On Consistent and Weak Transitive Neutrosophic Fuzzy  Matrices

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

Authors

K. Radhika Department of Mathematics, Rajah Serfoji Government College (Autonomous) (Affiliated to Bharathidasan University, Tiruchirappalli), Thanjavur - 613005, Tamilnadu, India
M.Kavitha Department of Mathematics, Panimalar Engineering College, Chennai, Tamilnadu, India
K. Thirumalai Department of Mathematics, Saveetha Engineering College, Chennai - 602105, Tamilnadu, India.
R. Geethanjaliyadav Department of Mathematics, Rajalakshmi institute of Technology, Poonamalle, Chennai, Tamilnadu, India.
N.Buvaneswari Department of Mathematics, Siga College of Management and Computer Science, Villupuram Affiliated to Annamalai University, Chidambaram, Tamilnadu, India.
V. Kamalakannan Department of Mathematics, Panimalar Engineering College, Chennai, Tamilnadu, India

Keywords:

Weakly transitive, Gödel implication operator, Consistent, Idempotent NFM.

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.

DOI: 10.5281/zenodo.14597598