Soft algebraic structures embedded with soft members and soft elements: an abstract approach

Abstract

As a new area of study in pure mathematics, the theory of soft sets is expanding by redefining fundamental ideas as algebraic structures, such as soft groups, soft rings, and soft fields. It also finds applications in other domains, regarding data analysis and decision-making. This study manipulates soft members and soft elements to explore soft structures from a traditional point of view, making it easier to comprehend soft algebraic structures. The soft inverse of a soft member and the soft identity member are generalized for any soft group, and a method to count the number of possible soft subgroups of a soft group is also provided.