Abstract

The concept of q-rung orthopair fuzzy set, where q is a positive integer, introduced by Yager, is studied in the present paper and fundamental properties of it are examined. The concept of the 1-rung orthopair fuzzy set coincides with Atanassov’s intuitionistic fuzzy set, a 2-rung orthopair fuzzy set is known as a Pythagorean fuzzy set, while a 3-rung orthopair fuzzy set is referred to as a Fermatean fuzzy set. Also the ordinary notion of topological space is extended in this work to a q-rung orthopair fuzzy environment, as well as the fundamental properties and concepts of convergence, continuity, compactness and of Hausdorff topological space. All these contents are illustrated by suitable examples.