (0.73, 0.18, 0.09) (0.72, 0.20, 0.08)

C5 (0.61, 0.28, 0.11) (0.77, 0.16, 0.07) (0.81, 0.14, 0.05) (0.76, 0.16, 0.08)

C6 (0.75, 0.17, 0.08) (0.72, 0.19, 0.09) (0.76, 0.19, 0.05) (0.57, 0.32, 0.11)

C7 (0.81, 0.15, 0.04) (0.62, 0.29, 0.09) (0.74, 0.18, 0.08) (0.69, 0.22, 0.09)

C8 (0.72, 0.20, 0.08) (0.78, 0.16, 0.06) (0.69, 0.22, 0.09) (0.74, 0.17, 0.09)

C9 (0.64, 0.27, 0.09) (0.72, 0.19, 0.09) (0.67, 0.21, 0.12) (0.82, 0.13, 0.05)

C10 (0.54, 0.35, 0.11) (0.58, 0.31, 0.11) (0.74, 0.18, 0.08) (0.72, 0.19, 0.09)

C11 (0.33, 0.57, 0.10) (0.78, 0.14, 0.08) (0.78, 0.14, 0.08) (0.67, 0.24, 0.09)

C12 (0.86, 0.10, 0.04) (0.87, 0.09, 0.04) (0.69, 0.22, 0.08) (0.69, 0.22, 0.09)

C13 (0.44, 0.46, 0.10) (0.60, 0.30, 0.10) (0.49, 0.41, 0.10) (0.23, 0.72, 0.04)

C14 (0.58, 0.33, 0.09) (0.49, 0.41, 0.10) (0.37, 0.52, 0.11) (0.32, 0.58, 0.10)

Table 5
The criteria weights

C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 C14

Weight 0.11 0.09 0.09 0.07 0.08 0.07 0.07 0.08 0.07 0.05 0.09 0.10 0.02 0.01

Table 6
The global dominance degree matrix

A1 A2 A3 A4

A1 0 $-$ 0.19 0.01 $-$ 0.78

A2 0.19 0 0.08 0.08

A3 $-$ 0.01 $-$ 0.08 0 $-$ 0.01

A4 0.09 $-$ 0.08 0.01 0

5. Case study

Linguistic variables	Corresponding IFNs
Extremely poor (EP)	(0.05, 0.95, 0.00)
Very poor (VP)	(0.15, 0.80, 0.05)
Poor (P)	(0.25, 0.65, 0.10)
Medium poor (MP)	(0.35, 0.55, 0.10)
Medium (M)	(0.50, 0.40, 0.10)
Medium good (MG)	(0.65, 0.25, 0.10)
Good (G)	(0.75, 0.15, 0.10)
Very good (VG)	(0.85, 0.10, 0.05)
Extremely good (EG)	(0.95, 0.05, 0.00)

	A1	A2	A3	A4
	D1	D2	D3	D4	D1	D2	D3	D4	D1	D2	D3	D4	D1	D2	D3	D4
C1	MG	VG	M	G	G	M	G	M	VG	EG	G	MG	EG	EG	VG	EG
C2	VG	G	VG	EG	G	M	G	G	G	G	M	M	G	VG	G	G
C3	G	M	EG	M	G	VG	VG	EG	VG	G	P	P	EG	MG	M	MG
C4	MG	G	G	VG	G	M	M	G	G	MP	G	VG	VG	MG	G	M
C5	G	G	M	P	VG	VG	G	M	EG	G	M	G	MG	G	VG	G
C6	VG	G	P	VG	VG	G	P	G	G	M	EG	M	MG	G	M	P
C7	G	VG	P	EG	M	MG	VG	P	G	VG	VG	P	VG	MG	M	MG
C8	VG	MG	G	M	G	P	EG	G	G	M	M	VG	G	M	G	VG
C9	VP	M	VG	G	G	P	G	VG	G	G	P	G	VG	EG	G	M
C10	MG	M	M	M	G	M	M	M	MG	VG	G	MG	G	P	G	VG
C11	M	P	MP	P	G	G	G	VG	G	G	VG	G	G	MP	VG	M
C12	EG	G	G	VG	VG	EG	VG	G	VG	M	G	M	G	M	M	VG
C13	M	MG	P	VP	MP	P	P	MP	M	MP	M	P	MG	M	VP	EG
C14	MP	P	VP	M	M	MP	M	P	M	VP	G	M	M	G	M	M

	A1	A2	A3	A4
C1	(0.71, 0.20, 0.09)	(0.65, 0.24, 0.11)	(0.84, 0.12, 0.04)	(0.93, 0.06, 0.01)
C2	(0.87, 0.09, 0.04)	(0.70, 0.19, 0.11)	(0.65, 0.25, 0.10)	(0.78, 0.14, 0.08)
C3	(0.76, 0.19, 0.05)	(0.87, 0.09, 0.04)	(0.62, 0.18, 0.10)	(0.77, 0.18, 0.05)
C4	(0.76, 0.15, 0.09)	(0.65, 0.24, 0.11)	(0.73, 0.18, 0.09)	(0.72, 0.20, 0.08)
C5	(0.61, 0.28, 0.11)	(0.77, 0.16, 0.07)	(0.81, 0.14, 0.05)	(0.76, 0.16, 0.08)
C6	(0.75, 0.17, 0.08)	(0.72, 0.19, 0.09)	(0.76, 0.19, 0.05)	(0.57, 0.32, 0.11)
C7	(0.81, 0.15, 0.04)	(0.62, 0.29, 0.09)	(0.74, 0.18, 0.08)	(0.69, 0.22, 0.09)
C8	(0.72, 0.20, 0.08)	(0.78, 0.16, 0.06)	(0.69, 0.22, 0.09)	(0.74, 0.17, 0.09)
C9	(0.64, 0.27, 0.09)	(0.72, 0.19, 0.09)	(0.67, 0.21, 0.12)	(0.82, 0.13, 0.05)
C10	(0.54, 0.35, 0.11)	(0.58, 0.31, 0.11)	(0.74, 0.18, 0.08)	(0.72, 0.19, 0.09)
C11	(0.33, 0.57, 0.10)	(0.78, 0.14, 0.08)	(0.78, 0.14, 0.08)	(0.67, 0.24, 0.09)
C12	(0.86, 0.10, 0.04)	(0.87, 0.09, 0.04)	(0.69, 0.22, 0.08)	(0.69, 0.22, 0.09)
C13	(0.44, 0.46, 0.10)	(0.60, 0.30, 0.10)	(0.49, 0.41, 0.10)	(0.23, 0.72, 0.04)
C14	(0.58, 0.33, 0.09)	(0.49, 0.41, 0.10)	(0.37, 0.52, 0.11)	(0.32, 0.58, 0.10)

	A1	A2	A3	A4
A1	0	$-$ 0.19	0.01	$-$ 0.78
A2	0.19	0	0.08	0.08
A3	$-$ 0.01	$-$ 0.08	0	$-$ 0.01
A4	0.09	$-$ 0.08	0.01	0

In this section, the extended TODIM method proposed in this paper will be applied to the partner selection problem for Inner Mongolia Power Company in order to illustrate the feasibility of this method.

5.1 Problem description

Inner Mongolia Power Company is a state-owned power grid enterprise affiliated with State Grid Corporation of China and responsible for the power supply of the west of Inner Mongolia. Since the power reform of China broke the monopoly of power sale market, Inner Mongolia Power Company intends to set up a power sale company cooperated with different types of companies such as new energy companies, Internet enterprises and big power users. With respect to the new energy companies, four candidates are determined by the managers of Inner Mongolia Power Company and the best partner will be selected using the proposed method. The brief introductions of the candidate companies are presented as follows.

(1) (1)
GCL New Energy Holdings Ltd (A1): It is a new energy enterprise mainly focusing on solar power generation as well as construction, development and construction of photovoltaic (PV) power stations including distributed and centralized stations. Its objective is to continuously provide safe, clean and efficient energy to the whole society.
(2)
Beijing Energy Investment Holding Co., Ltd (A2): Its main business includes electric power production and supply, heat production and supply, coal production and sales, real estate development business. It is also committed to investing on the new energy projects and products and the development of energy-saving technologies. After more than ten years of rapid development, it owns four listed companies and expands the business areas to 20 provinces.

Table 7
The final scores of alternatives

$\xi$ $\theta=1$ Ranking $\theta=1.5$ Ranking $\theta=2$ Ranking $\theta=2.5$ Ranking

A1 0 4 0 4 0 4 0 4

A2 1 1 1 1 1 1 1 1

A3 0.64 3 0.56 3 0.49 3 0.42 3

A4 0.76 2 0.72 2 0.69 2 0.67 2

Table 8
The final scores of alternatives

The proposed method Ranking PROMETHEE Ranking TOPSIS Ranking

A1 0 4 $-$ 0.06 4 0.46 4

A2 1 1 0.03 1 0.60 1

A3 0.64 3 0.01 3 0.54 3

A4 0.76 2 0.02 2 0.60 1

Table 9
Strengths and weaknesses of the discussed methods

Strengths Weaknesses

The proposed method This method can handle the uncertainty of the evaluation information and considers the decision makers’ knowledge and psychological behavior. This method sacrifices a little bit of score in exchange of certainty, but not too much.

TOPSIS The calculation of this method is easily processed and there are no requirements for samples. This method is not effective enough to distinguish the alternatives when the score gaps are too small and in this method, the highest ranked alternative is not always the closest to the ideal solution.

PROMETHEE This method has the ability to handle uncertain information in MCDM problems. It does not take the risk preference of decision makers into account.

(3)
China International Energy Sources Group Co., Ltd. (A3): It focuses on the investment of traditional energy including natural gas, oil and mineral, and new energy including PV power and wind power generation. It is also devoted to promote the application of low carbon technologies and provide an integrated solution of green and energy-saving system.
(4)
Huaneng Renewables Co., Ltd. (A4): Its main business involves the investment, construction and operation of clean energy projects including PV power and wind power and other renewable energies. It objective is to protect and improve the environment, develop the green energy and create a world-class clean energy company.

5.2 Procedure and decision-making results

$\xi$	$\theta=1$	Ranking	$\theta=1.5$	Ranking	$\theta=2$	Ranking	$\theta=2.5$	Ranking
A1	0	4	0	4	0	4	0	4
A2	1	1	1	1	1	1	1	1
A3	0.64	3	0.56	3	0.49	3	0.42	3
A4	0.76	2	0.72	2	0.69	2	0.67	2

	The proposed method	Ranking	PROMETHEE	Ranking	TOPSIS	Ranking
A1	0	4	$-$ 0.06	4	0.46	4
A2	1	1	0.03	1	0.60	1
A3	0.64	3	0.01	3	0.54	3
A4	0.76	2	0.02	2	0.60	1

	Strengths	Weaknesses
The proposed method	This method can handle the uncertainty of the evaluation information and considers the decision makers’ knowledge and psychological behavior.	This method sacrifices a little bit of score in exchange of certainty, but not too much.
TOPSIS	The calculation of this method is easily processed and there are no requirements for samples.	This method is not effective enough to distinguish the alternatives when the score gaps are too small and in this method, the highest ranked alternative is not always the closest to the ideal solution.
PROMETHEE	This method has the ability to handle uncertain information in MCDM problems.	It does not take the risk preference of decision makers into account.

In order to select one alternative as the best partner of Inner Mongolia Power Company, the extended TODIM method will be employed and the procedure will be described as follows.

Step 1. Step 1.
Let four experts evaluate each alternative regarding to the criteria using linguistic variables in Table 2 and the evaluation information is shown in Table 3. In this Table 1 to A4 represent the four alternatives and D1 to D4 represent the four DMs.
Step 2.
Transform the ratings in Table 3 into IFNs according to the rules in Table 2. Then aggregate the IFNs into the global criteria values using Eqs (9) and (11) and normalize the criteria values according to Eq. (12). The final criteria values are shown in Table 4.
Step 3.
According to Eqs (7) and (8) and the criteria values, the weights of each criterion can be calculated, shown in Table 5.
Step 4.
Calculate the dominance degree of each alternative over other alternatives using Eqs (13) and (Step 4.) and the results are shown in Table 6.
Step 5.
According to Eq. (15), the final prospect value of each alternative can be computed. In this case, $\theta=1$ is used and the results are obtained as follows and it can be seen that alternative A2, namely Beijing Energy Investment Holding Co., Ltd, is the best partner in this case.

$\displaystyle\xi_{1}=0,\xi_{2}=1,\xi_{3}=0.64,\xi_{4}=0.76.$ (15)

5.3 Discussion

The attenuation factor of losses $\theta$ should be ranged from 1 to 2.5 and Kahneman and Tversky [34] estimated that it should be approximately 2.25 after a large number of experiments. Therefore in this case, the influence of $\theta$ is discussed and the ranking orders with different $\theta$ are listed in Table 7. As the parameter $\theta$ increases, the prospect values of A1 and A2 remain stable while the scores of A3 and A4 show a downward trend. It can also be seen that the ranking order remains A2 $>$ A4 $>$ A3 $>$ A1 with the change of the parameter, which means that the selection result is robust regardless of the decision makers’ risk preference.

Next, a comparison analysis is performed. In this section, other two widely-used MCDM methods including PROMETHEE [36] and TOPSIS [37] will be employed to rank the alternatives in this case in order to compare the results with the proposed method. In TOPSIS method, the closeness coefficients are calculated and the alternative with minimum value is determined to be the optimal. The net preference flows are obtained by using PROMETHEE in which the preference function is Gaussian function, and alternatives should be ranked in a decreasing order. The results of these three methods are listed in Table 8. It can be seen that the ranking orders of the proposed method and PROMETHEE are A2 $>$ A4 $>$ A3 $>$ A1 while the TOPSIS method produced a ranking order of A2 $=$ A4 $>$ A3 $>$ A1. Also, the best alternative is A2 using these three methods, which can prove that the proposed method can obtain a satisfactory result and is effective for partner selection problem in state-owned power grid companies.

From this table, we can conclude the strengths and weaknesses of the proposed method and the other two methods, shown in Table 9.

It is obvious that the extended TODIM method shows an advantage over these two methods to make the decision-making result more persuasive by considering the decision makers’ knowledge and psychological behavior. It can be seen that the proposed method is more reasonable and veritable and it would have more confidence if there are more candidates.

6. Conclusions

As the electric power reform develops rapidly in China, more state-owned power grid enterprises are encouraged to cooperate strategically with other companies in some business and then develop mixed ownership. Therefore, it is essential to select an appropriate strategic partner. In this work, the partner selection problem of state-owned power grid enterprises developing mixed ownership was studied by using an extended TODIM method. It also proved that the proposed method can solve this problem efficiently and can be applied in other fields. The main conclusions of this paper are presented as follows.

(1) (1)

From the perspectives of the enterprise capacities, compatibility and risk, 14 qualitative decision-making criteria were identified by Delphi method in which 40 experts were invited and these criteria were also divided into two types including benefit type and cost type.

(2)

An extended TODIM method was proposed to rank the candidate partners under an IFN environment. In this method, intuitionistic fuzzy theory was introduced to deal with the fuzzy evaluation information provided by decision makers and the entropy weight method was employed to calculate the weight of each criterion. Also the calculation of the dominance degree was improved to obtain a more accurate result.

(3)

The proposed method was implemented in a case study where the Inner Mongolia Power Company intended to select a new energy company as a partner to set up a power sale company. The result indicated that the alternative A2, namely Beijing Energy Investment Holding Co., Ltd, was the best alternative and ranking order was A2 $>$ A4 $>$ A3 $>$ A1.

(4)

The influence of attenuation factor of losses was discussed to investigate the effect of the decision makers’ psychological behavior on the decision-making result. In this case, the ranking order remained stable with the change of the parameter $\theta$ , which proved that the decision-making result was robust.

(5)

A comparison analysis was also conducted and the results of the proposed method and two other MCDM methods including TOPSIS and PROMETH-EE were compared, which demonstrated the priority of the proposed method.

Footnotes

Acknowledgments

This research was supported by National Natural Science Foundation of China (grant no. 71771085) and Fundamental Research Fund for the Central Universities 2017XS101 and 2017XS102.

References

Yang

Wang

Liu

. Investment risk evaluation and countermeasures suggestions of Power Grid Corp under the background of electric power reform. in: the AIP Conference Proceedings. China. 2017; 040013.

Meuleman

Lockette

Manigart

Wright

. Partner selection decisions in interfirm collaborations: the paradox of relational embeddedness. J Manag Stud. 2010; 47: 995-1019.

Zhou

. Research on partner selection problem of virtual enterprise based on improved Genetic algorithm. in: Control and Decision Conference. China. 2014; 1047-1052.

Wang

Niu

Chen

. Privacy-preserving partner selection for ride-sharing services. IEEE T Veh Technol. 2018; 67(7): 5994-6005.

Kang

Nie

. An algorithm about partner selection problem on cloud service provider based on genetic. J Theor Appl Inf Technol. 2014; 62: 225-236.

Nikghadam

Sadigh

Ozbayoglu

Unver

Kilic

. A survey of partner selection methodologies for virtual enterprises and development of a goal programming-based approach. Int J Adv Manuf Technol. 2016; 85: 1713-1734.

Sung

Hong

YWP

Chao

. Resource allocation and partner selection for cooperative multicarrier systems. IEEE Trans Veh Technol. 2011; 60: 3228-3240.

Hong

Gao

. Partner selection of cloud computing federation based on Markov chains. Comput Model New Technol. 2014; 18: 590-594.

Salah

Yahia

Ayadi

Masmoudi

. Definition and classification of collaborative network: MCDM approaches for partner selection problem. in: International Conference Design and Modeling of Mechanical Systems. Tunisia. 2017; 733-744.

10.

Barnes

. Formulating partner selection criteria for agile supply chains: A dempster-shafer belief acceptability optimization approach. Int J Prod Econ. 2010; 125: 284-293.

11.

Dong

Wan

. Virtual enterprise partner selection integrating LINMAP and TOPSIS. J Oper Res Soc. 2016; 67: 1288-1308.

12.

Cao

Zhao

. Research of the supply chain partner selection in coexistence of the real number attribute and the interval attribute. in: 5th International Conference on New Trends in Information Science and Service Science. China. 2011; 357-360.

13.

Chen

Lee

. Applying ANP approach to partner selection for strategic alliance. Manag Decis. 2008; 46: 449-465.

14.

. Group multi-attribute decision model to partner selection in the formation of virtual enterprise under incomplete information. Expert Syst Appl. 2009; 36: 9350-9357.

15.

Sarkis

Talluri

Gunasekaran

. A strategic model for agile virtual enterprise partner selection. Int J Oper Prod Manag. 2007; 27: 1213-1234.

16.

Barnes

. An integrated model for green partner selection and supply chain construction. J Cleaner Prod. 2016; 112: 2114-32.

17.

Guo

. Partner selection optimization model of agricultural enterprises in supply chain. Adv J Food Sci Technol. 2013; 5: 1285-1291.

18.

Qin

Liang

Chen

. A TODIM-based multi-criteria group decision making with triangular intuitionistic fuzzy numbers. Appl Soft comput. 2017; 55: 93-107.

19.

Gomes

LFA

Lima

MMP

. TODIM: Basics and application to multicriteria ranking of projects with environmental impacts. Decis Sci. 1992; 16: 113-127.

20.

Barnes

. Partner selection in agile supply chains: A fuzzy intelligent approach. Prod Plan Control. 2014; 25: 821-839.

21.

Yue

. An intuitionistic fuzzy projection-based approach for partner selection. Appl Math Model. 2013; 37: 9538-9551.

22.

Luo

Ruan

. A fuzzy evaluation and AHP based method for the energy efficiency evaluation of EV charging station. J Comput. 2014; 9: 1185-1192.

23.

Lin

CWR

Chen

HYS

. A fuzzy strategic alliance selection framework for supply chain partnering under limited evaluation resources. Comput Ind. 2004; 55: 159-179.

24.

Yang

Yan

. Three-stage model of transportation enterprise alliance partner selection. J Highw Transp Res Dev. 2008; 25: 151-154.

25.

Rezaei

. A two-way approach to supply chain partner selection. Int J Prod Res. 2015; 53: 4888-4902.

26.

Moeller

. Partner selection, partner behavior, and business network performance: An empirical study on German business networks. J Account Organ Change. 2010; 6: 27-51.

27.

Zhang

Liu

. A GRA-based intuitionistic fuzzy multi-criteria group decision making method for personnel selection. Expert Syst Appl. 2011; 38: 11401-11405.

28.

Atanassov

. Intuitionistic fuzzy sets. Fuzzy Sets Syst. 1986; 20: 87-96.

29.

Hong

Choi

. Multicriteria fuzzy decision-making problems based on vague set theory. Fuzzy Set Syst. 2000; 114: 103-113.

30.

. Two effective measures of intuitionistic fuzzy entropy. Comput Vienna New York. 2010; 87: 55-62.

31.

Liu

Ren

. A new intuitionistic fuzzy entropy and application in multi-attribute decision making. Inf Switz. 2014; 5: 587-601.

32.

Cai

. Recent advances in intuitionistic fuzzy information aggregation. Fuzzy Optim Decis Mak. 2010; 9: 359-381.

33.

Gupta

Lin

Mehlawat

Grover

. A new method for intuitionistic fuzzy multiattribute decision making. IEEE Trans Syst Man Cybern Syst. 2016; 46: 1167-1179.

34.

Kahneman

Tversky

. Prospect theory: An analysis of decision under risk. Econometrica. 1979; 47: 263-291.

35.

Liao

. Multi-criteria decision making with intuitionistic fuzzy PROMETHEE. J Intell Fuzzy Syst Appl Eng Technol. 2014; 27: 1703-1717.

36.

Lourenzutti Krohling

. A study of TODIM in a intuitionistic fuzzy and random environment. Expert Syst Appl. 2013; 40: 6459-6468.

37.

Zeng

Xiao

. TOPSIS method for intuitionistic fuzzy multiple-criteria decision making and its application to investment selection. Kybernetes. 2016; 45: 282-296.

	A1				A2				A3				A4
	D1	D2	D3	D4	D1	D2	D3	D4	D1	D2	D3	D4	D1	D2	D3	D4
C1	MG	VG	M	G	G	M	G	M	VG	EG	G	MG	EG	EG	VG	EG
C2	VG	G	VG	EG	G	M	G	G	G	G	M	M	G	VG	G	G
C3	G	M	EG	M	G	VG	VG	EG	VG	G	P	P	EG	MG	M	MG
C4	MG	G	G	VG	G	M	M	G	G	MP	G	VG	VG	MG	G	M
C5	G	G	M	P	VG	VG	G	M	EG	G	M	G	MG	G	VG	G
C6	VG	G	P	VG	VG	G	P	G	G	M	EG	M	MG	G	M	P
C7	G	VG	P	EG	M	MG	VG	P	G	VG	VG	P	VG	MG	M	MG
C8	VG	MG	G	M	G	P	EG	G	G	M	M	VG	G	M	G	VG
C9	VP	M	VG	G	G	P	G	VG	G	G	P	G	VG	EG	G	M
C10	MG	M	M	M	G	M	M	M	MG	VG	G	MG	G	P	G	VG
C11	M	P	MP	P	G	G	G	VG	G	G	VG	G	G	MP	VG	M
C12	EG	G	G	VG	VG	EG	VG	G	VG	M	G	M	G	M	M	VG
C13	M	MG	P	VP	MP	P	P	MP	M	MP	M	P	MG	M	VP	EG
C14	MP	P	VP	M	M	MP	M	P	M	VP	G	M	M	G	M	M

	C1	C2	C3	C4	C5	C6	C7	C8	C9	C10	C11	C12	C13	C14
Weight	0.11	0.09	0.09	0.07	0.08	0.07	0.07	0.08	0.07	0.05	0.09	0.10	0.02	0.01

	A1				A2				A3				A4
	D1	D2	D3	D4	D1	D2	D3	D4	D1	D2	D3	D4	D1	D2	D3	D4
C1	MG	VG	M	G	G	M	G	M	VG	EG	G	MG	EG	EG	VG	EG
C2	VG	G	VG	EG	G	M	G	G	G	G	M	M	G	VG	G	G
C3	G	M	EG	M	G	VG	VG	EG	VG	G	P	P	EG	MG	M	MG
C4	MG	G	G	VG	G	M	M	G	G	MP	G	VG	VG	MG	G	M
C5	G	G	M	P	VG	VG	G	M	EG	G	M	G	MG	G	VG	G
C6	VG	G	P	VG	VG	G	P	G	G	M	EG	M	MG	G	M	P
C7	G	VG	P	EG	M	MG	VG	P	G	VG	VG	P	VG	MG	M	MG
C8	VG	MG	G	M	G	P	EG	G	G	M	M	VG	G	M	G	VG
C9	VP	M	VG	G	G	P	G	VG	G	G	P	G	VG	EG	G	M
C10	MG	M	M	M	G	M	M	M	MG	VG	G	MG	G	P	G	VG
C11	M	P	MP	P	G	G	G	VG	G	G	VG	G	G	MP	VG	M
C12	EG	G	G	VG	VG	EG	VG	G	VG	M	G	M	G	M	M	VG
C13	M	MG	P	VP	MP	P	P	MP	M	MP	M	P	MG	M	VP	EG
C14	MP	P	VP	M	M	MP	M	P	M	VP	G	M	M	G	M	M

Partner selection for state-owned power grid enterprises in China based on an extended TODIM method: A case study in Inner Mongolia

Abstract

Keywords

1. Introduction

Table 1 The decision-making criteria of partner selection for state-owned power grid enterprises

2.1 Enterprise capacities

(1) (1) Financial risk (C13) [3]: Refers to the possibility of financial losses due to some unexpected factors in the financial activities. (2) Market fluctuations (C14) [11]: Refers to aperiodic changes of the market environment that the candidate partners are faced to. 3. Preliminary concepts

3.1 Intuitionistic fuzzy sets

5.1 Problem description

6. Conclusions

Footnotes

Acknowledgments

References

Table 1
The decision-making criteria of partner selection for state-owned power grid enterprises

(1) (1)
Financial risk (C13) [3]: Refers to the possibility of financial losses due to some unexpected factors in the financial activities.
(2)
Market fluctuations (C14) [11]: Refers to aperiodic changes of the market environment that the candidate partners are faced to.

3. Preliminary concepts

	A1				A2				A3				A4
	D1	D2	D3	D4	D1	D2	D3	D4	D1	D2	D3	D4	D1	D2	D3	D4
C1	MG	VG	M	G	G	M	G	M	VG	EG	G	MG	EG	EG	VG	EG
C2	VG	G	VG	EG	G	M	G	G	G	G	M	M	G	VG	G	G
C3	G	M	EG	M	G	VG	VG	EG	VG	G	P	P	EG	MG	M	MG
C4	MG	G	G	VG	G	M	M	G	G	MP	G	VG	VG	MG	G	M
C5	G	G	M	P	VG	VG	G	M	EG	G	M	G	MG	G	VG	G
C6	VG	G	P	VG	VG	G	P	G	G	M	EG	M	MG	G	M	P
C7	G	VG	P	EG	M	MG	VG	P	G	VG	VG	P	VG	MG	M	MG
C8	VG	MG	G	M	G	P	EG	G	G	M	M	VG	G	M	G	VG
C9	VP	M	VG	G	G	P	G	VG	G	G	P	G	VG	EG	G	M
C10	MG	M	M	M	G	M	M	M	MG	VG	G	MG	G	P	G	VG
C11	M	P	MP	P	G	G	G	VG	G	G	VG	G	G	MP	VG	M
C12	EG	G	G	VG	VG	EG	VG	G	VG	M	G	M	G	M	M	VG
C13	M	MG	P	VP	MP	P	P	MP	M	MP	M	P	MG	M	VP	EG
C14	MP	P	VP	M	M	MP	M	P	M	VP	G	M	M	G	M	M