( 3 , 4 ) -fuzzy sets and their topological spaces

Abstract

The aim of this paper is to introduce the concept of \((3, 4)\)-fuzzy sets. We compare \((3, 4)\)-fuzzy sets with intuitionistic fuzzy sets, Pythagorean fuzzy sets, and Fermatean fuzzy sets. We focus on the complement of \((3, 4)\)-fuzzy sets. We construct some of the fundamental set of operations of the \((3, 4)\)-fuzzy sets. Due to their larger range of describing membership grades, \((3, 4)\)-fuzzy sets can deal with more uncertain situations than other types of fuzzy sets. For ranking \((3, 4)\)-fuzzy sets, we define a score function and an accuracy function. In addition, we introduce the concept of \((3, 4)\)-fuzzy topological space. Ultimately, we define \((3, 4)\)-fuzzy continuity of a map defined between \((3, 4)\)-fuzzy topological spaces and we characterize this concept.