Extending COPRAS Method with Linguistic Fermatean Fuzzy Sets and Hamy Mean Operators

The utilization of linguistic variables is of vital importance for qualitative information processing in mathematical modelling and decision making under uncertainty. The primary purpose of our study is to introduce a novel structure by the fusion of Fermatean fuzzy sets and linguistic term sets. This hybrid structure is termed as the linguistic Fermatean fuzzy set which can be employed for dealing with decision-making problems involving qualitative information. Several fundamental operations of linguistic Fermatean fuzzy sets are introduced. Furthermore, we present four classes of linguistic Fermatean fuzzy Hamy mean operators, namely, the linguistic Fermatean fuzzy Hamy mean operator, the linguistic Fermatean fuzzy dual Hamy mean operator, the linguistic Fermatean fuzzy weighted Hamy mean operator, and the linguistic Fermatean fuzzy weighted dual Hamy mean operator. Some basic properties of these linguistic Fermatean fuzzy Hamy mean operators are examined as well. In addition, we develop a linguistic Fermatean fuzzy extension of the COPRAS method. We also propose a novel approach to multi-attribute group decision making with linguistic Fermatean fuzzy information. With our proposed methods, we solve two practical problems regarding food company ranking and green supplier selection, respectively. Finally, the efficacy of our developed method is validated through a comparative analysis with existing methods.