Generalized Symmetric Fermatean Neutrosophic Fuzzy Matrices

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