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With the growing worldwide awareness of environmental protection and sustainable development, green purchasing has become an important issue for companies to gain environmental and developmental sustainability. Thermal power is the main power generation form in China, and the green supplier selection is essential to the smooth and sustainable construction of thermal power plants. Therefore, selecting the proper green supplier of thermal power equipment is very important to the company’s sustainable development and the sustainability of China’s electric power industry. In this paper, a hybrid fuzzy multi-attribute decision making approach (fuzzy entropy-TOPSIS) is proposed for selecting the best green supplier. The fuzzy set theory is applied to translate the linguistic preferences into triangular fuzzy numbers. The subjective criteria weights are determined by using decision makers’ superiority linguistic ratings and the objective ones are determined by combining the superiority linguistic ratings and fuzzy-entropy weighting method. The fuzzy TOPSIS is employed to generate an overall performance score for each green supplier. An empirical green supplier selection is conducted to illustrate the effectiveness of this proposed fuzzy entropy-TOPSIS approach. This proposed fuzzy entropy-TOPSIS approach can select the proper green supplier of thermal power equipment, which contributes to promoting the company’s sustainable development and the sustainability of China’s electric power industry to some extent.

Since China’s move towards reform and opening up, a large number of power plant projects have been constructed in order to meet the demands of social and economic development for electricity. In order to meet this development requirement, the public bidding and tendering system has been applied to the procurement of thermal power equipment since the year 1985. The selection of thermal power equipment suppliers is a very important part of the thermal power equipment bidding and tendering management, which is also essential to the smooth and sustainable construction of thermal power plants.

With the significant increase of fossil energy consumption and the ever-worsening pollution of our environment, ‘green development’ and ‘sustainable development’ have become the focus of global attention [

The selection of green suppliers is a multi-criteria decision making (MCDM) problem [

Nowadays, there are many approaches to be used for the supplier selection. However, the approaches that are proposed to apply in the selection of green suppliers are rather limited. Kannan,

In this paper, a new hybrid multi-criteria decision making approach is proposed to select the proper green supplier of thermal power equipment, namely the fuzzy entropy-TOPSIS approach. Due to the ambiguity and intangibility arising from human qualitative judgment as well as the vagueness and uncertainty arising from the lack of complete information, the fuzzy set theory [

The rest of the paper is organized as follows.

To solve the issues under uncertainty environment, the concept of fuzzy set theory was proposed by Zadeh [_{ã}_{ã}

A triangular fuzzy number is represented as a triplet ^{L}^{M}^{R}_{ã}^{L}^{M}^{R}^{L}^{M}^{R}_{ã}^{M}_{ã}^{L}^{L}^{R}

Triangular fuzzy number

Let ^{L}^{M}^{R}^{L}^{M}^{R}

^{L}^{L}^{M}^{M}^{R}^{R}

^{L}^{L}^{M}^{M}^{R}^{R}

^{L}^{L}^{M}^{M}^{R}^{R}^{L}^{L}

^{L}^{R}^{M}^{M}^{R}^{L}^{L}^{L}

^{L}^{M}^{R}

^{R}^{M}^{L}^{L}

Under the fuzzy decision-making environment, it is quite important to rank the alternatives under consideration. The graded mean integration representation method (GMIR) proposed by Chen and Hsieh (2000) is employed to rank the final alternatives’ ratings in this paper [

Let _{i}_{i}^{L}_{i}^{M}_{i}^{R}_{i}_{i}

Linguistic variable refers to the variable whose value is a word or a sentence rather than numeral in a natural or artificial language [

Linguistic terms for the ratings of criteria important weights.

Linguistic Term | Membership Function |
---|---|

Very low (VL) | (0,0,0.3) |

Low (L) | (0,0.3,0.5) |

Medium (M) | (0.2,0.5,0.8) |

High (H) | (0.5,0.7,1) |

Very high (VH) | (0.7,1,1) |

Linguistic terms for the ratings of alternatives with respect to subjective criteria.

Linguistic Term | Membership Function |
---|---|

Very poor (VP) | (0,0,0.2) |

Poor (P) | (0,0.2,0.4) |

Fair (F) | (0.3,0.5,0.7) |

Good (G) | (0.6,0.8,1) |

Very good (VG) | (0.8,1,1) |

The entropy method, firstly appeared in thermodynamics, is used to describe the matter status, and then was introduced into information theory by Shannon [

The procedure of the weight determination of objective criteria by using the entropy weighting method characterized by triangular fuzzy numbers is as follows.

_{ik}_{i}_{k}_{ik}_{ik}_{ik}_{ik}_{ik}_{m×p}

_{k}_{k}

_{k}_{k}

TOPSIS (Technique for Order Preference by Similarity to an Ideal Solution) is a classic multi-criteria decision making (MCDM) method proposed by Hwang and Yoon (1981) [

The specific steps of fuzzy TOPSIS approach are presented as follows.

Suppose that there are _{1}_{2}_{m}

Let _{i}_{j}_{k}_{i}_{k}

The determination of criteria weight is quite important, which has a big impact on the final evaluation and selection result. The subjective criteria weight determination methods can embody the consciousness tendency of decision-makers, while the objective criteria weight determination methods can reflect the information essence and measure the useful information of the provided data. Many articles assign the criteria weight subjectively, which may lead to the inaccuracy of green supplier selection based on company requirements [

Let _{k}_{j}_{k}

Allow _{ik}_{i}_{k}_{k}_{k}

The normalized subjective weight _{k}

In this paper, there are

Then, the integrated weight _{k}_{k}

Based on the above analysis, the integration weights _{k}

In this paper, the criteria are classified into objective criteria and subjective criteria. The objective criteria evaluation values of each alternative is given in the form of triangular fuzzy number according to the actual objective conditions, while the subjective criteria evaluation values of each alternative is given in the form of triangular fuzzy number by the decision-makers’ superiority linguistic ratings. Then, the initial fuzzy decision matrix

Considering the different dimensions and units of objective criteria, the raw data of objective criteria are needed to be converted to dimensionless scales in order to ensure the compatibility between fuzzy evaluation value of objective criteria and linguistic rating of subjective criteria [

Let _{k}

For benefit criterion

For cost criterion

The subjective criteria have no need for dimensionless processing. Let

The weighted normalized fuzzy decision matrix _{k}

Let and represent the fuzzy positive ideal solution and fuzzy negative ideal solution, respectively, both of which can be computed by
_{1} and _{2} represent the benefit criteria set and cost criteria set, respectively.

There are many methods that can be applied to calculate the distance between two triangular fuzzy numbers. A modified geometrical distance with the advantages of easy implementation and powerful concept is employed in this paper [_{i}_{j}_{i}_{j}

Then, the distance

The closeness coefficient represents the distances closet to the fuzzy positive ideal solution ^{+}^{−}

According to the closeness coefficient _{i}_{i}

The proposed fuzzy entropy-TOPSIS approach for green supplier selection of thermal power equipment has following two phases, which is shown in

Phase 1: Determine the alternatives and identify the evaluation criteria. In the first phase, an expert decision group which is composed of electricity senior executives, bidding project managers, supply chain experts, and environmental experts is formed for the green supplier selection of thermal power equipment. After reviewing the bidding documents of all the bidders, these executives, managers and experts select the potential alternatives for supplying the thermal power equipment. Then, according to the experts’ opinion and company characteristics as well as industry background, the determination of evaluation criteria for green supplier selection of thermal power equipment is performed.

Phase 2: Evaluation of the green suppliers of thermal power equipment and determines final rank by fuzzy entropy-TOPSIS approach. In this step, the linguistic ratings are firstly allocated to the criteria and to the potential alternatives with respect to subjective criteria. Four selected decision makers perform the linguistic ratings by using rating scales given in _{i}_{i}

This proposed fuzzy entropy-TOPSIS approach has the ability to evaluate and select the green suppliers of thermal power equipment under partial or lack of quantitative information. Using the triangular fuzzy numbers and linguistic values can overcome the uncertainty due to human qualitative judgment. The fuzzy-entropy weighting method can measure the average essence of information quantity of criteria data as well as grasp the actual conditions of evaluation criteria, and the superiority linguistic ratings can reflect the experts’ thoughts and opinions. The fuzzy TOPSIS method which uses the linguistic value rather than crisp value is much more suitable for solving the problems under a fuzzy environment in real life.

The framework of proposed hybrid fuzzy entropy-TOPSIS approach for green supplier selection of thermal power equipment.

In this section, the green suppliers of thermal power equipment are evaluated and selected by applying the proposed fuzzy entropy-TOPSIS approach, and the computational procedure of this proposed approach is demonstrated.

A thermal power plant owned by China Datang Corporation is under construction and need purchase thermal power equipment. After the 10 biding documents are reviewed by the expert decision group, three alternatives (green suppliers of thermal power equipment, GS1, GS2 and GS3) are chosen for the final selection.

The criteria determination of green supplier selection largely depends on the individual companies and industry background, such as enterprise culture, management strategy and organizational structure [

Four decision makers provide the linguistic ratings to the alternatives with respect to subjective criteria using

So,

Linguistic ratings for the three alternatives with respect to subjective criteria (I5).

(I5) | DM1 | DM2 | DM3 | DM4 |
---|---|---|---|---|

TS1 | F | G | P | G |

TS2 | G | G | G | F |

TS3 | F | G | F | G |

Likewise, the aggregate fuzzy ratings of another two green supplier (GS2 and GS3) in term of criteria I5 are computed. The aggregate fuzzy ratings of the alternatives are presented in

Aggregate fuzzy decision matrix for alternatives.

Equipment Quotation (10^{6} RMB) (I1) |
Delivery Accuracy Rate (%) (I2) | Equipment Operational Costs (10^{4} RMB) (I3) |
Equipment Efficiency (%) (I4) |
---|---|---|---|

Approximately 576 | Approximately 95 | Approximately 310 | Approximately 92.5 |

Approximately 595 | Approximately 96.5 | Approximately 305 | Approximately 90.2 |

Approximately 600 | Approximately 97 | Approximately 320 | Approximately 94.3 |

Calculate the aggregated fuzzy weights of all criteria

Four decision makers provide the linguistic ratings to all criteria using

So,

Linguistic ratings for all criteria.

DM1 | DM2 | DM3 | DM4 | |
---|---|---|---|---|

I1 | H | H | M | M |

I2 | L | H | M | L |

I3 | M | L | H | H |

I4 | M | L | H | M |

I5 | L | M | H | H |

Likewise, the aggregate weights of the remaining four criteria can be computed. The aggregated fuzzy weights of all criteria are list in

Aggregate fuzzy criteria weights.

Criteria | Decision Makers | Aggregated Fuzzy Weight | |||
---|---|---|---|---|---|

DM1 | DM2 | DM3 | DM4 | ||

I1 | (0.5,0.7,1) | (0.5,0.7,1) | (0.2,0.5,0.8) | (0.2,0.5,0.8) | (0.350,0.600,0.900) |

I2 | (0,0.3,0.5) | (0.5,0.7,1) | (0.2,0.5,0.8) | (0,0.3,0.5) | (0.175,0.450,0.700) |

I3 | (0.2,0.5,0.8) | (0,0.3,0.5) | (0.5,0.7,1) | (0.5,0.7,1) | (0.300,0.550,0.825) |

I4 | (0.2,0.5,0.8) | (0,0.3,0.5) | (0.5,0.7,1) | (0.2,0.5,0.8) | (0.225,0.500,0.775) |

I5 | (0,0.3,0.5) | (0.2,0.5,0.8) | (0.5,0.7,1) | (0.5,0.7,1) | (0.300,0.550,0.825) |

Then, the normalized subjective weights _{k}_{1} = 0.2285, _{2} = 0.1674, _{3} = 0.2081, _{4} = 0.1878, _{5} = 0.2081

Calculate the weights of objective criteria by using fuzzy-entropy weighting method

For the objective criteria I1, I2, I3 and I4, the graded mean integration representation value _{ik}

Then, the entropy values and weights of objective criteria can be computed according to Equation (3) and Equation (4), and the results are list in

Objective weights of objective criteria by using fuzzy-entropy weighting method.

Criteria | I1 | I2 | I3 | I4 |
---|---|---|---|---|

Entropy value _{k} |
0.999848 | 0.999964 | 0.999813 | 0.999857 |

Objective weight | 0.2934 | 0.0687 | 0.3619 | 0.2759 |

Calculate the integrated weight of all criteria

The integrated weight _{k}_{1} = 0.2581, _{2} = 0.0443, _{3} = 0.2900, _{4}

Then, the integration weights of all criteria can be obtained according to Equation (10), _{1} = _{1} = 0.2581, _{2} = _{2} = 0.0443, _{3} = _{3} = 0.2900, _{4} = _{4} = 0.1995, _{5} = _{5} = 0.2081

According to

For benefit criteria (I2 and I4)

For I2 (Delivery accuracy rate)

_{12}= (94.3,95,96),

_{22}= (96,96.5,97),

_{32}= (96.6,97,97.8)

According to Equation (11) and Equation (12), we can get _{2} = max {96,97,97.8}, and then

For I4 (Equipment efficiency)

_{14}= (91,92.5,93),

_{24}= (90,90.2,90.8),

_{34}= (93.8,94.3,94.6)

According to Equation (11) and Equation (12), we can get _{4} = max {93,90.8,94.6} = 94.6, and then

For cost criteria (I1 and I3)

For I1 (Equipment quotation)

_{11}= (55500,57600, 58800),

_{21}= (58300,59500,60150),

_{31}= (58200,60000,61500)

According to Equation (13) and Equation (14), we can get _{1} = min {55500,58300,58200} = 55500, and then

For I3 (Equipment operational costs)

_{13}= (304,310,315),

_{23}= (302,305,308),

_{33}= (315,320,326)

According to Equation (13) and Equation (14), we can get _{1} = min {304,302,315} = 302, and then

The subjective criteria have no need for dimensionless processing.

Then, the normalized fuzzy decision matrix

The weighted normalized fuzzy decision matrix _{k}

According to Equation (15), the fuzzy positive ideal solution ^{+}^{−}^{+}^{−}

According to Equation (17) and Equation (18), the distance of each alternative from fuzzy positive ideal solution and fuzzy negative ideal solution can be computed:

According to Equation (19), the closeness coefficient (_{i}

According to the closeness coefficient _{i}

Therefore, alternative GS2, namely green supplier #2 of thermal power equipment, is the best alternative and should be selected.

With the ever-worsening pollution of the environment, the worldwide awareness of environmental protection and sustainable development are growing, and green purchasing has become an important issue for companies to gain environmental sustainability and will determine their sustainability in the long term. The environmental performance of a company is not only related to its inner environmental efforts, but also affected by the suppliers’ environmental performances. Therefore, a performance evaluation on green suppliers is necessary to select the proper supplier to cooperate with the company. Selecting green suppliers is a strategic decision for a company, which can promote its sustainable development and be more competitive in today’s global market. In this paper, a new multi-criteria decision making approach based on incorporated fuzzy set theory, entropy, and TOPSIS is proposed to evaluate and select the green suppliers of thermal power equipment under fuzzy environment. The proposed fuzzy entropy-TOPSIS approach comprises of two steps. In the first step, the alternatives are determined and the evaluation criteria for green supplier selection of thermal power equipment are identified. These criteria are equipment quotation, delivery accuracy rate, equipment operational costs, equipment efficiency, and environmental consciousness. In the second step, the decision makers provide linguistic ratings to the criteria and to the alternatives with respect to subjective criteria, and all criteria which include the objective and subjective criteria are weighted by using subjective superiority linguistic ratings and objective fuzzy entropy weighting method, and then the fuzzy-TOPSIS is employed to aggregate the ratings and rank all the green suppliers of thermal power equipment. The alternative with the highest performance score is selected. The evaluation result shows the alternative GS2 is the best green supplier of thermal power equipment.

Our proposed approach has the ability to evaluate and select the green suppliers of thermal power equipment with partial or a lack of quantitative information, and using the triangular fuzzy numbers and linguistic values can overcome the uncertainty due to human qualitative judgment. A combination of subjective weight determination and objective weight determination for evaluation criteria is employed. The fuzzy-entropy weighting method can measure the average essence of information quantity of criteria data as well as grasp the actual conditions of evaluation criteria, and the superiority linguistic ratings can reflect the experts’ thoughts and opinions. This proposed method can facilitate its implementation as a computer-based decision support system for tackling the MCDM problems in a fuzzy environment, and it can also be applied to other MCDM issues. For further research, this proposed fuzzy entropy-TOPSIS evaluation result can be compared with other fuzzy MCDM techniques like fuzzy PROMETHEE [

The obtained results can help companies perform the green supplier selection of thermal power equipment, which can promote its own sustainable development and the sustainability of China’s electric power industry to some extent.

This study is supported by the National Natural Science Foundation of China (Project number: 71373076) and the Humanities and Social Science project of the Ministry of Education of China (Project number: 11YJA790217).

The authors declare no conflict of interest.