A Topological Approach to Soft Covering Approximation Space

TL;DR

This paper explores the topological properties of soft covering rough sets, establishing conditions for approximation operators to behave as interior and closure operators, and linking topology concepts with soft set approximations.

Contribution

It introduces a topological perspective to soft covering rough sets, providing new methods for generating topologies and analyzing their relationship with approximation operators.

Findings

Soft covering lower approximation can act as an interior operator under certain conditions.

Soft covering upper approximation can serve as a closure operator in specific scenarios.

New methods for generating topologies from soft covering structures are proposed.

Abstract

Theories of rough sets and soft sets are powerful mathematical tools for modelling various types of vagueness. Hybrid model combining a rough set with a soft set which is called soft rough set proposed by Feng et al. [3] in 2010. In this paper, we study soft covering based rough sets from the topological view. We present under which conditions soft covering lower approximation operation become interior operator and the soft covering upper approximation become closure operator. Also some new methods for generating topologies are obtained. Finally, we study the relationship between concepts of topology and soft covering lower and soft covering upper approximations.