Research Article

Complete Lattice Representation of Fuzzy Soft Topology through Matrices

Abstract

This paper develops a matrix-theoretic framework for the study of fuzzy soft topological spaces. A correspondence between fuzzy soft topologies and collections of fuzzy soft matrices is established, demonstrating that a fuzzy soft topology is equivalent to a complete distributive lattice of fuzzy soft matrices. This correspondence enables topological properties to be investigated through algebraic matrix operations. An order relation on fuzzy soft matrices is introduced and its fundamental properties are examined. Matrix-valued lower and upper operators are then defined to characterize fuzzy soft interior and fuzzy soft closure in an algebraic setting. The developed operators provide concise matrix representations for interior, closure, regular open, regular closed, semi-open, pre-open, α-open, β open, b-open, ∗b-open, b#-open and their corresponding closed classes. Several equivalence theorems are established, showing that these generalized fuzzy soft topological sets can be completely characterized by matrix inequalities and lattice identities. The proposed approach unifies topological and algebraic viewpoints, simplifies the representation of fuzzy soft topological concepts, and provides a systematic foundation for further investigations in fuzzy soft topology, lattice theory, and matrix-based computational methods.