Allahviranloo, T.; Mikaeilvand, N.; Barkhordary, M. Fuzzy linear matrix equation. (English) Zbl 1177.15016 Fuzzy Optim. Decis. Mak. 8, No. 2, 165-177 (2009). The authors analyze fuzzy linear matrix equations of the form \(AXB=C\) for finding its fuzzy solutions, using the parametric form of the fuzzy linear system. The authors also derive necessary and sufficient conditions for the existence of the set of fuzzy solutions. Reviewer: Răzvan Răducanu (Iaşi) Cited in 7 Documents MSC: 15A24 Matrix equations and identities 15B15 Fuzzy matrices Keywords:fuzzy linear matrix equation; embedding method; conditional inverse; system of fuzzy linear equations; fuzzy solutions PDF BibTeX XML Cite \textit{T. Allahviranloo} et al., Fuzzy Optim. Decis. Mak. 8, No. 2, 165--177 (2009; Zbl 1177.15016) Full Text: DOI References: [1] Abbasbandy S., Ezzati R., Jafarian A. (2006) LU decomposition method for solving fuzzy system of linear equations. Applied Mathematics and Computation 172: 633-643 · Zbl 1088.65023 [2] Allahviranloo T. (2003) Discussion: A comment on fuzzy linear systems. Fuzzy Sets and Systems 140: 559 · Zbl 1050.15003 [3] Allahviranloo T. (2004) Numerical methods for fuzzy system of linear equations. Applied Mathematics and Computation 155: 493-502 · Zbl 1067.65040 [4] Allahviranloo T. (2005a) Succesive over relaxation iterative method for fuzzy system of linear equations. Applied Mathematics and Computation 162: 189-196 · Zbl 1062.65037 [5] Allahviranloo T. (2005b) The Adomian decomposition method for fuzzy system of linear equations. Applied Mathematics and Computation 163: 553-563 · Zbl 1069.65025 [6] Allahviranloo T., Afshar Kermani M. (2006) Solution of a fuzzy system of linear equation. Applied Mathematics and Computation 175: 519-531 · Zbl 1095.65036 [7] Allahviranloo T., Ahmady E., Ahmady N., Shams Alketaby Kh. (2006) Block Jacobi two stage method with Gauss Sidel inner iterations for fuzzy systems of linear equations. Applied Mathematics and Computation 175: 1217-1228 · Zbl 1093.65032 [8] Asady B., Abasbandy S., Alavi M. (2005) Fuzzy general linear systems. Applied Mathematics and Computation 169: 34-40 · Zbl 1119.65325 [9] Dehghan M., Hashemi B. (2006) Iterative solution of fuzzy linear systems. Applied Mathematics and Computation 175: 645-674 · Zbl 1137.65336 [10] Friedman M., Ming M., Kandel A. (1998) Fuzzy linear systems. Fuzzy Sets and Systems 96: 201-209 · Zbl 0929.15004 [11] Friedman M., Ming M., Kandel A. (2003) Discussion: Author‘s reply. Fuzzy Sets and Systems 140: 561 [12] Goetschel R., Voxman W. (1986) Elementary calculus. Fuzzy Sets ans Systems 18: 31-43 · Zbl 0626.26014 [13] Kaleva O. (1987) Fuzzy differential equations. Fuzzy Sets and Systems 24: 301-317 · Zbl 0646.34019 [14] Lancaster P., Tismenetsky M. (1985) The theory of matrices. Academic Press, London · Zbl 0558.15001 [15] Ma M., Friedman M., Kandel A. (2000) Duality in fuzzy linear systems. Fuzzy Sets and Systems 109: 55-58 · Zbl 0945.15002 [16] Navarra A., Odell P.L., Young D.M. (2001) A representation of general common solution to the matrix equations A1 × B1 = C1 and A2 × B2 = C2 with applications. An International Journal of Computers and Mathematics with Applications 41: 929-935 · Zbl 0983.15016 [17] Rao C.R., Mitra S.K. (1971) Generalized inverse of matrices and its applications. Wiley, New York · Zbl 0236.15004 [18] Wang K., Zheng B. (2006) Inconsistent fuzzy linear systems. Applied Mathematics and Computations 181: 973-981 · Zbl 1122.15004 [19] Wanga X., Zhong Z., Ha M. (2001) Iteration algorithms for solving a system of fuzzy linear equations. Fuzzy Sets and Systems 119: 121-128 · Zbl 0974.65035 [20] Wu C.-X., Ma M. (1991) Embedding problem of fuzzy number space: Part I. Fuzzy Sets and Systems 44: 33-38 · Zbl 0757.46066 [21] Wu C.-X., Ma M. (1992) Embedding problem of fuzzy number space: Part III. Fuzzy Sets and Systems 46: 281-286 · Zbl 0774.54003 [22] Zheng B., Wang K. (2006) General fuzzy linear systems. Applied Mathematics and Computation 181: 1276-1286 · Zbl 1122.15005 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.