Soft Graphs: A Comprehensive Survey

Molodtsov’s introduction of soft set theory marked a significant advancement in managing uncertainty, addressing the limitations of classical set theory in handling imprecise and vague information. This versatile framework has since been extensively explored, leading to sophisticated models for decision-making and medical diagnosis. Building on the principles of soft set theory, the concept of soft graphs was introduced to enhance the representation and analysis of uncertain information. Soft graphs incorporate parametrization, enabling dynamic modeling of graph-based relationships across various contexts and applications. This innovative approach creates multiple, adaptable representations that better reflect real-world complexities. This survey paper provides a comprehensive guide to the evolution of soft graphs, starting with an overview of the origins and basic concepts of soft set theory, highlighting its strengths and applications. It then delves into the development of soft graphs, explaining their theoretical foundations and methodologies. The paper explores how soft graphs have been used to model and solve problems in different domains, emphasizing their flexibility and effectiveness. By examining both foundational concepts and contemporary research advancements, this paper serves as a valuable resource for researchers interested in the applications of soft set theory and soft graphs in managing uncertainty and imprecision.