A Fermatean Fuzzy ELECTRE Method for Multi-Criteria Group Decision-Making

This paper aims to develop a Fermatean fuzzy ELECTRE method for solving multicriteria 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 decisionmaking 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.

Automated summary

This paper proposes a Fermatean fuzzy ELECTRE method for solving multicriteria group decision-making problems with unknown weights of decision makers and incomplete weights of criteria. The paper introduces a new distance measure and defines the cross entropy for Fermatean fuzzy sets. Optimization models are constructed to obtain ideal decision-making information and calculate the credibility degree of each decision maker. The weights of criteria are determined using grey relational analysis. Experimental results show the feasibility and effectiveness of the proposed method.