Fermatean fuzzy set extensions of SAW, ARAS, and VIKOR with applications in COVID‐19 testing laboratory selection problem

Gül, Sait

The multiple attribute decision‐making models are empowered with the support of fuzzy sets such as intuitionistic, q‐rung orthopair, Pythagorean, and picture fuzzy sets, and also neutrosophic sets, etc. These concepts generate varying representation opportunities for the decision‐maker's preferences and expertise. Pythagorean and Fermatean fuzzy sets are special cases of q‐rung orthopair fuzzy set when q = 2 and q = 3, respectively. From a geometric perspective, the latter provides a broader representation domain than the former does. In this study, the emerging concept of Fermatean fuzzy set is studied in detail and three well‐known multi‐attribute evaluation methods, namely SAW, ARAS, and VIKOR are extended under Fermatean fuzzy environment. In this manner, the decision‐makers will have more freedom in specifying their preferences, thoughts, and expertise, and the abovementioned decision approaches will be able to handle this new type of data. The applicability of the propositions is shown in determining the best Covid‐19 testing laboratory which is an important topic of the ongoing global health crisis. To validate the proposed methods, a benchmark analysis covering the results of the existing Fermatean fuzzy set‐based decision methods, namely TOPSIS, WPM, and Yager aggregation operators is presented.