Hamacher operations on Pythagorean fuzzy matrices

• Autorzy: Silambarasan I. , Sriram S.

Identyfikatory

DOI

10.17512/jamcm.2019.3.06

• Języki publikacji: EN

Abstrakty

EN

In this paper, we introduce the Hamacher operations on Pythagorean fuzzy matrices and prove some desirable properties of these operations, such as commutativity, idempotancy and monotanicity. Further, we prove De Morgan’s laws for these operations over complement.

Słowa kluczowe

EN

intuitionistic fuzzy matrix; pythagorean fuzzy matrix; Hamacher sum; Hamacher product

PL

macierz rozmyta; suma Hamachera; produkt Hamacher

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2019
• Tom: Vol. 18, nr 3
• Strony: 69--78
• Opis fizyczny: Bibliogr. 19 poz., rys.

Twórcy

autor

Silambarasan I.

• Department of Mathematics, Annamalai University Annamalainagar, Tamilnadu, India

autor

Sriram S.

• Mathematics Wing, DDE, Annamalai University Annamalainagar, Tamilnadu, India

Bibliografia

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• [3] Thomason, M.G. (1977). Convergence of powers of fuzzy matrix. J. Mathematical Analysis and Applications, 57(2), 476-480.
• [4] Khan, S.K., & Pal, M. (2006). Some operations on intuitionistic fuzzy matrices. Acta Ciencia Indica, XXXII(M), 515-524.
• [5] Mondal, S., & Pal, M. (2013). Similarity relations, invertibility and eigenvalues of intutionistic fuzzy matrix. Fuzzy Information and Engineering, 5(4), 431-443.
• [6] Zhang, H.M., Xu, Z.S., & Chen, Q. (2007). Research on clustering method of intuitionistic fuzzy sets. Control and Decision Making, 22(8), 882-888.
• [7] Emam, E.G., & Fndh, M.A. (2016). Some results associated wiith the max-min and minmax compositions of bifuzzy matrices. Journal of the Egyption Mathematical Society, 24(4), 515-521.
• [8] Muthuraji, T., Sriram, S., & Murugadas, P. (2016). Decomposition of intuitionistic fuzzy matrices. Fuzzy Information and Engineering, 8(3), 345-354.
• [9] Silambarasan, I., & Sriram, S. (2017). Hamacher sum and Hamacher product of fuzzy matrices. Intern. J. Fuzzy Mathematical Archive, 13(2), 191-198.
• [10] Silambarasan, I., & Sriram, S. (2018). Hamacher operations of intuitionistic fuzzy matrices. Annals of Pure and Applied Mathematics, 16(1), 81-90.
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• [12] Zhang, X.L., & Xu, Z.S. (2014). Extension of TOPSIS to multiple criteria decision making with Pythagorean fuzzy sets. Int. J. of Intelligent Systems, 29(12), 1061-1078.
• [13] Silambarasan, I., & Sriram, S. (2018). Algebraic operations on Pythagorean fuzzy matrices. Mathematical Sciences International Research Journal, 7(2), 406-418.
• [14] Silambarasan, I., & Sriram, S. (2019). Commutative Monoid of Pythagorean fuzzy matrices. International Journal of Computer Sciences and Engineering, 7(4), 637-642.
• [15] Wu, S.J., & Wei, G.W. (2017). Pythagorean fuzzy Hamacher aggregation operators and their application to multiple attribute decision making. International Journal of Knowledge-based and Intelligent Engineering Systems, 21(3), 189-201.
• [16] Hamacher, H. (1978). Uber logische verknunpfungenn unssharfer Aussagen undderen Zugenhorige Bewertungsfunktione. In: Trappl, Klir, Riccardi (eds). Progress in Cybernatics and Systems Research. Hemisphere, Washington, 3, 276-288.
• [17] Deschrijver, G., Cornelis, C., & Kerre, E.E. (2004). On the representation of intuitionistic fuzzy t-norms and t-conorms. IEEE Transactions on Fuzzy Systems, 12(1), 45-61.
• [18] Roychowdhury S., Wang, B.H. (1998). On generalized Hamacher families of triangular operators. Int. J. Approx. Reason, 19(3-4), 419-439.
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Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).