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

Abstract

t. 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.