Decomposition of Bipolar Pythagorean Fuzzy Matrices

Authors

  • K. SIVARANJANI ANNAMALAI UNIVERSITY
  • S. SRIRAM Annamalai University

Keywords:

Intuitionistic fuzzy matrix, Bipolar pythagorean fuzzy matrix, Modal operator

Abstract

This paper presents novel findings on modal operators through the use of max-min composition, analyzing properties such as reflexivity, symmetry, transitivity, and idempotency related to necessity and possibility. It explores the necessary and sufficient conditions for transitive and c-transitive closure matrices using modal operators. Additionally, a new composition operator, labeled as ”∧m ” is introduced and its algebraic properties are thoroughly discussed. The study also achieves a decomposition of a BPyFM utilizing the new composition operator and modal operators.

Downloads

Download data is not yet available.

References

K.T.Atanassov, Intuitionistic Fuzzy sets, Fuzzy sets and systems, 20(1) (1986), 87-96,

doi:https://doi.org/10.1016/S0165-0114(86)80034-3.

M. Bhowmik and M. Pal, Generalized intuitionistic fuzzy matrices, Far East Journal of

Mathematical Sciences, 29(3) (2008), 142-152.

H. Bustince and P. Burillo, Structure on intuitionistic fuzzy relation, Fuzzy Sets and Sys-

tems, 78(3) (1996), 293-303, doi:https://doi.org/10.1016/0165-0114(96)84610-0.

V. Chinnadurai, G. Thirumurugan and M. Umamaheswari, Novel operations in bipolar

pythagorean fuzzy matrices, International Journal of Advanced Science and Technology, 16

(2020), 5387-5401.

D. Ezhilmaran and K. Sankar, Morphism of bipolar intuitionistic fuzzy graphs,

Journal of Discrete Mathematical Science and Cryptography, 18(5) (2015), 605-621,

doi:10.1080/09720529.2015.1013673.

H. Hashimoto, Decomposition of fuzzy matrices, Siam Journal of Algebraic and Discrete

Methods, 6(1) (1985), 32-38, doi:https://doi.org/10.1137/0606003.

K. H. Kim and R. W. Roush, Generalized fuzzy matrices, Fuzzy Sets and System, 4 (1980),

-315, doi:https://doi.org/10.1016/0165-0114(80)90016-0.

P. Murugadas and K. Lalitha, Demposition of an intuitionistic fuzzy matrices using impli-

cation operators, Annals of Fuzzy Mathematical and Informatics, 11(1) (2015), 11-18.

P. Murugadas, S. Sriram and T. Muthuraji, Modal operators in intuitionistic

fuzzy matrices, International Journal of Computer Application, 90(17) (2014), 1-4,

doi:10.5120/15809-4535.

P. Murugadas, Contributuion to a study on generalized fuzzy matrices, Ph.D Thesis, De-

partment of Mathematices, Annamalai University, (2011).

T. Muthuraji, S. Sriram and P. Murugadas, Decomposition of intuitionis-

tic fuzzy matrices, Fuzzy Information and Engineering, 8 (2016), 345-354,

doi:https://doi.org/10.1016/j.fiae.2016.09.003.

M. Pal, S. K. Khan and Amiya K Shyamal, Intuitionistic fuzzy matrices, Notes on Intu-

itionistic Fuzzy Sets, 8(2) (2002), 51-62.

R. Pradhan and M. Pal, Some results on generalized inverse of intuitionis-

tic fuzzy matrices, Fuzzy Information and Engineering, 6(2) (2014), 133-145,

doi:https://doi.org/10.1016/j.fiae.2014.08.001.

M. G. Thomason, Convergence of power of a fuzzy matrix, Journal of Mathematical Analysis

and Applications, 57 (1977), 476-480, doi:https://doi.org/10.1016/0022-247X(77)90274-8.

L. A. Zadeh, Fuzzy sets, Journal of Information and Control, 8 (1965), 338-353,

doi:https://doi.org/10.1016/S0019-9958(65)90241-X.

Published

14-11-2024

How to Cite

K. SIVARANJANI, & S. SRIRAM. (2024). Decomposition of Bipolar Pythagorean Fuzzy Matrices. Communications in Mathematics and Applications, 15(2). Retrieved from http://rgnpublications.com/journals/index.php/cma/article/view/2739

Issue

Vol. 15 No. 2 (2024)

Section

Research Article

License

Creative Commons Licence 4.0 by  

Authors who publish with this journal agree to the following terms:

  • Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a CCAL that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
  • Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
  • Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.