# A Study on Green Supplier Selection in Dynamic Environment

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## Abstract

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## 1. Introduction

## 2. Literature Review

_{2}) emissions) were considered during the selection.

## 3. PT3-Based Green Supplier Selection Decision-Making Model

#### 3.1. The Supplier Selection Evaluation Index System

#### 3.2. Green Supplier Decision Model Based on the Third-Generation Prospect Theory

- (1)
- When the index ${I}_{l}\in {I}^{K}$, record ${x}_{il}^{t}={x}_{il}^{\text{'}t}$, in which ${{x}^{\prime}}_{il}^{t}$ is a real number, $i\in M,l\in {N}^{K},t\in Y$. $M=\{1\uff0c2\uff0c\cdots ,m\}$.
- (2)
- When the index ${I}_{l}\in {I}^{L}$, record ${x}_{il}^{t}={\overline{x}}_{il}^{t}$, in which ${\overline{x}}_{il}^{t}$ is an interval number, i.e., ${\overline{x}}_{il}^{t}=[{x}_{il}^{t1},{x}_{il}^{t2}]$. In reality, the index value takes a random value from the interval $[{x}_{il}^{t1},{x}_{il}^{t2}]$ in uniform distribution, with the probability density function as:$${f}_{il}^{t}(x)=\{\begin{array}{c}\frac{1}{{x}_{il}^{t2}-{x}_{il}^{t1}},{x}_{il}^{t1}\le x\le {x}_{il}^{t2}\\ 0,other\end{array},i\in M,l\in {N}^{L},t\in Y,N=\{1,2,\cdots ,n\}|$$
- (3)
- When the index ${I}_{l}\in {I}^{F}$, record ${x}_{il}^{t}={\tilde{x}}_{il}^{t}$, in which ${\tilde{x}}_{il}^{t}$ is the intuitive trapezoidal fuzzy number, that is, ${\tilde{x}}_{il}^{t}=\langle \left(\left[{a}_{il}^{t},{b}_{il}^{t},{c}_{il}^{t},{d}_{il}^{t}\right];{\varphi}_{il}^{t}(x)\right),\left(\left[{a}_{il1}^{t},{b}_{il}^{t},{c}_{il}^{t},{d}_{il1}^{t}\right];{\tau}_{il}^{t}(x)\right)\rangle $, $0\le {\varphi}_{il}^{t}(x)\le 1$, $0\le {\tau}_{il}^{t}(x)\le 1$, ${\varphi}_{il}^{t}(x)+{\tau}_{il}^{t}(x)\le 1$, ${a}_{il}^{t}$, ${b}_{il}^{t}$, ${c}_{il}^{t}$, ${d}_{il}^{t}$, ${a}_{il1}^{t}$, ${d}_{il1}^{t}$ $\in R$, and its membership function ${\varphi}_{il}^{t}(x)$ is:$${\varphi}_{il}^{t}(x)=\{\begin{array}{c}\frac{x-{a}_{il}^{t}}{{b}_{il}^{t}-{a}_{il}^{t}},{a}_{il}^{t}\le x\le {b}_{il}^{t}\\ {\varphi}_{il}^{t},{b}_{il}^{t}\le x\le {c}_{il}^{t}\\ \frac{{d}_{il}^{t}-x}{{d}_{il}^{t}-{c}_{il}^{t}},{c}_{il}^{t}\le x\le {d}_{il}^{t}\\ 0\end{array}i\in M,l\in {N}^{F},t\in Y$$

#### 3.3. Calculation of Gains and Losses

#### 3.4. Prospect Value Calculation and Scheme Sorting

## 4. Weight Determination of Candidate Enterprises

#### 4.1. Generalized Optimal Ordinal Number

**Definition**

**1.**

**Definition**

**2.**

**Definition**

**3.**

_{l}at period t. ${v}_{{}_{i}}^{{}_{t}}$ represents the timing weight of the candidate green supplier.

#### 4.2. Determine the Index Weight Based on the Correlation Coefficient Method

#### 4.3. Timing Weight Based on Penalty Mechanism

#### 4.4. Supplier Selection Process Description

- Step 1: Develop the index system and index value of the reference point according to the enterprise development status.
- Step 2: Solve the corresponding gain and loss value according to the form and formula of each index value.
- Step 3: Convert the gain and loss value into a prospect decision matrix based on the gain and loss matrix and the corresponding probability weight.
- Step 4: Determine the weight of the generalized optimal ordinal number.
- Step 5: Determine the timing weight of the penalty mechanism.
- Step 6: Calculate the comprehensive prospect value of each candidate green supplier, according to the prospect decision matrix, the weight of the generalized optimal ordinal number, and the timing weight of the penalty mechanism.
- Step 7: Select the partner green supplier based on the comprehensive prospect value.

## 5. Case Study

## 6. Discussion and Comparative Analysis

## 7. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Appendix A

Index Type | Relationship between the Expectation and the Reference Point | Calculation of the Gain and Loss Values (Gain Value ${\mathit{G}}_{\mathit{i}\mathit{l}}^{\mathit{t}}$; Loss Value ${\mathit{L}}_{\mathit{i}\mathit{l}}^{\mathit{t}}$) |
---|---|---|

${I}_{l}\in {I}^{K}$ | ${{x}^{\prime}}_{il}^{t}<{e}_{l}^{t}$ | ${G}_{il}^{t}=\{\begin{array}{c}0i\in M,l\in {N}^{K}\cap {N}_{1},t\in Y\\ {e}_{il}^{t}-{{x}^{\prime}}_{il}^{t},i\in M,l\in {N}^{K}\cap {N}_{2},t\in Y\end{array}$ (A1) ${L}_{il}^{t}=\{\begin{array}{c}{{x}^{\prime}}_{il}^{t}-{e}_{il}^{t}i\in M,l\in {N}^{K}\cap {N}_{1},t\in Y\\ 0,i\in M,l\in {N}^{K}\cap {N}_{2},t\in Y\end{array}$ (A2) |

${{x}^{\prime}}_{il}^{t}\ge {e}_{l}^{t}$ | ${G}_{il}^{t}=\{\begin{array}{c}{{x}^{\prime}}_{il}^{t}-{e}_{il}^{t}i\in M,l\in {N}^{K}\cap {N}_{1},t\in Y\\ 0,i\in M,l\in {N}^{K}\cap {N}_{2},t\in Y\end{array}$ (A3) ${L}_{il}^{t}=\{\begin{array}{c}0i\in M,l\in {N}^{K}\cap {N}_{1},t\in Y\\ {e}_{il}^{t}-{{x}^{\prime}}_{il}^{t},i\in M,l\in {N}^{K}\cap {N}_{2},t\in Y\end{array}$ (A4) |

Index Type | Relationship between the Expectation and the Reference Point | Calculation of the Gain and Loss Value(Gain Value ${\mathit{G}}_{\mathit{i}\mathit{l}}^{\mathit{t}}$; Loss Value ${\mathit{L}}_{\mathit{i}\mathit{l}}^{\mathit{t}}$) |
---|---|---|

${I}_{l}\in {I}^{I}$ | ${x}_{il}^{t2}\le {e}_{l}^{t}$ | ${G}_{il}^{t}=\{\begin{array}{c}0i\in M,l\in {N}^{K}\cap {N}_{1},t\in Y\\ {\displaystyle {\int}_{{x}_{il}^{t1}}^{{x}_{il}^{t2}}({e}_{l}^{t}-x){f}_{il}^{t}(x)dx},i\in M,l\in {N}^{K}\cap {N}_{2},t\in Y\end{array}$ (A5) ${L}_{il}^{t}=\{\begin{array}{c}{\displaystyle {\int}_{{x}_{il}^{t1}}^{{x}_{il}^{t2}}(x-{e}_{l}^{t}){f}_{il}^{t}(x)dx}i\in M,l\in {N}^{K}\cap {N}_{2},t\in Y\\ 0,i\in M,l\in {N}^{K}\cap {N}_{2},t\in Y\end{array}$ (A6) |

${x}_{il}^{t1}\le {\overline{x}}_{il}^{t}\le {x}_{il}^{t2}$ | ${G}_{il}^{t}=\{\begin{array}{c}{\displaystyle {\int}_{{e}_{l}^{t}}^{{x}_{il}^{t2}}(x-{e}_{l}^{t}){f}_{il}^{t}(x)dx}i\in M,l\in {N}^{K}\cap {N}_{1},t\in Y\\ {\displaystyle {\int}_{{x}_{il}^{t1}}^{{e}_{l}^{t}}({e}_{l}^{t}-x){f}_{il}^{t}(x)dx},i\in M,l\in {N}^{K}\cap {N}_{2},t\in Y\end{array}$ (A7) ${L}_{il}^{t}=\{\begin{array}{c}{\displaystyle {\int}_{{x}_{il}^{t1}}^{{e}_{l}^{t}}(x-{e}_{l}^{t}){f}_{il}^{t}(x)dx}i\in M,l\in {N}^{K}\cap {N}_{1},t\in Y\\ {\displaystyle {\int}_{{e}_{l}^{t}}^{{x}_{il}^{tz}}({e}_{l}^{t}-x){f}_{il}^{t}(x)dx},i\in M,l\in {N}^{K}\cap {N}_{2},t\in Y\end{array}$ (A8) | |

${x}_{il}^{t1}\ge {e}_{l}^{t}$ | ${G}_{il}^{t}=\{\begin{array}{c}{\displaystyle {\int}_{{x}_{il}^{t1}}^{{x}_{il}^{tz}}(x-{e}_{l}^{t}){f}_{il}^{t}(x)dx}i\in M,l\in {N}^{K}\cap {N}_{1},t\in Y\\ 0,i\in M,l\in {N}^{K}\cap {N}_{2},t\in Y\end{array}$ (A9) ${L}_{il}^{t}=\{\begin{array}{c}0i\in M,l\in {N}^{K}\cap {N}_{1},t\in Y\\ {\displaystyle {\int}_{{x}_{il}^{t1}}^{{x}_{il}^{t2}}({e}_{l}^{t}-x){f}_{il}^{t}(x)dx},i\in M,l\in {N}^{K}\cap {N}_{2},t\in Y\end{array}$ (A10) |

Index Type | Relationship between the Expectation and the Reference Point | Calculation of the Gain and Loss Value (Gain Value ${\mathit{G}}_{\mathit{i}\mathit{l}}^{\mathit{t}}$; Loss Value ${\mathit{L}}_{\mathit{i}\mathit{l}}^{\mathit{t}}$) |
---|---|---|

${I}_{l}\in {I}^{F}$ | ${e}_{l}^{t}\le {a}_{il}^{t}$ | ${G}_{il}^{t}=\{\begin{array}{c}{\displaystyle {\int}_{{a}_{il}^{t}}^{{d}_{ij}^{t}}(x-{e}_{l}^{t}){\varphi}_{il}^{t}(x)dx}i\in M,l\in {N}^{K}\cap {N}_{1},t\in Y\\ 0,i\in M,l\in {N}^{K}\cap {N}_{2},t\in Y\end{array}$ (A11) ${L}_{il}^{t}=\{\begin{array}{c}0i\in M,l\in {N}^{K}\cap {N}_{1},t\in Y\\ {\displaystyle {\int}_{{a}_{il}^{t1}}^{{d}_{il}^{tz}}({e}_{l}^{t}-x){\varphi}_{il}^{t}(x)dx},i\in M,l\in {N}^{K}\cap {N}_{2},t\in Y\end{array}$ (A12) |

${a}_{il}^{t}\le {e}_{l}^{t}\le {d}_{il}^{t}$ | ${G}_{il}^{t}=\{\begin{array}{c}{\displaystyle {\int}_{{e}_{l}^{t}}^{{d}_{il}^{t}}(x-{e}_{l}^{t}){\varphi}_{il}^{t}(x)dx}i\in M,l\in {N}^{K}\cap {N}_{1},t\in Y\\ {\displaystyle {\int}_{{a}_{ij}^{t}}^{{e}_{j}^{t}}({e}_{j}^{t}-x){\varphi}_{il}^{t}(x)dx},i\in M,l\in {N}^{K}\cap {N}_{2},t\in Y\end{array}$ (A13) ${L}_{il}^{t}=\{\begin{array}{c}{\displaystyle {\int}_{{a}_{il}^{1}}^{{e}_{l}^{t}}(x-{e}_{l}^{t}){\varphi}_{il}^{t}(x)dx}i\in M,l\in {N}^{K}\cap {N}_{1},t\in Y\\ {\displaystyle {\int}_{{e}_{l}^{t}}^{{d}_{il}^{t2}}({e}_{l}^{t}-x){\varphi}_{il}^{t}(x)dx},i\in M,l\in {N}^{K}\cap {N}_{2},t\in Y\end{array}$ (A14) | |

${e}_{l}^{t}\ge {d}_{il}^{t}$ | ${G}_{il}^{t}=\{\begin{array}{c}0i\in M,l\in {N}^{K}\cap {N}_{1},t\in Y\\ {\displaystyle {\int}_{{a}_{il}^{t1}}^{{d}_{il}^{t2}}({e}_{l}^{t}-x){\varphi}_{il}^{t}(x)dx},i\in M,l\in {N}^{K}\cap {N}_{2},t\in Y\end{array}$ (A15) ${L}_{il}^{t}=\{\begin{array}{c}{\displaystyle {\int}_{{a}_{il}^{t}}^{{d}_{il}^{t}}(x-{e}_{l}^{t}){\varphi}_{il}^{t}(x)dx}i\in M,l\in {N}^{K}\cap {N}_{1},t\in Y\\ 0,i\in M,l\in {N}^{K}\cap {N}_{2},t\in Y\end{array}$ (A16) |

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Index Type | Index Name |
---|---|

Cost index | Product prices: the prices of raw materials include both the price of the purchase itself and the cost of handling all kinds of emergencies in the production process. |

Defective rate: the defective rate of raw materials directly affects the total purchase of the manufacturer. The provision of qualified raw materials is a basic requirement for manufacturer. | |

Delivery cycle: the supply time of suppliers directly affects the production schedule and the manufacturer’s plan. | |

Inventory costs: the suppliers’ level of inventory costs directly affects the direct costs of manufacturers. | |

Poor environmental records: mainly refers to a history of environmental problems, with a bad record of legal penalties. | |

Profitability index | After-sales service level: includes the performance of service commitments, the attitude and efficiency of after-sales service, customer satisfaction, etc. |

Product environmental protection design ability: mainly refers to the product recycling and environmental protection ability. | |

Research and innovation ability: it is not only critical to the survival of enterprises, but is also a key factor for manufacturing enterprises when choosing suppliers. | |

Environmental efficiency: refers to the “three wastes” (waste gas, waste water and waste residues) emissions, and energy usage of the suppliers | |

Resource recycling capacity: mainly refers to the ability of supplier to handle the defective product, the recycling goods, etc. |

Variable | Meaning |
---|---|

$S=\{{S}_{1},{S}_{2},\dots ,{S}_{i},\dots ,{S}_{m}\}$ | A collection of alternative green suppliers |

$I=\{{I}_{1},{I}_{2},\dots ,{I}_{l},\dots ,{I}_{n}\}$ | A collection of indexes |

${N}_{1}$ and ${N}_{2}$ | Profitability indexes, cost indexes |

$w=({w}_{1},{w}_{2},\dots ,{w}_{n}),{w}_{l}\ge 0\begin{array}{c}\end{array}{\displaystyle \sum _{l=1}^{n}{w}_{l}}=1$ | The weight vector of the indexes |

$Y=\{1,2,\dots ,t,\dots y\}$ | Natural state set |

${p}_{t},{p}_{t}\ge 0$ and $\sum _{t=1}^{y}{p}_{t}=1$ | The occurrence probability of state t |

$E=({e}_{1},{e}_{2},\dots ,{e}_{n})$ | The vector of indicator expectation |

${e}_{l}=({e}_{l}^{1},{e}_{l}^{2},\dots ,{e}_{l}^{y})$ | The decision makers’ expectations for index I_{l} |

${e}_{l}^{t}$ | In the state t, the decision maker’s expectations for the index I_{l} |

$X={\left[{x}_{il}^{t}\right]}_{n*m}$ | Risk decision matrix |

${x}_{il}^{t}$ | In the state t, the green supplier S_{i} has the risk decision result for the index I_{l} |

${I}^{K}=\{{I}_{1},{I}_{2},\dots ,{I}_{{l}_{1}}\}$ | An indicator set whose value is clear numbers |

${I}^{L}=\{{I}_{{l}_{1}+1},{I}_{{l}_{1}+2},\dots ,{I}_{{l}_{2}}\}$ | An indicator set whose value is interval numbers |

${I}^{F}=\{{I}_{{l}_{2}+1},{I}_{{l}_{2}+2},\dots ,{I}_{n}\}$ | An indicator set whose value is intuitionistic fuzzy number |

${N}^{K}=\{1,2,\dots ,{l}_{1}\}$ | Subscripted collections of index subset I^{K} |

${N}^{L}=\{{l}_{1}+1,{l}_{1}+2,\dots ,{l}_{2}\}$ | Subscripted collections of index subset I^{L} |

${N}^{F}=\{{l}_{2}+1,{l}_{2}+2,\dots ,n\}$ | Subscripted collections of index subset I^{F} |

Index | Statue | Probability | Green Suppliers | Exception | |||
---|---|---|---|---|---|---|---|

S_{1} | S_{2} | S_{3} | S_{4} | ||||

I_{1} | A_{1} | 0.3 | 10 | 12 | 11 | 13 | 10 |

A_{2} | 0.3 | 12 | 13 | 10 | 10 | 11 | |

A_{3} | 0.2 | 13 | 11 | 13 | 12 | 12 | |

A_{4} | 0.2 | 11 | 14 | 12 | 11 | 12 | |

I_{2} | A_{1} | 0.3 | 0.05 | 0.02 | 0.05 | 0.08 | 0.05 |

A_{2} | 0.3 | 0.05 | 0.07 | 0.05 | 0.07 | 0.06 | |

A_{3} | 0.2 | 0.07 | 0.1 | 0.15 | 0.09 | 0.1 | |

A_{4} | 0.2 | 0.09 | 0.11 | 0.11 | 0.1 | 0.1 | |

I_{3} | A_{1} | 0.3 | 9 | 10 | 8 | 11 | 9 |

A_{2} | 0.3 | 10 | 11 | 12 | 10 | 10 | |

A_{3} | 0.2 | 11 | 9 | 10 | 12 | 11 | |

A_{4} | 0.2 | 10 | 11 | 12 | 9 | 11 | |

I_{4} | A_{1} | 0.3 | 9 | 10 | 11 | 10 | 9 |

A_{2} | 0.3 | 10 | 11 | 9 | 11 | 10 | |

A_{3} | 0.2 | 8 | 12 | 10 | 12 | 10 | |

A_{4} | 0.2 | 11 | 10 | 12 | 9 | 10 | |

I_{5} | A_{1} | 0.3 | (0.05, 0.06) | (0.04, 0.05) | (0.05, 0.06) | (0.03, 0.04) | 0.04 |

A_{2} | 0.3 | (0.02, 0.03) | (0.02, 0.03) | (0.03, 0.04) | (0.03, 0.05) | 0.03 | |

A_{3} | 0.2 | (0.04, 0.05) | (0.02, 0.03) | (0.05, 0.06) | (0.04, 0.05) | 0.05 | |

A_{4} | 0.2 | (0.03, 0.04) | (0.03, 0.04) | (0.02, 0.04) | (0.01, 0.03) | 0.02 | |

I_{6} | A_{1} | 0.3 | ([5, 6, 7, 8]; 0.7, 0.3) | ([5, 7, 8, 9]; 00.8, 0.2) | ([3, 4, 5, 6]; 0.6, 0.4) | ([4, 5, 6, 7]; 0.8, 0.2) | 5 |

A_{2} | 0.3 | ([4, 6, 7, 8]; 0.6, 0.3) | ([5, 6, 8, 9]; 0.8, 0.2) | ([3, 4, 7, 8]; 0.6, 0.4) | ([5, 6, 7, 8]; 0.8,0.2) | 5 | |

A_{3} | 0.2 | ([4, 5, 6, 7]; 0.8, 0.2) | ([3, 4, 5, 6]; 0.8, 0.2) | ([2, 4, 5, 6]; 0.6, 0.3) | ([1, 3, 4, 5]; 0.6, 0.3) | 5 | |

A_{4} | 0.2 | ([2, 3, 5, 6]; 0.6, 0.3) | ([2, 4, 5, 6]; 0.6, 0.3) | ([4, 5, 6, 7]; 0.7, 0.2) | ([6, 7, 8, 9]; 0.8, 0.1) | 6 | |

I_{7} | A_{1} | 0.3 | ([4, 5, 7, 8]; 0.8, 0.2) | ([4, 5, 6, 7]; 0.8, 0.2) | ([3, 4, 7, 8]; 0.6, 0.4) | ([4, 6, 7, 8]; 0.6, 0.3) | 4 |

A_{2} | 0.3 | ([4, 5, 6, 7]; 0.8, 0.2) | ([3, 5, 6, 7]; 0.8, 0.2) | ([2, 4, 6, 7]; 0.8, 0.2) | ([3, 4, 6, 7]; 0.6, 0.2) | 5 | |

A_{3} | 0.2 | ([2, 3, 4, 5]; 0.6, 0.3) | ([5, 6, 8, 9]; 0.8, 0.2) | ([6, 7, 8, 9]; 0.8, 0.1) | ([5, 6, 7, 8]; 0.7, 0.2) | 6 | |

A_{4} | 0.2 | ([5, 6, 7, 8]; 0.8, 0.1) | ([3, 4, 5, 6]; 0.6, 0.2) | ([6, 7, 8, 9]; 0.8, 0.1) | ([6, 7, 8, 9]; 0.8, 0.2) | 6 | |

I_{8} | A_{1} | 0.3 | ([5, 6, 7, 8]; 0.7, 0.3) | ([4, 5, 6, 7]; 0.7, 0.2) | ([4, 5, 6, 7]; 0.8, 2) | ([2, 4, 5, 6]; 0.6, 0.3) | 6 |

A_{2} | 0.3 | ([3, 4, 5, 6]; 0.6, 0.2) | ([3, 4, 5, 6]; 0.8, 0.1) | ([4, 5, 6, 7]; 0.7, 0.2) | ([3, 4, 5, 6]; 0.6, 0.2) | 5 | |

A_{3} | 0.2 | ([5, 6, 8, 9]; 0.8, 0.2) | ([3, 5, 6, 7]; 0.8, 0.2) | ([4, 5, 6, 7]; 0.7, 0.2) | ([3, 5, 6, 7]; 0.7, 0.2) | 5 | |

A_{4} | 0.2 | ([5, 6, 7, 8]; 0.8, 0.1) | ([4, 5, 6, 7]; 0.8, 0.2) | ([2, 3, 4, 5]; 0.6, 0.4) | ([3, 5, 6, 7]; 0.8, 0.2) | 5 | |

I_{9} | A_{1} | 0.3 | ([4, 5, 6, 7]; 0.7, 0.2) | ([3, 4, 7, 8]; 0.6, 0.3) | ([6, 7, 8, 9]; 0.8, 0.1) | ([3, 4, 5, 6]; 0.5, 0.4) | 6 |

A_{2} | 0.3 | ([3, 4, 5, 6]; 0.6, 0.3) | ([2, 3, 4, 5]; 0.6, 0.3) | ([4, 5, 6, 7]; 0.8, 0.2) | ([3, 4, 6, 7]; 0.8,0.2) | 4 | |

A_{3} | 0.2 | ([5, 6, 7, 8]; 0.7, 0.3) | ([6, 7, 8, 9]; 0.8, 0.1) | ([3, 4, 7, 8]; 0.6, 0.4) | ([3, 4, 5, 6]; 0.6, 0.4) | 5 | |

A_{4} | 0.2 | ([3, 5, 6, 7]; 0.8, 0.2) | ([3, 4, 5, 6]; 0.6, 0.4) | ([3, 5, 6, 7]; 0.8, 0.2) | ([6, 7, 8, 9]; 0.8, 0.1) | 6 | |

I_{10} | A_{1} | 0.3 | ([4, 5, 6, 7]; 0.8, 0.2) | ([3, 4, 7, 8]; 0.6, 0.3) | ([2, 3, 4, 5]; 0.6, 0.3) | ([4, 5, 6, 7]; 0.8, 0.2) | 6 |

A_{2} | 0.3 | ([3, 4, 7, 8]; 0.6, 0.3) | ([6, 7, 8, 9]; 0.8, 0.1) | ([5, 6, 7, 8]; 0.8, 0.2) | ([3, 4, 6, 7]; 0.7, 0.2) | 5 | |

A_{3} | 0.2 | ([6, 7, 8, 9]; 0.8, 0.1) | ([3, 4, 5, 6]; 0.6, 0.2) | ([5, 6, 7, 8]; 0.7, 0.2) | ([4, 5, 6, 7]; 0.7, 0.2) | 7 | |

A_{4} | 0.2 | ([2, 3, 4, 5]; 0.7, 0.3) | ([6, 7, 8, 9]; 0.8, 0.1) | ([2, 3, 4, 5]; 0.6, 0.3) | ([5, 6, 7, 8]; 0.8, 0.2) | 5 |

Index | Statue | Probability | Suppliers (Prospect Value of Index) | |||
---|---|---|---|---|---|---|

S_{1} | S_{2} | S_{3} | S_{4} | |||

I_{1} | A_{1} | 0.02342 | 0.00000 | −1.35644 | −0.73705 | −1.93803 |

A_{2} | 0.02778 | −0.73705 | −1.35644 | 0.31837 | 0.31837 | |

A_{3} | 0.02503 | −0.57831 | 0.26076 | −0.57831 | 0.00000 | |

A_{4} | 0.02793 | 0.26076 | −1.06430 | 0.00000 | 0.26076 | |

I_{2} | A_{1} | 0.02608 | 0.00000 | 0.01455 | 0.00000 | −0.03368 |

A_{2} | 0.02896 | 0.00553 | −0.01281 | 0.00553 | −0.01281 | |

A_{3} | 0.02426 | 0.01192 | 0.00000 | −0.04142 | 0.00453 | |

A_{4} | 0.02519 | 0.00453 | −0.01005 | −0.01005 | 0.00000 | |

I_{3} | A_{1} | 0.02384 | 0.00000 | −0.73705 | 0.31837 | −1.35644 |

A_{2} | 0.02775 | 0.00000 | −0.73705 | −1.35644 | 0.00000 | |

A_{3} | 0.02417 | 0.00000 | 0.47990 | 0.26076 | −0.57831 | |

A_{4} | 0.02395 | 0.26076 | 0.00000 | −0.57831 | 0.47990 | |

I_{4} | A_{1} | 0.02538 | 0.00000 | −0.73705 | −1.35644 | −0.73705 |

A_{2} | 0.02485 | 0.00000 | −0.73705 | 0.31837 | −0.73705 | |

A_{3} | 0.02449 | 0.47990 | −1.06430 | 0.00000 | −1.06430 | |

A_{4} | 0.02409 | −0.57831 | 0.00000 | −1.06430 | 0.26076 | |

I_{5} | A_{1} | 0.02557 | −0.01830 | −0.00696 | −0.01830 | 0.00301 |

A_{2} | 0.02811 | 0.00301 | 0.00301 | −0.00696 | −0.01281 | |

A_{3} | 0.02607 | 0.00246 | 0.01015 | −0.00546 | 0.00246 | |

A_{4} | 0.02595 | −0.01436 | −0.01436 | −0.01850 | −0.00163 | |

I_{6} | A_{1} | 0.02358 | 0.72558 | 1.31227 | −0.79169 | 0.25325 |

A_{2} | 0.02377 | 1.01138 | 1.35835 | 0.20373 | 0.76301 | |

A_{3} | 0.02390 | 0.21267 | −0.64137 | −1.07268 | 0.00000 | |

A_{4} | 0.02536 | 0.00000 | 0.00000 | −0.62847 | 0.62495 | |

I_{7} | A_{1} | 0.02387 | 1.26596 | 0.76301 | 1.89386 | 1.19607 |

A_{2} | 0.02377 | 0.25325 | −0.11030 | −1.04971 | −0.47233 | |

A_{3} | 0.02407 | 0.00000 | 0.83133 | 0.62495 | 0.32107 | |

A_{4} | 0.02805 | 0.20154 | −0.11953 | 0.62495 | 0.62495 | |

I_{8} | A_{1} | 0.02380 | 0.23966 | −0.80721 | −0.82297 | 0.00000 |

A_{2} | 0.02478 | −0.79169 | −0.82297 | 0.23966 | −0.79169 | |

A_{3} | 0.02353 | 1.11257 | −0.07258 | 0.20154 | −0.08371 | |

A_{4} | 0.02399 | 0.62495 | 0.21267 | 0.00000 | −0.07258 | |

I_{9} | A_{1} | 0.02338 | −0.80721 | −1.84648 | 0.76301 | 0.00000 |

A_{2} | 0.02405 | 0.22601 | −0.79169 | 0.76301 | 1.00858 | |

A_{3} | 0.02386 | 0.59429 | 0.97966 | 0.19956 | −0.61575 | |

A_{4} | 0.02393 | −1.09904 | 0.00000 | −1.09904 | 0.62495 | |

I_{10} | A_{1} | 0.02513 | −0.82297 | −1.84648 | 0.00000 | −0.82297 |

A_{2} | 0.02364 | 0.20373 | 1.19607 | 0.76301 | −0.47233 | |

A_{3} | 0.02585 | 0.21267 | 0.00000 | −0.62847 | 0.00000 | |

A_{4} | 0.02480 | 0.00000 | 0.97966 | 0.00000 | 0.62495 |

Index | Statue | Probability | Suppliers (Penalty Function) | |||
---|---|---|---|---|---|---|

S_{1} | S_{2} | S_{3} | S_{4} | |||

I_{1} | A_{1} | 0.02342 | 1.00000 | 0.98394 | 1.00000 | 0.95419 |

A_{2} | 0.02778 | 0.98318 | 0.94497 | 1.00000 | 1.00000 | |

A_{3} | 0.02503 | 0.98181 | 1.00000 | 0.98348 | 1.00000 | |

A_{4} | 0.02793 | 1.00000 | 0.94529 | 0.98192 | 1.00000 | |

I_{2} | A_{1} | 0.02608 | 1.00000 | 1.00000 | 1.00000 | 0.94754 |

A_{2} | 0.02896 | 1.00000 | 0.97684 | 1.00000 | 0.97855 | |

A_{3} | 0.02426 | 1.00000 | 0.98130 | 0.95116 | 1.00000 | |

A_{4} | 0.02519 | 1.00000 | 0.98147 | 0.97693 | 1.00000 | |

I_{3} | A_{1} | 0.02384 | 1.00000 | 0.98491 | 1.00000 | 0.95226 |

A_{2} | 0.02775 | 1.00000 | 0.98052 | 0.94285 | 1.00000 | |

A_{3} | 0.02417 | 0.98316 | 1.00000 | 1.00000 | 0.95652 | |

A_{4} | 0.02395 | 1.00000 | 0.98036 | 0.95086 | 1.00000 | |

I_{4} | A_{1} | 0.02538 | 1.00000 | 1.00000 | 0.95037 | 1.00000 |

A_{2} | 0.02485 | 1.00000 | 0.98474 | 1.00000 | 0.98388 | |

A_{3} | 0.02449 | 1.00000 | 0.98362 | 1.00000 | 0.98475 | |

A_{4} | 0.02409 | 0.98352 | 1.00000 | 0.95619 | 1.00000 | |

I_{5} | A_{1} | 0.02557 | 0.98290 | 1.00000 | 0.98409 | 1.00000 |

A_{2} | 0.02811 | 1.00000 | 1.00000 | 0.98033 | 0.94548 | |

A_{3} | 0.02607 | 1.00000 | 1.00000 | 0.94650 | 1.00000 | |

A_{4} | 0.02595 | 1.00000 | 1.00000 | 0.95045 | 1.00000 | |

I_{6} | A_{1} | 0.02358 | 1.00000 | 1.00000 | 0.95370 | 0.98645 |

A_{2} | 0.02377 | 1.00000 | 1.00000 | 0.95232 | 0.98089 | |

A_{3} | 0.02390 | 1.00000 | 0.98618 | 0.95564 | 1.00000 | |

A_{4} | 0.02536 | 1.00000 | 1.00000 | 0.94987 | 1.00000 | |

I_{7} | A_{1} | 0.02387 | 1.00000 | 0.95376 | 1.00000 | 0.98426 |

A_{2} | 0.02377 | 1.00000 | 1.00000 | 0.95645 | 0.97876 | |

A_{3} | 0.02407 | 0.95366 | 1.00000 | 1.00000 | 0.98271 | |

A_{4} | 0.02805 | 0.98307 | 0.94543 | 1.00000 | 1.00000 | |

I_{8} | A_{1} | 0.02380 | 1.00000 | 0.98433 | 0.95211 | 1.00000 |

A_{2} | 0.02478 | 1.00000 | 0.95162 | 1.00000 | 1.00000 | |

A_{3} | 0.02353 | 1.00000 | 0.98595 | 1.00000 | 0.95533 | |

A_{4} | 0.02399 | 1.00000 | 1.00000 | 0.98237 | 0.95494 | |

I_{9} | A_{1} | 0.02338 | 0.98611 | 0.95830 | 1.00000 | 1.00000 |

A_{2} | 0.02405 | 0.98565 | 0.95609 | 1.00000 | 1.00000 | |

A_{3} | 0.02386 | 1.00000 | 1.00000 | 0.98673 | 0.95205 | |

A_{4} | 0.02393 | 0.98076 | 1.00000 | 0.98335 | 1.00000 | |

I_{10} | A_{1} | 0.02513 | 1.00000 | 0.95240 | 1.00000 | 1.00000 |

A_{2} | 0.02364 | 0.98226 | 1.00000 | 1.00000 | 0.95614 | |

A_{3} | 0.02585 | 1.00000 | 1.00000 | 0.94947 | 1.00000 | |

A_{4} | 0.02480 | 0.98167 | 1.00000 | 0.98095 | 1.00000 |

S_{1} | S_{2} | S_{3} | S_{4} | |
---|---|---|---|---|

A_{1} | 0.69793 | 0.69663 | 0.69832 | 0.69667 |

A_{2} | 0.14829 | 0.14755 | 0.14770 | 0.14860 |

A_{3} | 0.08680 | 0.08814 | 0.08669 | 0.08714 |

A_{4} | 0.06045 | 0.06079 | 0.05994 | 0.06138 |

Value of the Time Attenuation Factor $\mathit{\phi}$ | Comprehensive Prospect Value of Suppliers | Results | |||
---|---|---|---|---|---|

${\mathit{S}}_{1}$ | ${\mathit{S}}_{2}$ | ${\mathit{S}}_{3}$ | ${\mathit{S}}_{4}$ | ||

$\phi =1$ | 0.01489 | −0.09507 | −0.0186 | −0.06297 | ${S}_{1}\succ {S}_{3}\succ {S}_{4}\succ {S}_{2}$ |

$\phi =2$ | 0.01299 | −0.09601 | −0.01982 | −0.05846 | ${S}_{1}\succ {S}_{3}\succ {S}_{4}\succ {S}_{2}$ |

$\phi =3$ | 0.01306 | −0.08817 | −0.02007 | −0.05228 | ${S}_{1}\succ {S}_{3}\succ {S}_{4}\succ {S}_{2}$ |

$\phi =4$ | 0.01314 | −0.08251 | −0.02036 | −0.04781 | ${S}_{1}\succ {S}_{3}\succ {S}_{4}\succ {S}_{2}$ |

**Table 8.**Comparison result of the proposed method with the Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) and the variable weight dynamic multi-attribute method.

Method | Evaluation Results |
---|---|

TOPSIS | ${S}_{1}\succ {S}_{3}\succ {S}_{4}\succ {S}_{2}$ |

Dynamic multi-attribute decision-making method | ${S}_{1}\succ {S}_{3}\succ {S}_{2}\succ {S}_{4}$ |

Generalized Ordinal Number Based on the Third Generation Prospect Theory | ${S}_{1}\succ {S}_{3}\succ {S}_{4}\succ {S}_{2}$ |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Song, W.; Chen, Z.; Liu, A.; Zhu, Q.; Zhao, W.; Tsai, S.-B.; Lu, H.
A Study on Green Supplier Selection in Dynamic Environment. *Sustainability* **2018**, *10*, 1226.
https://doi.org/10.3390/su10041226

**AMA Style**

Song W, Chen Z, Liu A, Zhu Q, Zhao W, Tsai S-B, Lu H.
A Study on Green Supplier Selection in Dynamic Environment. *Sustainability*. 2018; 10(4):1226.
https://doi.org/10.3390/su10041226

**Chicago/Turabian Style**

Song, Wei, Zhiya Chen, Aijun Liu, Qiuyun Zhu, Wei Zhao, Sang-Bing Tsai, and Hui Lu.
2018. "A Study on Green Supplier Selection in Dynamic Environment" *Sustainability* 10, no. 4: 1226.
https://doi.org/10.3390/su10041226