A Total Ordering on n-Valued Refined Neutrosophic Sets using Dictionary Ranking based on Total ordering on n - Valued Neutrosophic Tuplets

Abstract

The notion of fuzzy subsets was first introduced by Zadeh in 1965, and was later extended to intuitionistic fuzzy subsets by Atanassov in 1983. Since the inception of fuzzy set theory, we have encountered a number of generalizations of sets, one of which is neutrosophic sets introduced by Smarandache [15]. Later neutrosophic sets was generalized into interval valued neutrosophic, triangular valued neutrosophic, trapezoidal valued neutrosophic and n - valued refined neutrosophic sets in the literature [19, 31, 33, 35]. Further, the ordering on single-valued neutrosophic triplets and interval valued neutrosophic triplets have been proposed by Smarandache in [16] and they are further extended to total ordering on interval valued neutrosophic triplets in [32].The total ordering of n - valued neutrosophic tuplets is very significant in multi-criteria decision making (MCDM) involving n - valued neutrosophic tuplets. Hence, in this paper, different methods for ordering n - valued neutrosophic tuplets (NVNT) are developed with the goal of achieving a total ordering on n - valued neutrosophic tuplets and the applicability of the proposed methods is shown by illustrative examples in MCDM problems involving n - valued neutrosophic tuplets. Further, a total ordering algorithm for n - valued refined neutrosophic sets by following dictionary ranking method at the final stage is developed using those proposed total ordering methods on n - valued neutrosophic tuplets.

Keywords

• n-valued refined neutrosophic sets
• dictionary
• neutrosophic tuplets
• uncertainty