Open Access   Article Go Back

Commutative Monoid of Pythagorean Fuzzy Matrices

I. Silambarasan1 , S. Sriram2

Section:Research Paper, Product Type: Journal Paper
Volume-7 , Issue-4 , Page no. 637-643, Apr-2019

CrossRef-DOI:   https://doi.org/10.26438/ijcse/v7i4.637643

Online published on Apr 30, 2019

Copyright © I. Silambarasan, S. Sriram . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

View this paper at   Google Scholar | DPI Digital Library

XML View
PDF Download

How to Cite this Paper

  • IEEE Citation
  • MLA Citation
  • APA Citation
  • BibTex Citation
  • RIS Citation

IEEE Style Citation: I. Silambarasan, S. Sriram, “Commutative Monoid of Pythagorean Fuzzy Matrices,” International Journal of Computer Sciences and Engineering, Vol.7, Issue.4, pp.637-643, 2019.

MLA Style Citation: I. Silambarasan, S. Sriram "Commutative Monoid of Pythagorean Fuzzy Matrices." International Journal of Computer Sciences and Engineering 7.4 (2019): 637-643.

APA Style Citation: I. Silambarasan, S. Sriram, (2019). Commutative Monoid of Pythagorean Fuzzy Matrices. International Journal of Computer Sciences and Engineering, 7(4), 637-643.

BibTex Style Citation:
@article{Silambarasan_2019,
author = {I. Silambarasan, S. Sriram},
title = {Commutative Monoid of Pythagorean Fuzzy Matrices},
journal = {International Journal of Computer Sciences and Engineering},
issue_date = {4 2019},
volume = {7},
Issue = {4},
month = {4},
year = {2019},
issn = {2347-2693},
pages = {637-643},
url = {https://www.ijcseonline.org/full_paper_view.php?paper_id=4090},
doi = {https://doi.org/10.26438/ijcse/v7i4.637643}
publisher = {IJCSE, Indore, INDIA},
}

RIS Style Citation:
TY - JOUR
DO = {https://doi.org/10.26438/ijcse/v7i4.637643}
UR - https://www.ijcseonline.org/full_paper_view.php?paper_id=4090
TI - Commutative Monoid of Pythagorean Fuzzy Matrices
T2 - International Journal of Computer Sciences and Engineering
AU - I. Silambarasan, S. Sriram
PY - 2019
DA - 2019/04/30
PB - IJCSE, Indore, INDIA
SP - 637-643
IS - 4
VL - 7
SN - 2347-2693
ER -

VIEWS PDF XML
610 336 downloads 166 downloads
  
  
           

Abstract

In this paper, we prove the set of all Pythagorean fuzzy matrices form a commutative monoid with respect to algebraic sum and algebraic product. Also, the De Morgan`s laws and Distributive laws are provided and we define the @ operations on Pythagorean fuzzy matrices and analyze its algebraic properties. Further, some results prove equalities and inequalities of Pythagorean fuzzy matrices.

Key-Words / Index Term

Intuitionistic fuzzy matrix, Pythagorean fuzzy set, Pythagorean fuzzy matrix, Algebraic sum and Algebraic product

References

[1] E. G. Emam and M. A. Fndh, Some results associated wiith the max-min and min-max compositions of bifuzzy matrices, Journal of the Egyption Mathematical Society, Vol. 24, Issue.4, pp. 515-521. 2016.
[2] Y.B.Im, E.B.Lee and S.W.Park, The determinant of square intuitionistic fuzzy matrices, Far East Journal of Mathematical Sciences, Vol.3, Issue.5 pp.789-796. 2001.
[3] Y.B.Im, E.B.Lee and S.W.Park, The adjoint of square intuitionistic fuzzy matrices, Int.Appl.math. computing(series A) Vol.11,Issue.1-2,pp.401-412.2003.
[4] M.Pal, S.K.Khan and A.K.Shyamal., Intuitionistic Fuzzy Matrices, Notes on Intuitionistic Fuzzy Sets, Vol.8, Issue.2, pp.51-62. 2002.
[5] S. K. Khan and M. Pal, Some operations on Intuitionistic Fuzzy Matrices, Acta Ciencia Indica, Vol.32, pp.515-524.2006.
[6] S.Mondal and M.Pal, Similarity relations, invertibility and eigenvalues of IFM, Fuzzy Information and Engg, Vol.5, Issue.4, pp.431-443. 2013.
[7] P.Murugadas, S.Sriram, T.Muthuraji, Modal operators in intuitionistic fuzzy matrices, International Journal of Computer Application, Vol.90, Issue.17, pp.1-4. 2014.
[8] T.Muthuraji, S.Sriram and P.Murugadas, Decomposition of intuitionistic fuzzy matrices, Fuzzy Information and Engineering,Vol. 8 , pp. 345-354. 2016.
[9] T. Muthuraji, S. Sriram, Reduction of an intuitionistic fuzzy matrix to fuzzy matrix with some algebraic properties, Annals of Fuzzy Mathematics and Informatics, Vol.13, Issue.4, pp.475-483. 2017.
[10] T.Muthuraji, S. Sriram, Representation and Decomposition of an Intuitionistic fuzzy matrix using some cuts, Applications and Applied Mathematics ,Vol.12, Issue.1, pp. 241-258. 2017.
[11] M.Pal, Intuitionistic fuzzy determinant, V.U.J. Physical Sciences, Vol.7, pp.87-93. 2001.
[12] A.K.Shyamal and M.Pal, Distances between intuitionistic fuzzy matrices, V.U.J. Physical Sciences, Vol.8, pp.81-91.2002.
[13] I.Silambarasan and S.Sriram, Bounded Sum and Bounded Product of Fuzzy Matrices,Annals of Pure and Applied Mathematics,Vol.14, Issue.3, pp. 513-523. 2017.
[14] I.Silambarasan and S.Sriram, Hamacher Sum and Hamacher Product of Fuzzy Matrices, Intern.J.Fuzzy Mathematical Archive, Vol.13, Issue.2, pp. 191-198. 2017.
[15] I.Silambarasan and S.Sriram, Hamacher Operations of Intuitionistic Fuzzy Matrices, Annals of Pure and Applied Mathematics, Vol.16, Issue.1, pp. 81-90. 2018.
[16] I.Silambarasan and S.Sriram, Algebraic operations on Pythagorean fuzzy matrices, Mathematical Sciences International Research Journal, Vol.7, Issue.2, pp.406-414. 2018.
[17] S.Sriram,J.Boobalan, Arithmetic operations on Intuitionistic fuzzy matrices,Proceedings of International Conference on Mathematical Sciences-(Published by Elsevier) organized by Sathyabama university, Chennai, pp.484-487. 2014.
[18] S. Sriram, J. Boobalan, Monoids of intuitionistic fuzzy matrices, Annals of fuzzy Mathematics and Informatics, Vol.11, Issue.3, pp.505-510. 2016.
[19] M.G.Thomason, Convergence of powers of fuzzy matrix, J. Mathematical Analysis and Applications, Vol.57, pp.476-480.1977.
[20] R. R. Yager, Pythagorean fuzzy subsets, In:Proc Joint IFSA World Congress and NAFIPS Annual Meeting, Edmonton, Canada, pp.57-61. 2013.
[21] R.R.Yager, Pythagorean membership grades in multi-criteria decision making, IEEE Transactions on Fuzzy Systems, Vol.22, pp.958-965. 2014.
[22] R.R.Yager and A.M.Abbasov, Pythagorean membership grades, complex numbers, and decision making, Int. J.of Intelligent Systems, Vol.28, pp.436-452. 2013.
[23] Zeshui xu and Ronald R.Yagar, Some aggregation operators based on IFS, International journal of general system, Vol.35, Issue.4, pp.417-433. 2006.
[24] Zhang. Xu., A new method for ranking intuitionistic fuzzy values and its application in multi attribute decision making, Fuzzy optimal decision making , Vol .11, pp.135-146. 2012.
[25] X.L.Zhang and Z.S.Xu, Extension of TOPSIS to multiple criteria decision making with Pythagorean fuzzy sets, Int. J.of Intelligent Systems, Vol.29 , pp. 1061-1078. 2014.
[26] Shrija Madhu, “An approach to analyze suicidal tendency in blogs and tweets using Sentiment Analysis”, International Journal of Scientific Research in Computer Science and Engineering, Vol.6, Issue.4, pp.34-36, 2018.