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2020 | 150 | 148-161
Article title

An Interval-Valued Intuitionistic Fuzzy Matrices Based on Hamacher Operations

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EN
Abstracts
EN
The objective of this paper is to apply the concept of fuzzy matrices to interval-valued intuitionistic fuzzy matrices. In this paper, we introduce the Hamacher operations of interval-valued intuitionistic fuzzy matrices and prove some desirable properties of these operations, such as commutativity, idempotency and monotonicity. Further, we prove De Morgan's laws over complement for these operations. Then we constructe the scalar multiplication (n._h A) and exponentiation (A^(∧_h n)) operations of interval-valued fuzzy intuitionistic matrices and investigates the algebraic properties.
Year
Volume
150
Pages
148-161
Physical description
Contributors
  • Department of Mathematics, Annamalai University, Annamalainagar - 608002, Tamil Nadu, India
References
  • [1] H. Hamacher. Uber logische verknunpfungenn unssharfer Aussagen udderen Zugenhorige Bewertungsfunktione. In:Trappl, Riccardi (eds) Progress in Cybernatics and systems research, 3(1978), 276-288. Hemisphere, Washington.
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  • [3] S.K. Khan, M. Pal, A.K. Shyamal. Intuitionistic Fuzzy Matrices. Notes on Intuitionistic Fuzzy Sets 8(2) (2002) 51-62
  • [4] S.K. Khan, M. Pal. Interval-valued intutionistic fuzzy matrices. Notes on Intuitionistic Fuzzy Sets 11(1)(2005) 16-27
  • [5] S.K. Khan, M. Pal. Some operations on Intuitionistic Fuzzy Matrices. Acta Ciencia Indica XXXII (M) (2006) 515-524
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  • [11] M.Z. Ragab, E.G. Emam. On the min-max composition of fuzzy matrices. Fuzzy Sets and Systems 75(1) (1995) 83-92
  • [12] A.K. Shyamal, M. Pal. Interval Valued Fuzzy Matrices. Journal of Fuzzy Mathematics 14(3) (2006) 582 592
  • [13] I. Silambarasan, S. Sriram. Hamacher Sum and Hamacher Product of Fuzzy Matrices. Int. J. Fuzzy Mathematical Archive 13 (2) (2017) 191-198
  • [14] I. Silambarasan, S. Sriram. Hamacher Operations of Intuitionistic Fuzzy Matrices. Annals of Pure and Applied Mathematics 16 (1) (2018) 81-90
  • [15] M.G. Thomason. Convergence of powers of Fuzzy matrix. J. Mathematical Analysis and Applications 57(2) (1977) 476-480
  • [16] 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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bwmeta1.element.psjd-f3bece23-4998-4998-b17e-c9d1bef33bf1
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