TOPSIS for Solving Multi-Attribute Decision Making Problems under Bi-Polar Neutrosophic Environment

The paper investigates a technique for order preference by similarity to ideal solution (TOPSIS) method to solve multi-attribute decision making problems with bipolar neutrosophic information. We define Hamming distance function and Euclidean distance function to determine the distance between bipolar neutrosophic numbers. In the decision making situation, the rating of performance values of the alternatives with respect to the attributes are provided by the decision maker in terms of bipolar neutrosophic numbers. The weights of the attributes are determined using maximizing deviation method. We define bipolar neutrosophic relative positive ideal solution (BNRPIS) and bipolar neutrosophic relative negative ideal solution (BNRNIS). Then, the ranking order of the alternatives is obtained by TOPSIS method and most desirable alternative is selected. Finally, a numerical example for car selection is solved to demonstrate the applicability and effectiveness of the proposed approach and comparison with other existing method is also provided.