Applications of nth Power Root Fuzzy Sets in Multicriteria Decision Making

An n(th) power root fuzzy set is a useful extension of a fuzzy set for expressing uncertain data. Because of their wider range of showing membership grades, n(th) power root fuzzy sets can cover more ambiguous situations than intuitionistic fuzzy sets. In this article, we present several novel operations on n(th) power root fuzzy sets, as well as their various features. Besides, we develop a new weighted aggregated operator, namely, n(th) power root fuzzy weighted power average (nPR-FWPA) over n(th) power root fuzzy sets to deal with choice information and show some of their basic properties. In addition, we define a scoring function for n(th) power root fuzzy sets ranking. Furthermore, we use this operator to determine the optimal location for constructing a home and demonstrate how we may choose the best alternative by comparing aggregate outputs using score values. Finally, we compare the nPR-FWPA operator outcomes to those of other well-known operators.