Generalized Symmetric Fermatean Neutrosophic Fuzzy Matrices

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

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Published

2024-08-01

How to Cite

M.Anandhkumar, A. Bobin, S. M. Chithra, & V. Kamalakannan. (2024). Generalized Symmetric Fermatean Neutrosophic Fuzzy Matrices . Neutrosophic Sets and Systems, 70, 85-106. https://fs.unm.edu/nss8/index.php/111/article/view/4754