| Title of paper:
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Resolution of a system of the max-min product intuitionistic fuzzy relation equations using LU-factorization
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| Author(s):
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| S. Melliani
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| LMACS – Laboratoire de Mathematiques Appliqu ´ ees & Calcul Scientifique Sultan Moulay Slimane University, PO Box 523, 23000 Beni Mellal, Morocco
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| melliani@fstbm.ac.ma
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| M. Elomari
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| LMACS – Laboratoire de Mathematiques Appliqu ´ ees & Calcul Scientifique Sultan Moulay Slimane University, PO Box 523, 23000 Beni Mellal, Morocco
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| L. S. Chadli
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| LMACS – Laboratoire de Mathematiques Appliqu ´ ees & Calcul Scientifique Sultan Moulay Slimane University, PO Box 523, 23000 Beni Mellal, Morocco
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| R. Ettoussi
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| LMACS – Laboratoire de Mathematiques Appliqu ´ ees & Calcul Scientifique Sultan Moulay Slimane University, PO Box 523, 23000 Beni Mellal, Morocco
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| Published in:
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Notes on Intuitionistic Fuzzy Sets, Volume 20 (2014), Number 5, pages 36–49
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| Download:
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 PDF (184 Kb, File info)
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| Abstract:
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In this paper, the LU-factorization is extended to the intuitionistic fuzzy square matrix with respect to the max-min product composition operator. Initially The algorithms are given to find two intuitionistic fuzzy (lower and upper) triangular matrices L and U for an intuitionistic fuzzy square matrix A such A = LU and a result for the existence and uniqueness of this decomposition. An algorithm is also proposed to find the solution set of a square system of Intuitionistic Fuzzy Relation Equations (IFRE) using the LU-factorization. Finally an example is given to illustrate our work.
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| Keywords:
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Intuitionistic fuzzy sets, Intuitionistic fuzzy relation equation, Intuitionistic fuzzy matrix, Max-min product operator, LU-factorization, Intuitionistic fuzzy number.
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| AMS Classification:
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03E72, 08A72.
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| References:
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- Atanassov, K., Intuitionistic fuzzy sets, Fuzzy Sets and Systems, Vol. 20, 1986, 87–96.
- Atanassov, K., Intuitionistic Fuzzy Sets: Theory and Applications, Physica-Verlag 1999.
- Atanassov, K. T., P. M. Vassilev, R. T. Tsvetkov, Intuitionistic Fuzzy Sets, Measures and Integrals, Bulgarian Academic Monographs (12), “Professor Marin Drinov” Academic Publishing House, Sofia, 2013.
- Molai, A. A. Resolution of a system of the max-product fuzzy relation equations using L ◦ U-factorization, Information Sciences, Vol. 234, 2013, 86–96.
- Meenakshi, A. R., C. Inbam, Fuzzy matrices and Linear transformations on fuzzy vector spaces, Int. J. Fuzzy Math., Vol. 11, 2003, 955–966.
- Meenakshi, A. R., T. Gandhimathi, Special Types of Intuitionistic Fuzzy Linear Transformations, International Journal of Mathematical Sciences and Applications, Vol. 1, 2011, No. 1.
- Pradhan, R., M. Pal, Solvability of system of intuitionistic fuzzy linear equations, International Journal of Fuzzy Logic Systems (IJFLS), Vol. 4, 2014, No. 3, 13–24
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| Citations:
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