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Soft Cushioned and Soft Star Refinements of Open Covers in Intuitionistic Fuzzy Soft Topological Spaces and Their Covering Dimension

. ABDULGAWAD. A. Q. AL-QUBATI and ABDO QAHIS


Abstract

The concept of intuitionistic fuzzy soft topological spaces has emerged as a natural extension that integrates the ideas of intuitionistic fuzzy sets (IFS) and soft sets, providing a flexible framework for addressing complex problems characterized by uncertainty and imprecision. Within this context, open coverings and their refined forms such as cushioned refinements and star refinements play a crucial role in understanding the topological structure of spaces, particularly in relation to the notion of covering dimension.  In this paper, we introduce the notions of intuitionistic fuzzy soft cushioned refinement, intuitionistic fuzzy soft star refinement, and intuitionistic fuzzy soft strongly star refinement of coverings within the framework of intuitionistic fuzzy soft topological spaces. These concepts are utilized to establish fundamental results concerning the covering dimension of intuitionistic fuzzy soft normal topological spaces. The obtained results contribute to a deeper understanding of covering properties in intuitionistic fuzzy soft topology and extend several classical topological concepts to the intuitionistic fuzzy soft framework.

 

Keywords. Intuitionistic fuzzy soft set, intuitionistic fuzzy soft topology, intuitionistic fuzzy soft star refinements, covering dimension.

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