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 singlevalued 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.