Pythagorean fuzzy N-Soft groups

Abstract

We elaborate in this paper a new structure pythagorean fuzzy $N$-soft groups which is the generalization of intuitionistic fuzzy soft group initiated by Karaaslan in 2013. In Pythagorean fuzzy N-soft sets concepts of fuzzy sets, soft sets, N-soft sets, fuzzy soft sets, intuitionistic fuzzy sets, intuitionistic fuzzy soft sets, Pythagorean fuzzy sets, Pythagorean fuzzy soft sets are generalized. We also talk about some elementary basic concepts and operations on Pythagorean fuzzy N-soft sets with the assistance of illusions. We additionally define three different sorts of complements for Pythagorean fuzzy N-soft sets and examined a few outcomes not hold in Pythagorean fuzzy N-soft sets complements as they hold in crisp set hypothesis with the assistance of counter examples. We further talked about {$(\alpha, \beta, \gamma)$-cut of Pythagorean fuzzy N-soft set and their properties}. We likewise talk about some essential properties of Pythagorean fuzzy N-soft groups like groupoid, normal group, left and right cosets, $(\alpha, \beta,\gamma)$-cut subgroups and some fundamental outcomes identified with these terms. Pythagorean fuzzy N-soft sets is increasingly efficient and adaptable model to manage uncertainties. The proposed models of Pythagorean fuzzy N-soft groups can defeat a few disadvantages of the existing statures.