research-article
Authors: Mengyu He, Hongjie Jiang, and Xiaoji Liu
Volume 480, Issue C
Published: 25 June 2024 Publication History
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Abstract
This paper aims to solve the fuzzy Sylvester matrix equation (FSME) A X ˜ + X ˜ B = C ˜, in which A, B are n × n and m × m crisp matrices, and C ˜ is a n × m fuzzy matrix. Using the Kronecker product, we transform the FSME into an m n × m n fuzzy linear system. Firstly, we obtain the necessary and sufficient conditions for the existence of strong fuzzy solutions to the FSME by using the BT inverse of the coefficient matrix. Secondly, we investigate the existence of a nonnegative BT inverse by using its block structure. Next, we derive general strong fuzzy solutions to a class of FSME and establish an algorithm to obtain general strong fuzzy solutions to the FSME by the BT inverse. Finally, we give three numerical examples and an applied example in the economy to illustrate the proposed methods.
References
[1]
V. Kučera, The matrix equation A X + X B = C, SIAM J. Appl. Math. 26 (1) (1974) 15–25.
[2]
L.A. Zadeh, The concept of a linguistic variable and its application to approximate reasoning-III, Inf. Sci. 8 (1) (1975) 199–249.
[3]
S.S.L. Chang, L.A. Zadeh, On fuzzy mapping and control, IEEE Trans. Syst. Man Cybern. 1 (1972) 30–34.
[4]
D. Dubois, H. Prade, Operations on fuzzy numbers, Int. J. Syst. Sci. 9 (6) (1978) 613–626.
[5]
S. Nahmias, Fuzzy variables, Fuzzy Sets Syst. 1 (2) (1978) 97–110.
[6]
M. Friedman, M. Ming, A. Kandel, Fuzzy linear systems, Fuzzy Sets Syst. 96 (2) (1998) 201–209.
[7]
T. Allahviranloo, Numerical methods for fuzzy system of linear equations, Appl. Math. Comput. 155 (2) (2004) 493–502.
[8]
T. Allahviranloo, M.A. Kermani, Solution of a fuzzy system of linear equation, Appl. Math. Comput. 175 (1) (2006) 519–531.
[9]
T. Allahviranloo, M. Ghanbari, On the algebraic solution of fuzzy linear systems based on interval theory, Appl. Math. Model. 36 (11) (2012) 5360–5379.
[10]
W.A. Lodwick, D. Dubois, Interval linear systems as a necessary step in fuzzy linear systems, Fuzzy Sets Syst. 281 (2015) 227–251.
[11]
R.H. Bartels, G.W. Stewart, Solution of the matrix equation A X + X B = C, Commun. ACM 15 (9) (1972) 820–826.
Digital Library
[12]
G. Golub, S. Nash, C. Van Loan, A Hessenberg-Schur method for the problem A X + X B = C, IEEE Trans. Autom. Control 24 (6) (1979) 909–913.
[13]
X.B. Guo, Approximate solution of fuzzy Sylvester matrix equations, in: Seventh International Conference on Computational Intelligence and Security, IEEE, 2011, pp. 52–56.
[14]
D.K. Salkuyeh, On the solution of the fuzzy Sylvester matrix equation, Soft Comput. 15 (5) (2011) 953–961.
[15]
F. Araghi, M. Hosseinzadeh, ABS method for solving fuzzy Sylvester matrix equation, Int. J. Math. Model. Comput. 2 (3) (2016) 231–237.
[16]
Q. He, L. Hou, J. Zhou, The solution of fuzzy Sylvester matrix equation, Soft Comput. 22 (2018) 6515–6523.
[17]
G. Wang, Y. Wei, S. Qiao, et al., Generalized Inverses: Theory and Computations, Springer, Singapore, 2018.
[18]
O.M. Baksalary, G. Trenkler, Core inverse of matrices, Linear Multilinear Algebra 58 (6) (2010) 681–697.
[19]
K.M. Prasad, K.S. Mohana, Core-EP inverse, Linear Multilinear Algebra 62 (6) (2014) 792–802.
[20]
H. Wang, Core-EP decomposition and its applications, Linear Algebra Appl. 508 (2016) 289–300.
[21]
B. Mihailović, V.M. Jerković, B. Malešević, Solving fuzzy linear systems using a block representation of generalized inverses: the Moore-Penrose inverse, Fuzzy Sets Syst. 353 (2018) 44–65.
[22]
B. Mihailović, V.M. Jerković, B. Malešević, Solving fuzzy linear systems using a block representation of generalized inverses: the group inverse, Fuzzy Sets Syst. 353 (2018) 66–85.
[23]
H. Jiang, H. Wang, X. Liu, Solving fuzzy linear systems by a block representation of generalized inverse: the core inverse, Comput. Appl. Math. 39 (2) (2020) 1–20.
[24]
H. Jiang, X. Liu, C. Jiang, On the general strong fuzzy solutions of general fuzzy matrix equation involving the Core-EP inverse, AIMS Math. 7 (2) (2022) 3221–3238.
[25]
O.M. Baksalary, G. Trenkler, On a generalized core inverse, Appl. Math. Comput. 236 (2014) 450–457.
[26]
W. Jiang, K. Zuo, Revisiting of the BT-inverse of matrices, AIMS Math. 6 (3) (2021) 2607–2622.
[27]
H. Wang, J. Chen, Weak group inverse, Open Math. 16 (1) (2018) 1218–1232.
[28]
H. Wang, Some new characterizations of generalized inverses, Front. Math. 18 (6) (2023) 1397–1420.
[29]
D.E. Ferreyra, N. Thome, C. Torigino, The W-weighted BT inverse, Quaest. Math. 46 (2) (2023) 359–374.
[30]
S. Xu, D. Wang, New characterizations of the generalized BT inverse, Filomat 36 (3) (2022) 945–950.
[31]
P. Lancaster, M. Tismenetsky, The Theory of Matrices with Application, Elsevier, 1985.
[32]
A.J. Laub, Matrix Analysis for Scientists and Engineers, Siam, 2005.
[33]
A. Berman, R.J. Plemmons, Nonnegative Matrices in the Mathematical Sciences, Siam, 1994.
[34]
T. Allahviranloo, M. Ghanbari, On the algebraic solution of fuzzy linear systems based on interval theory, Appl. Math. Model. 36 (11) (2012) 5360–5379.
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Published In
Fuzzy Sets and Systems Volume 480, Issue C
Mar 2024
218 pages
ISSN:0165-0114
Issue’s Table of Contents
Elsevier B.V.
Publisher
Elsevier North-Holland, Inc.
United States
Publication History
Published: 25 June 2024
Author Tags
- Fuzzy Sylvester matrix equation
- BT inverse
- General strong fuzzy solution
- Kronecker product
- Block structure
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