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A Fermatean Fuzzy ELECTRE Method for Multi-Criteria Group Decision-Making
Volume 33, Issue 1 (2022), pp. 181–224
Pub. online: 18 November 2021      Type: Research Article      Open accessOpen Access
Received
1 March 2021
Accepted
1 October 2021
Published
18 November 2021

Abstract

This paper aims to develop a Fermatean fuzzy ELECTRE method for solving multi-criteria group decision-making problems with unknown weights of decision makers and incomplete weights of criteria. First, a new distance measure between Fermatean fuzzy sets is proposed based on the Jensen–Shannon divergence. The cross entropy for Fermatean fuzzy sets is defined. Three kinds of dominance relationships for Fermatean fuzzy sets are proposed. Then, two optimization models are constructed to obtain positive ideal decision-making information and negative ideal decision-making information, respectively. Accordingly, the credibility degree of each decision maker is calculated. Decision makers’ dynamic weights are determined by their credibility degrees. Besides, to obtain the weights of criteria, an optimization model is constructed based on grey relational analysis for Fermatean fuzzy numbers. Finally, the strong, medium and weak Fermatean fuzzy concordance and discordance sets are identified to construct the Fermatean fuzzy concordance and discordance matrices, respectively. A practical case study is carried out to illustrate the feasibility and applicability of the proposed ELECTRE method. Comparative analyses are performed to demonstrate the superiority and effectiveness of the proposed ELECTRE method.

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Biographies

Zhou Li-Ping
zlp168198@163.com

L.-P. Zhou received the PhD degree in management science and engineering from Nanchang University, in 2014. He is currently an associate professor at the School of Humanities and Public Management, Jiangxi Agricultural University. His current research interests include aggregation operators, decision-making under uncertainty.

Wan Shu-Ping
shupingwan@163.com

S.-P. Wan was born in 1974. He received the PhD in control theory and control engineering from Nankai University, in 2005. He is currently a professor at the School of Information Technology, Jiangxi University of Finance and Economics. He has contributed more than 150 journal articles to professional journals, such as Information Sciences, European Journal of Operation Research, IEEE Transaction on Fuzzy Systems, Information Fusion, Knowledge Based Systems, Applied Soft Computing, and so on. His current research interests include decision analysis, fuzzy game theory, information fusion, and financial engineering.

Dong Jiu-Ying
jiuyingdong@126.com

J.-Y. Dong received the PhD degree in graph theory and combinatorial optimization from Nankai University, in 2013. She is currently an associate professor at the School of Statistics, Jiangxi University of Finance and Economics. She has contributed more than 30 journal articles to professional journals, such as Information Sciences, Discrete Mathematics, Graphs and Combinatorics, Information Fusion, and so on. Her current research interests include decision analysis, graph theory and combinatorial optimization.


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© 2022 Vilnius University
Open access article under the CC BY license.

Keywords
Fermatean fuzzy sets ELECTRE method outranking relations dynamic weights

Funding
This work was supported by the National Natural Science Foundation of China (Nos. 71740021 and 11861034), the Humanities Social Science Programming Project of Ministry of Education of China (No. 20YJA630059), the Science and Technology Project of Jiangxi Province educational department of China (No. GJJ190251), Research project on degree and postgraduate education and teaching reform in Jiangxi Province (JXYJG-2019-073).

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