n,m^{<italic>th</italic>} 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 $\text{n}^{th}$ power root fuzzy set. In light of this, in this paper, we define an n, $\text{m}^{th}$ power root fuzzy set, which is a new type of fuzzy set extension and introduce their relationship with n-rung orthopair fuzzy set, $\text{n}^{th}$ 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, $\text{m}^{th}$ 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, $\text{m}^{th}$ 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, $\text{m}^{th}$ power root fuzzy topology and study its fundamental properties. Furthermore, we describe the concept of disconnected n, $\text{m}^{th}$ power root fuzzy sets after introducing separated n, $\text{m}^{th}$ power root fuzzy sets. Moreover, we thoroughly investigate and characterize n, $\text{m}^{th}$ power root fuzzy continuous maps. Also we build $T_{0}$ and $T_{1}$ in n, $\text{m}^{th}$ power root fuzzy topology and find their connections. Finally, we construct a new concept of relation in n, $\text{m}^{th}$ 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.

Keywords

• n,mPR-fuzzy sets
• operations
• n,mPR-fuzzy topology
• separated n,mPR-FSs
• connected n,mPR-FS
• n,mPR-fuzzy continuous maps