Structural Analysis Of Soft Influence Sets Via Bipartite Graphs

Abstract

The concept of soft sets was introduced by Dmitri Molodtsov as a mathematical tool for handling uncertainty and imprecise information, and has since been widely applied to decision-making problems involving vague or ambiguous data. In this paper, we introduce a new class of soft sets, namely soft generalized** -closed sets (briefly,  -closed sets) and soft generalized** -open sets (briefly,  -open sets), in the framework of soft topological spaces. We examine the relationships between  -closed sets and several existing classes of soft closed sets, and establish some of their fundamental properties. Furthermore, we propose a novel approach for representing soft sets by means of bipartite graphs, and show that various operations on soft sets—such as union, intersection, and logical operations—can be modeled and visualized through bipartite graph structures. And we introduce a bipartite graph representation of  -closed sets and to investigate their associated operations within this graphical framework.