Rough fuzzy bipolar soft sets and application in decision-making problems

The rough set theory is a successful tool to study the vagueness in data, while the fuzzy bipolar soft sets have ability to handle the uncertainty, as well as bipolarity of the information in many situations. We connect the Pawlak's rough sets with the fuzzy bipolar soft sets and introduce the concept of rough fuzzy bipolar soft sets. We also examine some structural properties of rough fuzzy bipolar soft sets and study the effects of the equivalence relation in Pawlak approximation space on the roughness of the fuzzy bipolar soft sets. We also discuss some similarity relations among the fuzzy bipolar soft sets, based on their roughness. At the end, an application of the rough fuzzy bipolar soft sets in a decision-making problem is discussed and an algorithm for this application is proposed, supported by an example.