On Soft Separation Axioms and Their Applications on Decision-Making Problem

In this work, we introduce new types of soft separation axioms called pt-soft alpha regular and pt-soft alpha T-i-spaces (i = 0, 1, 2, 3, 4) using partial belong and total nonbelong relations between ordinary points and soft alpha-open sets. These soft separation axioms enable us to initiate new families of soft spaces and then obtain new interesting properties. We provide several examples to elucidate the relationships between them as well as their relationships with e-soft T-i, soft alpha T-i, and tt-soft alpha T-i-spaces. Also, we determine the conditions under which they are equivalent and link them with their counterparts on topological spaces. Furthermore, we prove that pt-soft alpha T-i-spaces (i = 0, 1, 2, 3, 4) are additive and topological properties and demonstrate that pt-soft alpha T-i-spaces (i=0, 1, 2) are preserved under finite product of soft spaces. Finally, we discuss an application of optimal choices using the idea of pt-soft T-i-spaces (i = 0, 1, 2) on the content of soft weak structure. We provide an algorithm of this application with an example showing how this algorithm is carried out. In fact, this study represents the first investigation of real applications of soft separation axioms.