Pairwise Approach to Neutrosophic Soft Bi-Topological Spaces: Exploring Neutrosophic Soft Open Sets and Their Real-Life Applications

In this article, eight new definitions are introduced in the context of neutrosophic soft bi-topological spaces with respect to the soft points of the space. Among these new definitions, one important concept known as the soft open set is selected for a pairwise discussion of different structures. These structures include separation axioms, subspaces, the connections between separation axioms and closures, results concerning interiors and closures, the product of separation axioms, and their relationships with neutrosophic soft coordinate spaces regarding soft points. Finally, the most significant structure known as entropy is discussed, and based on this structure, an example related to engineering is presented. In this example, to achieve effective risk supervision in the field of engineering, certain risks are classified along with specific parameters, and these risks are evaluated by a team of expert engineers.