Approximate Solution of Complex LR Fuzzy Linear Matrix Equation
الموضوعات : Transactions on Fuzzy Sets and Systems
Xiaobin Guo
1
,
Xiangyang Fan
2
,
Hangru Lin
3
1 - Department of Mathematics and Statistics, Northwest Normal University, Lanzhou, China.
2 - Department of Mathematics and Statistics, Northwest Normal University, Lanzhou, China.
3 - Department of Mathematics and Statistics, Northwest Normal University, Lanzhou, China.
الکلمات المفتاحية: Complex fuzzy numbers, Matrix analysis, Fuzzy matrix equations, Approximate solutions.,
ملخص المقالة :
This paper aims at solving a class of linear LR complex fuzzy matrix equations $A\widetilde{X}B=\widetilde{C}$ using a matrix approach. By using the basic operation of LR fuzzy number matrix, the original complex fuzzy matrix equation is transformed into a clear matrix equation group. Two new and simplified models for calculating fuzzy solutions are designed in detail, and sufficient conditions for strong fuzzy solutions are analyzed. Finally, two examples are given to illustrate the feasibility and effectiveness of the proposed method. Now that the complex fuzzy numbers can describe uncertain factors more vivid and reasonable than the real fuzzy numbers sometimes and the wide application of matrix equations under uncertain conditions, our research work enriches the fuzzy linear systems theory.
[1] Abbasbandy S, M. Otadi, M. Mosleh, Minimal solution of general dual fuzzy linear systems, Chaos, Solitons & Fractals. 2008; 37(4):1113-1124,. DOI: https://doi.org/10.1016/j.chaos.2006.10.045.
[2] Allahviranloo T. Numerical methods for fuzzy system of linear equations. Applied Mathematics and Computation. 2004; 155(2): 493-502. DOI: https://doi.org/10.1016/S0096-3003(03)00793-8
[3] Allahviranloo T. The Adomian decomposition method for fuzzy system of linear equations. Applied Mathematics and Computation. 2005; 163(2): 553-563. DOI: https://doi.org/10.1016/j.amc.2004.02.020
[4] Allahviranloo T, M. Ghanbari, A.A. Hosseinzadeh, E. Haghi, R. Nuraei, A note on Fuzzy linear systems. Fuzzy Sets and Systems 2011; 177(1): 87-92. DOI: https://doi.org/10.1016/j.fss.2011.02.010.
[5] Allahviranloo T, Hosseinzadeh Lotfi F, Khorasani Kiasari M, Khezerloo M. On the fuzzy solution of LR fuzzy linear systems. Applied Mathematical Modelling. 2013; 37(3): 1170-1176. DOI: https://doi.org/10.1016/j.apm.2012.03.037
[6] Allahviranloo T, Mikaeilvand N, Barkhordary M. Fuzzy linear matrix equations. Fuzzy Optimization and Decision Making. 2009; 8: 165-177. DOI: https://doi.org/10.1007/s10700-009-9058-1
[7] Amirfakhrian M, Fallah M, Rodrguez-Lpez R. A method for solving fuzzy matrix equations. Soft Computing. 2018; 22: 2095-2103. DOI: https://doi.org/10.1007/s00500-017-2680-x
[8] Asady B, Abbasbandy S, Alavi M. Fuzzy general linear systems. Applied Mathematics and Computation. 2005; 169(1): 34-40. DOI: https://doi.org/10.1016/j.amc.2004.10.042
[9] Babbar N, Kumar A, Bansal A. Solving fully fuzzy linear system with arbitrary triangular fuzzy numbers. Soft Computing. 2013; 17(4): 691-702. DOI: https://doi.org/10.1007/s00500-012-0941-2
[10] Behera D,S. Chakraverty,Solving fuzzy complex system of linear equations.Information Sciences. 2014; 277: 154-162. DOI: https://doi.org/10.1016/j.ins.2014.02.014.
[11] Buckley JJ. Fuzzy complex number. Fuzzy Sets and Systems. 1989; 33(3): 333-345. DOI: https://doi.org/10.1016/0165-0114(89)90122-X
[12] Dehghan M, Hashemi B. Iterative solution of fuzzy linear systems. Applied Mathematics and Computation. 2006; 175(1): 645-674. DOI: https://doi.org/10.1016/j.amc.2005.07.033
[13] Dehghan M, Hashemi B, Ghatee M. Solution of the full fuzzy linear systems using iterative techniques. Chaos, Solitons $ Fractals. 2007; 34(2): 316-336. DOI: https://doi.org/10.1016/j.chaos.2006.03.085
[14] Dubois D, Prade H. Operations on fuzzy numbers. International Journal of Systems Science. 1978; 9(6): 613-626. DOI: https://doi.org/10.1080/00207727808941724
[15] Friedman M, Ming M, Kandel A. Fuzzy linear systems. Fuzzy Sets and Systems. 1998; 96(2): 201-209. DOI:
https://doi.org/10.1016/S0165-0114(96)00270-9
[16] Synergistic Strategy of Sustainable Hospital Site Selection in Saudi Arabia Using Spherical Fuzzy MCDM Methodology. Journal of Uncertain Systems. 2024; 17(03): 2450004(64 pages). DOI:https://doi.org/10.1142/S1752890924500041
[17] Ghanbari R. Solutions of fuzzy LR algebraic linear systems using linear programs. Applied Mathematical Modelling. 2015; 39(17): 5164-5173. DOI: https://doi.org/10.1016/j.apm.2015.03.042
18] Ghanbari M, T. Allahviranloo, W. Pedrycz, On the rectangular fuzzy complex linear systems, Applied Soft Computing. 2020; 91: 106196. DOI:https://doi.org/10.1016/j.asoc.2020.106196.
[19] Ghanbari M, Allahviranloo T, Pedrycz W. A straightforward approach for solving dual fuzzy linear systems. Fuzzy Sets and Systems. 2022; 435: 89-106. DOI: https://doi.org/10.1016/j.fss.2021.04.007
[20] Gong Z, Guo X. Inconsistent fuzzy matrix equations and its fuzzy least squares solutions. Applied Mathematical Modelling. 2011; 35(3): 1456-1469. DOI: https://doi.org/10.1016/j.apm.2010.09.022
[21] Gong Z, Guo X, Liu K. Approximate solution of dual fuzzy matrix equations. Information Sciences. 2014; 266: 112-133. DOI: https://doi.org/10.1016/j.ins.2013.12.054
[22] Guo X, Chen Y, Zhuo Q. Generalized fuzzy eigenvectors of real symmetric matrices. Journal of Intelligent & Fuzzy Systems. 2023; 44(5): 7459-7467. DOI: https://doi.org/10.3233/JIFS-222641
[23] Guo X, Han Y. Further investigation to dual fuzzy matrix equation. Journal of Intelligent & Fuzzy Systems. 2017; 33(4): 2617-2629. DOI: https://doi.org/10.3233/JIFS-17072
[24] Guo X, Li Z, Yan R. Solving complex LR fuzzy matrix equation ∼ ZC = ∼ W. Journal of Intelligent & Fuzzy Systems. 2018; 34(6): 4367-4375. DOI: https://doi.org/10.3233/JIFS-17963
[25] Guo X, Liu K. Near zero fuzzy solutions of fully fuzzy linear system. Journal of Intelligent & Fuzzy Systems. 2023; 44(5): 8043-8052. DOI: https://doi.org/10.3233/JIFS-222421
[26] Guo X, Zhang K. Minimal solution of complex fuzzy linear systems. Advances in Fuzzy Systems. 2016; 2016(1): 5293917. DOI: https://doi.org/10.1155/2016/5293917
[27] Guo X, Zhang K. Solving fuzzy matrix equation of the form ∼ XA = ∼ B. Journal of Intelligent & Fuzzy Systems. 2017; 32(3): 2771-2778. DOI: https://doi.org/10.3233/JIFS-16895
[28] Guo X, Zhuo Q. Perturbation analysis of fully fuzzy linear systems. Journal of Intelligent and Fuzzy Systems. 2023; 44(4): 5589-5599. DOI: https://doi.org/10.3233/JIFS-222392
[29] Nahmias S. Fuzzy variables. Fuzzy Sets and Systems. 1978; 1(2): 97-110. DOI: https://doi.org/10.1016/0165-0114(78)90011-8
[30] Puri ML, Ralescu DA. Differentials for fuzzy functions. Journal of Mathematics Analyisis and Application. 1983; 91(2): 552-558. DOI: https://doi.org/10.1016/0022-247X(83)90169-5
[31] Qiu J, Wu C, Li F. On the restudy of fuzzy complex analysis: Part I. The sequence and series of fuzzy complex numbers and their convergences. Fuzzy Sets and Systems. 2000; 115(3): 445-450. DOI: https://doi.org/10.1016/S0165-0114(98)00160-2
[32] Shang D, Guo X. Solving LR fuzzy linear matrix equation, Journal of Physics: Conference Series, 2020; 1592(1): 012051. DOI: https://doi.org/10.1088/1742-6596/1592/1/012051.
[33] Wu J, Jiang H, He M, Liu X. General strong fuzzy solutions of complex fuzzy matrix equations involving the Moore-Penrose weak group inverse. Information Sciences. 2024; 654: 119832. DOI:https://doi.org/10.1016/j.ins.2023.119832
[34] Zadeh LA. Fuzzy sets. Information and Control. 1965; 8: 338-353. DOI: https://doi.org/10.2307/2272014
