Measure of Distance and Similarity for Single Valued Neutrosophic Sets with Application in Multi-attribute making decisions

Abstract

A single valued neutrosophic sets (SvNSs) is a particular case of neutrosophic set, which can handle scientific and engineering
applications in real world. Distance, similarity, entropy and cross bentropy measures of SvNSs are major tool is to solve various real world problems In the paper, an average distance measure based on Hamming and Hausdorff distance is defined for SvNSs. Similarity measure is proposed on the basis of defined averaged distance using  the relationship between distance and similarity measures. Further, one more similarity measure is defined and its validity is proved. Then a multi-attribute decision making is also established under single valued neutrosophic environment,in which attribute values are assigned to each course of action by the decision makers/experts and attribute weights are known, whereas the optimal point is defined using the decision matrix using the proposed method. Also, an algorithm is presented to determine the ranking of available course of actions on the basis of values of measure of similarity amongst optimal point and the available course of actions. Lastly, an example is used to demonstrate the application of proposed similarity measures in multi-attribute decision making.