Bipolar Neutrosophic Projection Based Models for Multi-attribute Decision Making Problems

Bipolar neutrosophic sets are the extension of neutrosophic sets and are based on the idea of positive and negative preferences of information. Projection measure is a useful apparatus for modeling real life decision making problems. In the paper, we have defined projection, bidirectional projection and hybrid projection measures between bipolar neutrosophic sets and the proposed measures are then applied to multi-attribute decision making problems. The ratings of performance values of the alternatives with respect to the attributes are expressed by bipolar neutrosophic values. We calculate projection, bidirectional projection, and hybrid projection measures between each alternative and ideal alternative with bipolar neutrosophic information and then all the alternatives are ranked to identify best option. Finally, a numerical example is provided to demonstrate the applicability and effectiveness of the developed method. Comparison analysis with other existing methods is also provided.