(untitled) (European Journal of Pure and Applied Mathematics, 2025)
The objective of this research is to explore ternary soft sets over three initial universal sets, incorporating a parameter set, also known as the set of decision variables. Fundamental operations such as subset, superset, equality, complement, null set, and absolute set are examined, along with the union and intersection of two ternary soft sets. The study further investigates the difference and symmetric difference between two ternary soft sets, as well as the “AND” and “OR” operations, particularly in relation to the crisp points of the sets. The behavior and properties of ternary soft sets are analyzed, with examples provided for clarification. A novel mathematical structure, ternary soft topological structures, is introduced, focusing on three initial universal sets and a fixed parameter set. Key concepts such as ternary soft open sets, closed sets, closures, interiors, boundaries, and neighborhoods are defined and explored in depth. The relationships between these concepts are examined to provide a comprehensive understanding. Illustrative examples demonstrate the practical applications of these ideas. Additionally, ternary soft semi-separation axioms, along with various properties, such as ternary soft semi-regular,semi-normal, and invariance properties, including the ternary soft topological and hereditary properties, are discussed.