Rough approximations of bipolar soft sets by soft relations and their application in decision making

The rough set theory is an effective method for analyzing data vagueness, while bipolar soft sets can handle data ambiguity and bipolarity in many cases. In this article, we apply Pawlak's concept of rough sets to the bipolar soft sets and introduce the rough bipolar soft sets by defining a rough approximation of a bipolar soft set in a generalized soft approximation space. We study their structural properties and discuss how the soft binary relation affects the rough approximations of a bipolar soft set. Two sorts of bipolar soft topologies induced by soft binary relation are examined. We additionally discuss some similarity relations between the bipolar soft sets, depending on their roughness. Such bipolar soft sets are very useful in the problems related to decision-making such as supplier selection problem, purchase problem, portfolio selection, site selection problem etc. A methodology has been introduced for this purpose and two algorithms are presented based upon the ongoing notions of foresets and aftersets respectively. These algorithms determine the best/worst choices by considering rough approximations over two universes i.e. the universe of objects and universe of parameters under a single framework of rough bipolar soft sets.