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

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.