Harran University, Art and Science Faculty, Department of Mathematics, Şanlıurfa
Abstract
Mathematical modelling has been developed for the solution of many complex problems that are incomplete and vagueness. One of these modelling is soft set theory, which has reached a very wide study potential in recent years. The soft set theory, proposed by Molodtsov, is seen as an effective mathematical tool to deal with uncertainty. This theory has been applied to various fields that involve uncertainty, such as information systems, decision-making problems, optimization theory, algebraic structures, and mathematical analysis.This study explores the interplay between soft set theory and the algebraic structure of epigroups by introducing the notion of soft epigroups. Foundational properties of soft epigroups are developed, along with key characterizations that underpin their structure. Furthermore, the study constructs the category of soft epigroups, providing a categorical framework for their analysis. The concept of soft subepigroup is also introduced, and several structural properties pertaining to these substructures are investigated in detail.
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