Bipolar Soft Sets: Relations between Them and Ordinary Points and Their Applications

Bipolar soft set is formulated by two soft sets; one of them provides us the positive information and the other provides us the negative information. The philosophy of bipolarity is that human judgment is based on two sides, positive and negative, and we choose the one which is stronger. In this paper, we introduce novel belong and nonbelong relations between a bipolar soft set and an ordinary point. These relations are considered as one of the unique characteristics of bipolar soft sets which are somewhat expression of the degrees of membership and nonmembership of an element. We discuss essential properties and derive the sufficient conditions of some equivalence of these relations. We also define the concept of soft mappings between two classes of bipolar soft sets and study the behaviors of an ordinary point under these soft mappings with respect to all relations introduced herein. Then, we apply bipolar soft sets to build an optimal choice application. We give an algorithm of this application and show the method for implementing this algorithm by an illustrative example. In conclusion, it can be noted that the relations defined herein give another viewpoint to explore the concepts of bipolar soft topology, in particular, soft separation axioms and soft covers.