Reduction of Neutrosophic Fuzzy Matrices Using  Implication Operator

K. Karuppiah; R. Sudharani; R. Ambrose Prabhu; A. Anandan; D. Ramesh; K. Lawrence Mary

Authors

K. Karuppiah Department of Mathematics, Government College of Engineering, Bodinayakkanur – 625582, Theni District,Tamil Nadu.
R. Sudharani Department of Mathematics, Panimalar Engineering College, Nasarathpettai, Poonamallee, Bangalore Trunk Road, 600123;
R. Ambrose Prabhu Department of Mathematics, Rajalakshmi Institute of Technology, Poonamalle, Chennai, Tamilnadu, India
A. Anandan Department of Mathematics, VelTech MultiTech Dr.Rangarajan Dr.Sakunthala Engineering College, Avadi, Chennai, Tamilnadu, India
D. Ramesh Department of Engineering Mathematics, College of Engineering, Koneru Lakshmaiah Educational Foundation, Vaddeswaram, Andhra Pradesh-522302, India
K. Lawrence Mary Department of S&H, IFET College of Engineering (Autonomous), Villupuram, Tamilnadu, India.

Keywords:

Neutrosophic Fuzzy Matrix; Neutrosophic Fuzzy irreflexive matrix; Neutrosophic Fuzzy nilpotent matrix, s-transitive Neutrosophic Fuzzy matrix, w-transitive Neutrosophic Fuzzy matrix

Abstract

This research explores the reduction of Neutrosophic Fuzzy Matrices (NFMs) and
highlights their significant properties, focusing particularly on nilpotent NFMs. The study examines
the reduction of irreflexive and transitive NFMs and applies these principles to nilpotent NFMs,
which are represented as acyclic graphs. These acyclic graphs play a critical role in defining
consistent systems, especially when their union forms a cyclic graph that is isomorphic. Failure to
meet these conditions results in non-isomorphic graphs. To demonstrate these ideas, numerical
examples are provided, and the equivalent conditions for reduction are thoroughly established.
Furthermore, the collection of s-transitive and w-transitive NFMs is shown to encompass the set of
transitive NFMs for which reduction models have been verified. The properties of these reduction
models are also proven to be applicable to s-transitive and w-transitive NFMs

DOI: 10.5281/zenodo.15468302