Ranking of single-valued neutrosophic numbers through the index of optimism and its reasonable properties

Abstract

In this paper an innovative method of ranking neutrosophic number based on the notions of value and ambiguity of a single-valued neutrosophic number is being developed. The method is based on the convex combination of value and ambiguity of truth-membership function with the sum of values and ambiguities of indeterminacy-membership and falsity-membership functions. This convex combination is also termed as an index of optimism. The index of optimism, $$\lambda =1$$ , is termed as optimistic decision-maker as it considers the value and the ambiguity of the truth-membership function, ignoring the contributions from indeterminacy-membership and falsity-membership functions. Similarly, the index of optimism, $$\lambda =0$$ , is termed as pessimistic decision-maker as it considers the values and the ambiguities of the indeterminacy-membership and falsity-membership functions, ignoring the contribution from truth-membership function. Further, the index of optimism, $$\lambda =0.5$$ , is termed as moderate decision-maker as it considers the values and the ambiguities of all the membership functions. The approach is a novel as it completely oath to follow the reasonable properties of a ranking method. It is worth to mention that the current approach consistently ranks the single-valued neutrosophic numbers as well as their corresponding images.