On Fuzzy Filter Topological Group Spaces

Basim Mohammed  Melgat

Basim Mohammed Melgat College of Education Department of Mathematic, Al-Qasim Green University, Babylon, Iraq

Keywords: fuzzy filter, fuzzy topological group, fuzzy nbhd filter, fuzzy open filter set, fuzzy closed filter set, mixed fuzzy filter fuzzy topological group

Abstract

The work investigates a new idea in fuzzy topological group spaces that combines fuzzy open and closed filter sets: Mixed Fuzzy Filter Topological Group Spaces. There is a research gap in the study of mixed fuzzy topologies, as prior work concentrated on individual fuzzy topologies. This study investigates properties such as fuzzy continuity and open filter sets by defining and analyzing fuzzy filter topological groups using mathematical structures and proofs. The goal is to introduce a bi-fuzzy filter structure in order to generalize fuzzy topological groupings. The findings show that mixed fuzzy filter topological groups can be formed, which has ramifications for further research into applying this concept to rings and other algebraic structures.

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