Generalized Symmetric Fermatean Neutrosophic Fuzzy Matrices

M.Anandhkumar; A. Bobin; S. M. Chithra; V. Kamalakannan

Authors

M.Anandhkumar Department of Mathematics, IFET College of Engineering (Autonomous), Villupuram, Tamilnadu, India.
A. Bobin Department of Mathematics, IFET College of Engineering (Autonomous), Villupuram, Tamilnadu, India.
S. M. Chithra Department of Mathematics, R.M.K College of Engineering and Technology, Chennai, Tamilnadu, India.
V. Kamalakannan Department of Mathematics, Panimalar Engineering College, Chennai, Tamilnadu, India

Keywords:

PNFM, FNFM, NFM

Abstract

This study explores a new type of matrix called a range-symmetric Fermatean
neutrosophic fuzzy matrix (FNFM), inspired by the concept of range-Hermitian matrices. We
demonstrate that all FNFMs inherently possess a specific property we term "Pythagorean
neutrosophic fuzzy," (PNFM) but the reverse is not always true. Furthermore, we delve into
graphical representations of FNFMs with specific symmetry properties (kernel-symmetric (KS),
column symmetric, and range-symmetric (RS)) and show that these properties hold for all
isomorphic graphs. The study goes on to establish equivalent characterizations for range-symmetric
FNFMs and identify conditions for KS FNFMs. We introduce a novel concept: k-KS and RS FNFMs.
Examples illustrate that KS FNFMs inherently possess k-KS, but not necessarily the other way
around. This research contributes to a deeper understanding of symmetric FNFM and their potential
applications, highlighting their importance in mathematical and computational fields.

DOI: 10.5281/zenodo.13172740