Soft Hyperstructures and Their Applications

Abstract

The real world is full of uncertainties, which we require appropriate mathematical structures to model and handle them. One such structure is the soft set, which can be combined with various algebraic and topological structures. The paper discusses how soft sets and hyperstructures can be combined to create new soft structures that can handle uncertainty and imprecision in algebraic structures. Soft sets are mappings from parameters to subsets of a universal set, and they can model fuzzy concepts. Hyperstructures are generalizations of classical algebraic structures, where the composition of two elements is a set instead of a single element. They can capture complex and diverse phenomena that cannot be modeled by single-valued operations. The paper gives examples of soft structures, such as soft polygroups, soft topological polygroups, soft topological soft polygroups and their applications in mathematics and science. The paper aims to show the usefulness and versatility of soft structures in dealing with uncertainty and imprecision in algebraic structures. We will define the concept of soft topological soft polygroups and examine its characteristics.