Bipolar soft ideal rough set with applications in COVID-19

Abstract

Bipolar soft rough set represents an important mathematical model to deal with uncertainty. This theory represents a link between bipolar soft set and rough set theories. This study introduced the concept of topological bipolar soft set by combining a bipolar soft set with topologies. Also, the topological structure of bipolar soft rough set has been discussed by defining the bipolar soft rough topology. The main objective of this paper is to present some solutions to develop and modify the approach of the bipolar soft rough sets. Two kinds of bipolar soft ideal approximation operators which represent extensions of bipolar soft rough approximation operator have been presented. Moreover, a new kind of bipolar approximation space via two ideals, called bipolar soft biideal approximation space, was introduced and studied by two different methods. Their properties are discussed and the relationships between these methods and the previous ones are proposed. The importance of these methods is reducing the vagueness of uncertainty areas by increasing the bipolar lower approximations and decreasing the bipolar upper approximations. Also, the bipolar soft biideal rough sets represent two opinions instead of one opinion. Finally, an application in multicriteria group decision making (MCGDM) in COVID-19 by using bipolar soft ideal rough sets is suggested by using two methods.