n,m ^th Power Root Fuzzy Set and Its Applications to Topology and Decision-Making

Abstract

One of the most helpful fuzzy set extensions for dealing with information uncertainties is an n th power root fuzzy set. In light of this, in this paper, we define an n,m th power root fuzzy set, which is a new type of fuzzy set extension and introduce their relationship with n-rung orthopair fuzzy set, n th power root fuzzy set and n,m-rung orthopair fuzzy set. There is a symmetry between the values of this membership and non-membership functions. To broaden the scope of the decision-making problems, any power function scales are used here. When disputing the symmetry between two or more objects, the innovative concept of an n,m th power root fuzzy set over dual universes is more flexible than the current notion of an intuitionistic fuzzy set, as well as Pythagorean fuzzy set. Then, for the n,m th power root fuzzy sets, we present the essential set of operations as well as their varied characteristics. In addition, we develop the idea of n,m th power root fuzzy topology and study its fundamental properties. Furthermore, we describe the concept of disconnected n,m th power root fuzzy sets after introducing separated n,m th power root fuzzy sets. Moreover, we thoroughly investigate and characterize n,m th power root fuzzy continuous maps. Also we build T 0 and T 1 in n,m th power root fuzzy topology and find their connections. Finally, we construct a new concept of relation in n,m th power root fuzzy set, and based on sufficient experience, we provide the candidate's decision-making technique via the proposed relation to determine the suitability of companies to applicants.

Novel Approach to Multi-Criteria Decision-Making Based on the n,mPR-Fuzzy Weighted Power Average Operator

“…The concept of the n,m-th power root fuzzy set (n,mPR-FS) was demonstrated by Saeed and Ibrahim [40], who also provided its fundamental set of operations. It is more likely to be used in uncertain situations than other types of fuzzy sets due to its wider range of displayed membership grades.…”