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

Dhrubajyoti Bhattacharjee     (Department of Mathematics, NIT Agartala, 7990035, West Tripura, India)
Jayasree Chakraborty     (Department of Mathematics, NIT Agartala, 7990035, West Tripura, India)
Baby Bhattacharya     (Department of Mathematics, NIT Agartala, 7990035, West Tripura, India)
Md Mirazul Hoque     (Department of Mathematics, NIT Agartala, 7990035, West Tripura, India)

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.

Keywords


fs\(\gamma\)-open sets, fs\(\gamma\)-quasi neighbourhood, fs\(\gamma\)-topology, fs-independent topology, fs\(\gamma\)-continuity

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DOI: http://dx.doi.org/10.15826/umj.2025.2.004

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