A STUDY ON SET ALGEBRAIC OPERATIONS CHARACTERISTICS WITH INTUITIONISTIC FUZZY SUBGROUPS UNDER THE CONDITIONS OF INTUITIONISTIC FUZZY TOPOLOGICAL VECTOR SPACE - Ansari, Raza; Khan, Mushtaque (ShodhKosh: Journal of Visual and Performing Arts, 2024)
In this work, a study on intuitionistic fuzzy topology and algebra behavior of IFSGs in context of intuitionistic fuzzy topological vector spaces (IFTVS) is presented. Especially the case of normal space is discussed in terms of the union and intersection algebraic operations of level intuitionistic subgroups. The study, thus presents a special case of union and intersection among IFSGs, examining their structural constitution and impact within the larger network of IFTVS. The findings show that the nice algebraic and topological properties persist under the intersection of any level IFSGs, producing consistently well-defined algebraic and topological characteristics. The union operation does not naturally preserve subgroup structure unless certain containment conditions are satisfied, highlighting the robust dichotomy between these two operations. Theoretical justifications are tutored to elucidate these findings, underlining their efforts been made to towards future real-time mathematical and computational applications. The scope is only limited to conceptual development and formal analysis. The approaches presented and resulting conclusions are instrumental for practical model-building in fuzzy algebra. Generalized containment conditions, graded membership thresholds, fuzzy closure operators, and more could be used to further investigate IFSG families and help develop a general theory to elucidate their behavior. Moreover, the generalization of this framework to more generalized mathematical structures like IFβ-normal spaces and IF-modules can increase the practical relevance of these results through the multiple fields like topological group theory and applied fuzzy systems.