Abstract
A Fermatean fuzzy set (FRFS) is the extension of a fuzzy set, an intuitionistic fuzzy set, and a Pythagorean fuzzy set, and is used in different fields. Unlike other fuzzy structures, the sum of cubes of membership grades in FRFSs approximates a unit interval, increasing uncertainty. In this study, we intend to provide unique operational rules and aggregation operators (AOs) inside a Fermatean fuzzy environment. To develop a fair remedy for the membership degree and non-membership degree features of “Fermatean fuzzy numbers (FRFNs)”, our solution introduces new neutral or fair operating principles, which include the concept of proportional distribution. Based on the suggested operating principles, we provide the “Fermatean fuzzy fairly weighted average operator and the Fermatean fuzzy fairly ordered weighted averaging operator”. Our suggested AOs provide more generalized, reliable, and exact data than previous techniques. Combining the recommended AOs with multiple decision-makers and partial weight information under FRFSs, we also devised a technique for “multi-criteria decision-making”. To illustrate the application of our novel method, we provide an example of the algorithm’s effectiveness in addressing decision-making challenges.
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