Separation Axioms and Their Descriptions Within the Framework of Fuzzy Soft Topology Defined on Fuzzy Soft Sets

In recent years, fuzzy soft topology has emerged as a powerful approach that contributes significantly to advancing practical applications in uncertain environments, especially in information systems design, predictive modeling, and decision-making. The structure of fuzzy soft topology, defined over fuzzy soft sets as a universal set instead of a crisp universal set, was introduced and discussed. This article aims to develop and present a comprehensive study of this structure in more depth by investigating new concepts, properties, and related findings, supported by illustrative examples. We also explore several forms and instances of this type of fuzzy soft topologies. The focus of this article is the exploration of new classes of separation and regularity axioms in the context of these types of fuzzy soft topology. We study these classes, establish their key properties, and reveal the interconnections between them. The relationships between the presented separation axioms and those in the induced crisp and soft topologies are examined. Moreover, we demonstrate that the separation and regularity axioms have the harmonic and hereditary properties. The new concepts, examples, and systematic investigation of the fuzzy soft separation and regularity axioms with their interrelationships achieved in this study contribute to the development of the theoretical foundation for the structure of topology defined over fuzzy soft sets. Moreover, our results not only deepen the understanding of this framework but also pave the way for its improved applications, especially in dealing with uncertain cases in real-life problems.