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AIMS Mathematics

2022, Volume 7, Issue 2: 3221-3238. doi: 10.3934/math.2022178
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On the general strong fuzzy solutions of general fuzzy matrix equation involving the Core-EP inverse

  • School of mathematics and Physics, Guangxi Key Laboratory of Hybrid Computation and IC Design Analysis, Guangxi University for Nationalities, Nanning, 530006, China
  • Received: 27 April 2021 Accepted: 11 November 2021 Published: 26 November 2021

  • MSC : 08A72, 15A09

  • The inconsistent or consistent general fuzzy matrix equation are studied in this paper. The aim of this paper is threefold. Firstly, general strong fuzzy matrix solutions of consistent general fuzzy matrix equation are derived, and an algorithm for obtaining general strong fuzzy solutions of general fuzzy matrix equation by Core-EP inverse is also established. Secondly, if inconsistent or consistent general fuzzy matrix equation satisfies $ X\in R(S^{k}) $, the unique solution or unique least squares solution of consistent or inconsistent general fuzzy matrix equation are given by Core-EP inverse. Thirdly, we present an algorithm for obtaining Core-EP inverse. Finally, we present some examples to illustrate the main results.

    Citation: Hongjie Jiang, Xiaoji Liu, Caijing Jiang. On the general strong fuzzy solutions of general fuzzy matrix equation involving the Core-EP inverse[J]. AIMS Mathematics, 2022, 7(2): 3221-3238. doi: 10.3934/math.2022178

    Related Papers:

  • The inconsistent or consistent general fuzzy matrix equation are studied in this paper. The aim of this paper is threefold. Firstly, general strong fuzzy matrix solutions of consistent general fuzzy matrix equation are derived, and an algorithm for obtaining general strong fuzzy solutions of general fuzzy matrix equation by Core-EP inverse is also established. Secondly, if inconsistent or consistent general fuzzy matrix equation satisfies $ X\in R(S^{k}) $, the unique solution or unique least squares solution of consistent or inconsistent general fuzzy matrix equation are given by Core-EP inverse. Thirdly, we present an algorithm for obtaining Core-EP inverse. Finally, we present some examples to illustrate the main results.


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    [1] S. Abbasi, A. Jalali, A novel approach for solving fully fuzzy linear systems and their duality, J. Intell. Fuzzy Syst., 37 (2019), 1–11. doi: 10.3233/JIFS-182837. doi: 10.3233/JIFS-182837
    [2] S. Abbasi, A. Jalali, Fuzzy tracking control of fuzzy linear dynamical systems, ISA T., 97 (2020), 102–115. doi:10.1016/j.isatra.2019.07.028. doi: 10.1016/j.isatra.2019.07.028
    [3] B. Asady, S. Abbasbandy, M. Alavi, Fuzzy general linear systems, Appl. Math. Comput., 169 (2005), 34–40. doi:10.1016/j.amc.2004.10.042. doi: 10.1016/j.amc.2004.10.042
    [4] A. Papadopoulos, Nonnegative matrices in the mathematical sciences, J. Korean. Soc. Ind. Appl. Math., 35 (1994), 31–39. doi:10.1137/1.9781611971262. doi: 10.1137/1.9781611971262
    [5] O. M. Baksalary, G. Trenkler, Core inverse of matrices, Linear. Multilinear. A., 58 (2010), 681–697. doi:10.1080/03081080902778222. doi: 10.1080/03081080902778222
    [6] S. S. L. Chang, L. A. Zadeh, On fuzzy mapping and control, IEEE. T. Syst. Man. Cy. B., 2 (1996), 180–184. doi:10.1109/TSMC.1972.5408553. doi: 10.1109/TSMC.1972.5408553
    [7] Q. Dong, Y. Xing, S. Chen, Solving fuzzy matrix games through a ranking value function method, J. Math. Comput. Sci., 18 (2018), 175–183. doi:10.22436/jmcs.018.02.05. doi: 10.22436/jmcs.018.02.05
    [8] D. Dubois, H. Prade, Operations on fuzzy numbers, Int. J. Syst. Sci., 9 (1978), 613–626. doi:10.1080/00207727808941724. doi: 10.1080/00207727808941724
    [9] M. Friedman, M. Ming, A. Kandel, Fuzzy linear systems, Fuzzy. Set. Syst., 96 (1998), 201–209. doi: 10.1016/S0165-0114(96)00270-9. doi: 10.1016/S0165-0114(96)00270-9
    [10] D. E. Ferreyra, F. E. Levis, N. Thome, Characterizations of k-commutative equalities for some outer generalized inverses, Linear. Multilinear. A., 15 (2018), 1–16. doi:10.1080/03081087.2018.1500994. doi: 10.1080/03081087.2018.1500994
    [11] D. E. Ferreyra, F. E. Levis, N. Thome, Revisiting the core EP inverse and its extension to rectangular matrices, Quaest. Math., 41 (2018), 265–281. doi: 10.1007/s00010-018-0570-7. doi: 10.1007/s00010-018-0570-7
    [12] H. Jiang, H. Wang, X. Liu, Solving fuzzy linear systems by a block representation of generalized inverse: The core inverse, Comput. Appl. Math., 39 (2020), 1–20. doi:10.1007/s40314-020-01156-0. doi: 10.1007/s40314-020-01156-0
    [13] Z. Gong, X. Guo, Inconsistent fuzzy matrix equations and its fuzzy least squares solutions, Appl. Math. Model., 35 (2011), 1456–1469. doi:10.1016/j.apm.2010.09.022. doi: 10.1016/j.apm.2010.09.022
    [14] M. Mazandarani, N. Pariz, A. V. Kamyad, Granular Differentiability of Fuzzy-Number-Valued Functions, IEEE. T. Fuzzy. Syst., 99 (2017), 310–323. doi:10.1109/TFUZZ.2017.2659731. doi: 10.1109/TFUZZ.2017.2659731
    [15] B. Mihailovi$\acute{c}$, V. M. Jerkovi$\acute{c}$, B. Male$\check{s}$evi$\acute{c}$, Solving fuzzy linear systems using a block representation of generalized inverses: The Moore-Penrose inverse, Fuzzy. Set. Syst., 353 (2018), 44–65. doi:10.1016/j.fss.2017.11.007. doi: 10.1016/j.fss.2017.11.007
    [16] B. Mihailovi$\acute{c}$, V. M. Jerkovi$\acute{c}$, B. Male$\check{s}$evi$\acute{c}$, Solving fuzzy linear systems using a block representation of generalized inverses: The group inverse, Fuzzy. Set. Syst., 353 (2018), 66–85. doi:10.1016/j.fss.2018.04.015. doi: 10.1016/j.fss.2018.04.015
    [17] S. Nahmias, Fuzzy variables, Fuzzy. Set. Syst., 1 (1978), 97–110. doi:10.1016/0165-0114(78)90011-8. doi: 10.1016/0165-0114(78)90011-8
    [18] K. M. Prasad, K. S. Mohana, Core-EP inverse, Linear. Multilinear. A., 62 (2014), 792–802. doi:10.1080/03081087.2013.791690. doi: 10.1080/03081087.2013.791690
    [19] Rompicharla, L. N. Charyulu, Putcha, Venkata Sundaranand, G. V. S. R. Deekshithulu, Controllability and observability of fuzzy matrix discrete dynamical systems, J. Nonlinear. Sci. Appl., 12 (2019), 816–828. doi:10.1134/S0012266115110075. doi: 10.1134/S0012266115110075
    [20] H. Wang, Core-EP decomposition and its applications, Linear. Algebra. Appl., 508 (2016), 289–300. doi:10.1016/j.laa.2016.08.008. doi: 10.1016/j.laa.2016.08.008
    [21] G. Wang, Y. Wei, S. Qiao, Generalized inverses: Theory and computations, 2Eds., Beijing: Science Press, 2005. doi: 10.1016/j.laa.2005.04.020.
    [22] K. Wang, B. Zheng, Inconsistent fuzzy linear systems, Appl. Math. Comput., 181 (2006), 973–981. doi:10.1016/j.amc.2006.02.019. doi: 10.1016/j.amc.2006.02.019
    [23] L. A. Zadeh, The concept of a linguistic variable and its application to approximate reasoning-Ⅲ, Inform. Sci., 8 (1975), 199–249. doi:10.1016/0020-0255(75)90017-1. doi: 10.1016/0020-0255(75)90017-1
    [24] B. Zheng, K. Wang, General fuzzy linear systems, Appl. Math. Comput., 181 (2006), 1276–1286, doi:10.1016/j.amc.2006.02.027. doi: 10.1016/j.amc.2006.02.027
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