Fermatean Fuzzy Schweizer-Sklar Operators and BWM-Entropy-Based Combined Compromise Solution Approach: An Application to Green Supplier Selection

doi:10.3390/e24060776

. 2022 May 31;24(6):776.

doi: 10.3390/e24060776.

Fermatean Fuzzy Schweizer-Sklar Operators and BWM-Entropy-Based Combined Compromise Solution Approach: An Application to Green Supplier Selection

Dongmei Wei^{1

2}, Dan Meng³, Yuan Rong⁴, Yi Liu⁵, Harish Garg⁶, Dragan Pamucar⁷

Affiliations

¹ School of Computer and Software Engineering, Xihua University, Chengdu 610039, China.
² School of Computing and Artificial Intelligence, Southwestern University of Finance and Economics, Chengdu 611130, China.
³ School of Management Science and Engineering, Southwestern University of Finance and Economics, Chengdu 611130, China.
⁴ School of Management, Shanghai University, Shanghai 200444, China.
⁵ Data Recovery Key Laboratory of Sichuan Province, Neijiang Normal University, Neijiang 641100, China.
⁶ School of Mathematics, Thapar Institute of Engineering and Technology (Deemed University), Patiala 147004, India.
⁷ Department of Logistics, University of Defence in Belgrade, 11000 Belgrade, Serbia.

PMID: 35741498
PMCID: PMC9223001
DOI: 10.3390/e24060776

Free PMC article

Fermatean Fuzzy Schweizer-Sklar Operators and BWM-Entropy-Based Combined Compromise Solution Approach: An Application to Green Supplier Selection

Dongmei Wei et al. Entropy (Basel). 2022.

Free PMC article

. 2022 May 31;24(6):776.

doi: 10.3390/e24060776.

Authors

Dongmei Wei^{1

2}, Dan Meng³, Yuan Rong⁴, Yi Liu⁵, Harish Garg⁶, Dragan Pamucar⁷

Affiliations

¹ School of Computer and Software Engineering, Xihua University, Chengdu 610039, China.
² School of Computing and Artificial Intelligence, Southwestern University of Finance and Economics, Chengdu 611130, China.
³ School of Management Science and Engineering, Southwestern University of Finance and Economics, Chengdu 611130, China.
⁴ School of Management, Shanghai University, Shanghai 200444, China.
⁵ Data Recovery Key Laboratory of Sichuan Province, Neijiang Normal University, Neijiang 641100, China.
⁶ School of Mathematics, Thapar Institute of Engineering and Technology (Deemed University), Patiala 147004, India.
⁷ Department of Logistics, University of Defence in Belgrade, 11000 Belgrade, Serbia.

PMID: 35741498
PMCID: PMC9223001
DOI: 10.3390/e24060776

Abstract

The Fermatean fuzzy set (FFS) is a momentous generalization of a intuitionistic fuzzy set and a Pythagorean fuzzy set that can more accurately portray the complex vague information of elements and has stronger expert flexibility during decision analysis. The Combined Compromise Solution (CoCoSo) approach is a powerful decision-making technique to choose the ideal objective by fusing three aggregation strategies. In this paper, an integrated, multi-criteria group-decision-making (MCGDM) approach based on CoCoSo and FFS is used to assess green suppliers. To begin, several innovative operations of Fermatean fuzzy numbers based on Schweizer-Sklar norms are presented, and four aggregation operators utilizing the proposed operations are also developed. Several worthwhile properties of the advanced operations and operators are explored in detail. Next, a new Fermatean fuzzy entropy measure is propounded to determine the combined weight of criteria, in which the subjective and objective weights are computed by an improved best-and-worst method (BWM) and entropy weight approach, respectively. Furthermore, MCGDM based on CoCoSo and BWM-Entropy is brought forward and employed to sort diverse green suppliers. Lastly, the usefulness and effectiveness of the presented methodology is validated by comparison, and the stability of the developed MCGDM approach is shown by sensitivity analysis. The results shows that the introduced method is more stable during ranking of green suppliers, and the comparative results expound that the proposed method has higher universality and credibility than prior Fermatean fuzzy approaches.

Keywords: CoCoSo method; Fermatean fuzzy set; Schweizer–Sklar; entropy; green supplier selection.

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Conflict of interest statement

The authors declare no conflict of interest.

Figures

**Figure 1**
Fermatean fuzzy CoCoSo grou-decision framework.

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References

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1. Gupta S., Soni U., Kumar G. Green supplier selection using multi-criterion decision making under fuzzy environment: A case study in automotive industry. Comput. Ind. Eng. 2019;136:663–680. doi: 10.1016/j.cie.2019.07.038. - DOI
1. Liu P., Gao H., Ma J. Novel green supplier selection method by combining quality function deployment with partitioned Bonferroni mean operator in interval type-2 fuzzy environment. Inf. Sci. 2019;490:292–316. doi: 10.1016/j.ins.2019.03.079. - DOI
1. Liou J.J., Chang M.H., Lo H.W., Hsu M.H. Application of an MCDM model with data mining techniques for green supplier evaluation and selection. Appl. Soft Comput. 2021;109:107534. doi: 10.1016/j.asoc.2021.107534. - DOI
1. Fazlollahtabar H., Kazemitash N. Green supplier selection based on the information system performance evaluation using the integrated Best-Worst Method. Facta Univ. Ser. Mech. Eng. 2021;19:345–360. doi: 10.22190/FUME201125029F. - DOI

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[1] Banaeian N., Mobli H., Fahimnia B., Nielsen I.E., Omid M. Green supplier selection using fuzzy group decision making methods: A case study from the agri-food industry. Comput. Oper. Res. 2018;89:337–347. doi: 10.1016/j.cor.2016.02.015. - DOI

[2] Banaeian N., Mobli H., Fahimnia B., Nielsen I.E., Omid M. Green supplier selection using fuzzy group decision making methods: A case study from the agri-food industry. Comput. Oper. Res. 2018;89:337–347. doi: 10.1016/j.cor.2016.02.015. - DOI

[3] Gupta S., Soni U., Kumar G. Green supplier selection using multi-criterion decision making under fuzzy environment: A case study in automotive industry. Comput. Ind. Eng. 2019;136:663–680. doi: 10.1016/j.cie.2019.07.038. - DOI

[4] Gupta S., Soni U., Kumar G. Green supplier selection using multi-criterion decision making under fuzzy environment: A case study in automotive industry. Comput. Ind. Eng. 2019;136:663–680. doi: 10.1016/j.cie.2019.07.038. - DOI

[5] Liu P., Gao H., Ma J. Novel green supplier selection method by combining quality function deployment with partitioned Bonferroni mean operator in interval type-2 fuzzy environment. Inf. Sci. 2019;490:292–316. doi: 10.1016/j.ins.2019.03.079. - DOI

[6] Liu P., Gao H., Ma J. Novel green supplier selection method by combining quality function deployment with partitioned Bonferroni mean operator in interval type-2 fuzzy environment. Inf. Sci. 2019;490:292–316. doi: 10.1016/j.ins.2019.03.079. - DOI

[7] Liou J.J., Chang M.H., Lo H.W., Hsu M.H. Application of an MCDM model with data mining techniques for green supplier evaluation and selection. Appl. Soft Comput. 2021;109:107534. doi: 10.1016/j.asoc.2021.107534. - DOI

[8] Liou J.J., Chang M.H., Lo H.W., Hsu M.H. Application of an MCDM model with data mining techniques for green supplier evaluation and selection. Appl. Soft Comput. 2021;109:107534. doi: 10.1016/j.asoc.2021.107534. - DOI

[9] Fazlollahtabar H., Kazemitash N. Green supplier selection based on the information system performance evaluation using the integrated Best-Worst Method. Facta Univ. Ser. Mech. Eng. 2021;19:345–360. doi: 10.22190/FUME201125029F. - DOI

[10] Fazlollahtabar H., Kazemitash N. Green supplier selection based on the information system performance evaluation using the integrated Best-Worst Method. Facta Univ. Ser. Mech. Eng. 2021;19:345–360. doi: 10.22190/FUME201125029F. - DOI

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Fermatean Fuzzy Schweizer-Sklar Operators and BWM-Entropy-Based Combined Compromise Solution Approach: An Application to Green Supplier Selection

Affiliations

Fermatean Fuzzy Schweizer-Sklar Operators and BWM-Entropy-Based Combined Compromise Solution Approach: An Application to Green Supplier Selection

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