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2020 | 150 | 78-91
Article title

Some Algebraic Structures of Picture Fuzzy Matrices

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EN
Abstracts
EN
In this paper, the concept of Picture fuzzy matrices, which are direct extensions of an intuitionistic fuzzy matrices. Then we define some algebraic operations of Picture fuzzy matrices, such as max-min, min-max, complement, algebraic sum, algebraic product, scalar multiplication (nA) and exponentiation (A^n). We also investigate their algebraic properties of these operations. Furthermore, we define a new operation(@) on Picture fuzzy matrices and discuss distributive laws in the case where the operations of ⊕_℘,〖 ⊗〗_℘,〖 ∧〗_℘ and ∨_℘ are combined each other.
Year
Volume
150
Pages
78-91
Physical description
Contributors
  • Department of Mathematics, Annamalai University, Annamalainagar - 608002, Tamil Nadu, India
References
  • [1] K.T. Atanassov. Intuitionistic Fuzzy Sets. Fuzzy Sets and Systems 20 (1) (1986) 87-96
  • [2] S. Dogra, M. Pal. Picture fuzzy matrix and its application. Soft Comput 24 (2020) 9413-9428. https://doi.org/10.1007/s00500-020-05021-4
  • [3] E.G. Emam, M.A. Fndh. Some results associated wiith the max-min and min-max compositions of bifuzzy matrices. Journal of the Egyption Mathematical Society 24(4) (2016) 515-521
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  • [10] I. Silambarasan, S. Sriram. Hamacher Operations of Intuitionistic Fuzzy Matrices. Annals of Pure and Applied Mathematics 16 (1) (2018) 81-90
  • [11] I. Silambarasan, S. Sriram. Algebraic operations on Pythagorean fuzzy matrices. Mathematical Sciences International Research Journal 7(2) (2018) 406-418
  • [12] I. Silambarasan, S. Sriram. Hamacher operations on Pythagorean Fuzzy Matrices, Journal of Applied Mathematics and Computational Mechanics 18(3) (2019) 69-78
  • [13] M.G. Thomason. Convergence of powers of Fuzzy matrix. J. Mathematical Analysis and Applications 57(2) (1977) 476-480
  • [14] X. Zhang, Z. Xu, Z. A new method for ranking intuitionistic fuzzy values and its application in multi attribute decision making. Fuzzy Optimization Decision Making 11(2) (2012) 135-146
  • [15] L. A. Zadeh. Fuzzy sets. Information and Control 8(3) (1965) 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X
Document Type
article
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YADDA identifier
bwmeta1.element.psjd-b8c139eb-9e96-4882-8a39-bbc378026b5c
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