An introduction to the independent topological structure generated by fuzzy soft $\gamma$-open sets

Dhrubajyoti Bhattacharjee, Jayasree Chakraborty, Baby Bhattacharya, Md. Mirazul Hoque

National Institute of Technology Agartala

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. \ref{fig3}) 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

Language: English

DOI: 10.15826/umj.2025.2.004

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