Minimal structure approximation space and some of its application

Abstract

Topological concepts play an important role in applications and solving real-life problems. Among of these concepts are neighbourhood and minimal structure. In this paper, we introduce a new space-based on a generalized system with a binary relation on a nonempty set by using the concept of a minimal structure, which is called a minimal structure approximation space (briefly, MSAS), and study some of its properties. Also, we compare the advantages of MSAS with neighbourhood approximation space which are based on the same starting point, and apply the concept of MSAS in some examples of chemistry to extraction and reduct the information. Finally, we investigate the concepts of the separation axioms on MSAS and study some of its properties in the information system as the process of approximation of information.