Structure Model of Fuzzy Soft Homotopy Theory

Abstract

   The paper aims to introduce a new concept of fuzzy soft homotopy (FSH) within the framework of fuzzy soft topological space (FSTS). The research provides a definition of the fuzzy soft set (FSS). Additionally, we define continuity in FSTSs and prove the main properties of this continuity. We also present the concept of fuzzy soft path homotopy as a flexible growth of classical homotopy, and it is proven that it forms a soft fuzzy equivalence relation. This work contributes to strengthening the topological foundations of fuzzy soft spaces and provides an analytical framework applicable to modeling complex systems characterized by high degrees of vagueness and uncertainty.