A Study of Soft Sets with Soft Members and Soft Elements: A New Approach

Soft set theory has gained significant worth since its emergence. Soft algebraic structures have been discussed in numerous researches with the help of sub algebraic structures. Properties of soft algebraic structures, somehow, are hard to study in parallel to the study of the classical approach of algebraic structures. In this study, we perform an extensive inspection of the concept of soft elements and soft members in soft sets. By using soft members and soft elements, soft sets operations and soft sets relations are discussed which enables us to study the concept of soft algebraic structures with this new approach. To elaborate on the new introduced concept, Cayley's table for the soft group has been constructed from where some properties of the soft groups are verified.