AN INTRODUCTION TO THE INDEPENDENT TOPOLOGICAL STRUCTURE GENERATED BY FUZZY SOFT $\gamma$-OPEN SETS

Abstract

In this study, we propose a new generalized fuzzy soft open set, namely the fuzzy soft $\gamma$-open set. Notably, the newly defined fuzzy soft $\gamma$-open set is a special type of fuzzy soft-pre-open set. Additionally, a diagram (Fig. 3) is used to show how fuzzy soft $\gamma$-open sets are related to various existing stronger and weaker forms of fuzzy soft-open sets. The main focus of this paper is on the autonomous topological structure produced by fuzzy soft $\gamma$-open sets. Furthermore, we introduce the concepts of fuzzy soft $\gamma$-interior and $\gamma$-closure operators, which provide another way to define fuzzy soft $\gamma$-topology. Finally, we introduce and explore fuzzy soft $\gamma$-continuity as the application of the defined notions in this regard