A Total Order on Single Valued and Interval Valued Neutrosophic Triplets

Abstract

L.A. Zadeh (1965) proposed the concept of fuzzy subsets, which was later expanded to include intuitionistic fuzzy subsets by K.Atanassov (1983). We have come across several generalisations of sets since the birth of fuzzy sets theory, one of which is Florentine Smarandache [15] introduced the neutrosophic sets as a major category. Many real-life decision-making problems have been studied in [10], [13], [16]. In multi-criteria decision making (MCDM) situations [1], [2], [6], the ordering of neutrosophic triplets (T; I; F) is crucial. In this study, we define and analyse new membership, non-membership, and average score functions on single-valued neutrosophic triplets (T; I; F). We create a technique for ordering single valued neutrosophic triplets (SVNT) using these three functions, with the goal of achieving a total ordering on neutrosophic triplets. The total ordering on IVNT is then provided by extending these score functions and ranking mechanism to interval valued neutrosophic triplets (IVNT). A comparison is also made between the suggested method and the present ranking method in the literature.

Keywords

• neutrosophic sets
• interval valued neutrosophic triplets