δβ-Open sets in Pythagorean fuzzy nano topological spaces

Abstract

The purpose of this paper is to define and study a new class of sets called Pythagorean fuzzy nano δ (resp. δ pre, δ semi, δα and δβ)-open sets in Pythagorean fuzzy nano topological spaces. Analyse the basic properties of Pythagorean fuzzy nano δ (resp. δ pre, δ semi, δα and δβ)-open (resp. closed) sets. We also used them to introduce the new notions like Pythagorean fuzzy nano δ (resp. δ pre, δ semi, δα and δβ)-closure (resp. interior) and investigate their relations with already existing well known sets. We apply entropy measure for decision making problem of selecting the optimum wastewater treatment method for the dying factories based on the required criteria.