Solving LR fuzzy linear matrix equation†

[1] S. Abbasbandy, A. Jafarian, R. Fzzati, Conjugate gradient method for fuzzy symmetric positive definite system of
linear equations, Applied Mathematics and Computation, 171 (2005), 1184{1191.
[2] S. Abbasbandy, R. Ezzati, A. Jafarian, LU decomposition method for solving fuzzy system of linear equations,
Applied Mathematics and Computation, 172 (2006), 633{643.
[3] S. Abbasbandy, M. Otadi, M. Mosleh, Minimal solution of general dual fuzzy linear systems, Chaos, Solitions and
Fractals, 29 (2008), 638{652.
[4] T. Allahviranloo, Numerical methods for fuzzy system of linear equations, Applied Mathematics and Computation,
153 (2004), 493{502.
[5] T. Allahviranloo, Successive over relaxation iterative method for fuzzy system of linear equations, Applied Mathe-
matics and Computation, 162 (2005), 189{196.
[6] T. Allahviranloo, The adomian decomposition method for fuzzy system of linear equations, Applied Mathematics
and Computation, 163 (2005), 553{563
[7] T. Allahviranloo, F. H. Lot, M. K. Kiasari, M. Khezerloo, On the fuzzy solution of LR fuzzy linear systems, Applied
Mathematical Modelling, 37 (2013), 1170{1176.
[8] T. Allahviranloo, M. Ghanbari, R. Nuraei, A note on fuzzy linear systems, Fuzzy Sets and Systems, 177(1) (2011),
87-92.
[9] T. Allahviranloo, N. Mikaeilvand, M. Barkhordary, Fuzzy linear matrix equations, Fuzzy Optimization and Decision
Making, 8 (2009), 165{177.
[10] M. Amirfakhrian, M. Fallah, R. Rodriguez-Lopez, A method for solving fuzzy matrix equations, Soft Computing,
22 (2018), 2095{2103.

[11] B. Asady, S. Abbasbandy, M. Alavi, Fuzzy general linear systems, Applied Mathematics and Computation, 169
(2005), 34{40.
[12] N. Babbar, A. Kumar, Abhinav Bansal, Solving fully fuzzy linear system with arbitrary triangular fuzzy numbers,
Soft Computing, 17 (2013) 691-702.
[13] A. Ben-Israel, T. N. E. Greville, Generalized inverses: Theory and applications, second edition, Springer-Verlag,
New York, 2003.
[14] A. Berman, R. J. Plemmons, Nonnegative matrices in the mathematical sciences, Academic press, New York, 1979.
[15] W. S. W. Daud, N. Ahmad, G. Malkawi, A preliminary study on the solution of fully fuzzy Sylvester matrix
equation, In AIP Conference Proceedings, 1775 (2016), 30{36.
[16] M. Dehghan, B. Hashemi, M. Ghatee, Solution of the full fuzzy linear systems using iterative techniques, Chaos,
Solitons and Fractals, 34 (2007) 316{336.
[17] M. Dehghan, B. Hashemi, Iterative solution of fuzzy linear systems, Applied Mathematics and Computation, 175
(2006), 645{674.
[18] K. Dookhitram, R. Lollchund, R. K. Tripathi, M. Bhuruth, Fully fuzzy Sylvester matrix equation, Journal of
Intelligent and Fuzzy Systems, 28 (2015), 2199{2211.
[19] D. Dubois, H. Prade, Operations on fuzzy numbers, Journal of Systems Science, 9 (1978), 613{626.
[20] S. A. Edalatpanah, Modied iterative methods for solving fully fuzzy linear systems, In I, Management Association
(Ed.) Fuzzy Systems: Concepts, Methodologies, Tools, and Applications, (2017), 55{73.
[21] M. Friedman, M. Ma, A. Kandel, Fuzzy linear systems, Fuzzy Sets and Systems, 96 (1998), 201{209.
[22] R. Ghanbari, Solutions of fuzzy LR algebraic linear systems using linear programs, Applied Mathematical Mod-
elling, 39 (2015), 5164-5173.
[23] R. Goetschel, W. Voxman, Elementary calculus, Fuzzy Sets and Systems, 18 (1986), 31{43.
[24] Z. T. Gong, X. B. Guo, Inconsistent fuzzy matrix equations and its fuzzy least squares solutions, Applied Mathe-
matical Modelling, 35 (2011), 1456{1469.
[25] Z. T. Gong, X. B. Guo, K. Liu, Approximate solution of dual fuzzy matrix equations, Information Sciences, 266
(2014), 112-133.
[26] X. B. Guo, D. Q. Shang, Approximate solutions of LR fuzzy Sylvester matrix equations, Journal of Applied Math-
ematics, 2013 (2013), 1{10.
[27] X. B. Guo, K. Zhang, Solving fuzzy matrix equation of the form eXA = eB, Journal of Intelligent and Fuzzy Systems,
32 (2017), 2771{2778.
[28] X. B. Guo, Y. L. Han, Further investigation to dual fuzzy matrix equation, Journal of Intelligent and Fuzzy Systems,
33 (2017), 2617{2629.
[29] J. J. Kaur, A. Kumar, A note on approximate solution of dual fuzzy matrix equations, Information Sciences, 418
(2017), 184{185.
[30] M. Ma, M. Friedman, A. Kandel, Duality in fuzzy linear systems, Fuzzy Sets and Systems, 109 (2000), 55{58.
[31] S. Nahmias, Fuzzy variables, Fuzzy Sets and Systems, 1(2) (1978) 97{111.
[32] H. S. Najafi, S. A. Edalatpanah, An improved model for iterative algorithms in fuzzy linear systems, Computational
Mathematics and Modeling, 24 (2013), 443{451.
[33] H. S. Najafi, S. A. Edalatpanah, H-Matrices in fuzzy linear systems, International Journal of Computational
Mathematics, 6 (2013), 52{56.

[34] R. Nuraei, T. Allahviranloo, M. Ghanbari, Finding an inner estimation of the solution set of a fuzzy linear system,
Applied Mathematical Modelling, 37 (2013), 5148{5161.
[35] M. Otadi, M. Mosleh, Solving fully fuzzy matrix equations, Applied Mathematical Modelling, 36 (2012), 6114{6121.
[36] R. J. Plemmons, Regular nonnegative matrices, Proceedings of the American Mathematical Society, 39 (1973),
26-32.
[37] M. L. Puri, D. A. Ralescu, Differentials for fuzzy functions, Journal of Mathematics Analyisis and Application, 91
(1983), 552{558.
[38] C. X. Wu, M. Ma, Embedding problem of fuzzy number space: Part I, Fuzzy Sets and Systems, 44 (1991), 33{38.
[39] C. X.Wu, M. Ma, Embedding problem of fuzzy number space: Part III, Fuzzy Sets and Systems, 46 (1992), 281{286.
[40] L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338{353.
[41] B. Zheng, K. Wang, General fuzzy linear systems, Applied Mathematics and Computation, 181 (2006), 1276{1286.