New approach of the neighborhood structure of fuzzy points

Abstract

This paper provides a comparative analysis of the fuzzy Q-neighborhood and the fuzzy neighborhood system of a fuzzy point. Specifically, we investigate the relationship between the elements of these systems when both are defined at the same fuzzy point. We address questions such as: how are these elements interconnected, and which system contains the other? Furthermore, we give the dual of the fuzzy Q-neighborhood system, which is named the fuzzy DQ-neighborhood system, and prove that these two systems are not equivalent. Finally, we examine the properties of these systems to determine whether they satisfy the conditions of fuzzy topology, Supra topology, or filter theory.