Bipolar neutrosophic sets and their application based on multi-criteria decision making problems

In this paper, we introduce concept of bipolar neutrosophic set and its some operations. Also, we propose score, certainty and accuracy functions to compare the bipolar neutrosophic sets. Then, we develop the bipolar neutrosophic weighted average operator (A_w) and bipolar neutrosophic weighted geometric operator (G_w) to aggregate the bipolar neutrosophic information. Furthermore, based on the (A_w) and (G_W) operators and the score, certainty and accuracy functions, we develop a bipolar neutrosophic multiple criteria decision-making approach, in which the evaluation values of alternatives on the attributes take the form of bipolar neutrosophic numbers to select the most desirable one(s). Finally, a numerical example of the method was given to demonstrate the application and effectiveness of the developed method.