Total Order Based Similarity Measures for Single Valued and  Interval Valued Neutrosophic Triplets

Lakshmana Gomathi Nayagam V; Daniel P; Bharanidharan R

Authors

Lakshmana Gomathi Nayagam V Department of Mathematics (DST-FIST Sponsored), National Institute of Technology, Tiruchirappalli-620015, INDIA;
Daniel P Department of Mathematics, St. Xavier’s College (Autonomous), Palayamkottai, Trunelveli-627002, INDIA;
Bharanidharan R Department of Mathematics (DST-FIST Sponsored), National Institute of Technology, Tiruchirappalli-620015, INDIA;

Keywords:

Neutrosophic sets ; Similarity measure ; Total ordering ; MCDM

Abstract

Smarandeche (1995) introduced neutrosophic sets to address difficulties involving imprecise, inde
terminate, and inconsistent information, as a generalization of Zadeh’s fuzzy set and Atanassov’s intuitionistic
fuzzy set. It paved the way for that Smarandeche’s single valued neutrosophic triplets (SVNT) and interval
valued neutrosophic triplets IVNT for modelling real time applications based on such information. In this pa
per, we introduce the S1-similarity measure for SVNT and the S2-similarity measure for IVNT, through which
S1-ordering algorithm for SVNT and the S2-ordering algorithm for IVNT are obtained, respectively. Further,
we demonstrate that the S1-ordering algorithm and the S2-ordering algorithm inherit a total order on the set
of all SVNTs and IVNTs, respectively. Finally, we present numerical illustrations and a comparative analysis
to demonstrate that the proposed similarity measures outperform previous methods.

DOI: 10.5281/zenodo.15467786