Pythagorean Fuzzy N-Soft Groups

Abstract

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