On Consistent and Weak Transitive Neutrosophic Fuzzy Matrices

Authors

K. Radhika
M. Kavitha
K. Thirumalai
R. Geethanjaliyadav
N. Buvaneswari
V. Kamalakannan

Abstract

This paper delves into the properties of two specific types of Neutrosophic Fuzzy Matrices (NFM) namely consistent and weakly transitive NFM. A significant focus is placed on nilpotent and transitive NFM, highlighting their critical role in the analysis. It is demonstrated that these two types of matrices are controllable, and a formula is derived for determining the canonical form of a weakly transitive NFM. To support and clarify the findings, counterexamples are provided throughout the discussion. We introduce an operation on NFM, referred to as the Gödel implication operator. Utilizing this operator, we establish several significant results for NFM, with a particular emphasis on properties related to pre-orders. Our analysis focuses primarily on reflexive and transitive NFM, enabling us to derive meaningful insights. Additionally, we demonstrate a method for constructing an idempotent NFM from any given matrices.

Recommended Citation

Radhika, K.; M. Kavitha; K. Thirumalai; R. Geethanjaliyadav; N. Buvaneswari; and V. Kamalakannan. "On Consistent and Weak Transitive Neutrosophic Fuzzy Matrices." Neutrosophic Sets and Systems 79, 1 (2025). https://digitalrepository.unm.edu/nss_journal/vol79/iss1/34