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Pure Mathematics 2026
基于梯形模糊数的模糊矩阵方程的解法
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Abstract:
本文研究了求解对偶模糊矩阵方程的AX~+B~=CX~+D~方法. 利用模糊集的分解定理, 结合梯形模糊数水平截集的左右端点, 介绍了对偶模糊矩阵方程的广义解和代数解的计算方法, 研究了两种解之间的关系以及给出了唯一代数解存在的充分条件, 并以数值算例进行说明。
This paper investigates the methods for solving the dual fuzzy matrix equation . By leveraging the decomposition theorem of fuzzy sets and combining the
left and right endpoints of the level cuts of trapezoidal fuzzy numbers, the calculation
methods for the generalized solution and algebraic solution of the dual fuzzy matrix
equation are introduced. The relationship between the two types of solutions is stud-
ied, sufficient conditions for the existence of a unique algebraic solution are provided,
and numerical examples are presented for illustration.
| [1] | Friedman, M., Ming, M. and Kandel, A. (1998) Fuzzy Linear Systems. Fuzzy Sets and Systems, 96, 201-209.
https://doi.org/10.1016/s0165-0114(96)00270-9 |
| [2] | Allahviranloo, T. and Ghanbari, M. (2012) On the Algebraic Solution of Fuzzy Linear Systems Based on
Interval Theory. Applied Mathematical Modelling, 36, 5360-5379.
https://doi.org/10.1016/j.apm.2012.01.002 |
| [3] | Nuraei, R., Allahviranloo, T. and Ghanbari, M. (2013) Finding an Inner Estimation of the Solution Set of
a Fuzzy Linear System. Applied Mathematical Modelling, 37, 5148-5161.
https://doi.org/10.1016/j.apm.2012.10.020 |
| [4] | Ghanbari, M., Allahviranloo, T. and Pedrycz, W. (2020) On the Rectangular Fuzzy Complex Linear Sys-
tems. Applied Soft Computing, 91, Article 106196. https://doi.org/10.1016/j.asoc.2020.106196 |
| [5] | Ma, M., Friedman, M. and Kandel, A. (2000) Duality in Fuzzy Linear Systems. Fuzzy Sets and Systems,
109, 55-58. https://doi.org/10.1016/s0165-0114(98)00102-x |
| [6] | Wang, X., Zhong, Z. and Ha, M. (2001) Iteration Algorithms for Solving a System of Fuzzy Linear Equa-
tions. Fuzzy Sets and Systems, 119, 121-128. https://doi.org/10.1016/s0165-0114(98)00284-x |
| [7] | Abbasbandy, S., Babolian, E. and Alavi, M. (2007) Numerical Method for Solving Linear Fredholm Fuzzy
Integral Equations of the Second Kind. Chaos, Solitons & Fractals, 31, 138-146.
https://doi.org/10.1016/j.chaos.2005.09.036 |
| [8] | 刘坤, 巩增泰. 广义完全模糊线性系统解的讨论[J]. 西北师范大学学报(自然科学版), 2008, 143(6): 6-10. |
| [9] | 刘坤, 巩增泰. 完全模糊线性系统的模糊近似解[J]. 兰州大学学报(自然科学版), 2009, 45(1): 78-82. |
| [10] | Sun, X. and Guo, S. (2009) Solution to General Fuzzy Linear System and Its Necessary and Sufficient
Condition. Fuzzy Information and Engineering, 1, 317-327. https://doi.org/10.1007/s12543-009-0024-y |
| [11] | Guo, X.B. and Gong, Z.T. (2010) Block Gaussian Elimination Methods for Fuzzy Matrix Equations. In-
ternational Journal of Pure and Applied Mathematics, 58, 157-168. |
| [12] | Gong, Z. and Guo, X. (2011) Inconsistent Fuzzy Matrix Equations and Its Fuzzy Least Squares Solutions.
Applied Mathematical Modelling, 35, 1456-1469. https://doi.org/10.1016/j.apm.2010.09.022 |
| [13] | Fariborzi Araghi, M.A. and Hoseinzadeh, M.M. (2012) Solution of General Dual Fuzzy Linear Systems
Using ABS Algorithm. Applied Mathematical Sciences, 6, 163-171. |
| [14] | Gong, Z., Guo, X. and Liu, K. (2014) Approximate Solution of Dual Fuzzy Matrix Equations. Information
Sciences, 266, 112-133. https://doi.org/10.1016/j.ins.2013.12.054 |
| [15] | 巩增泰, 杨甲荣. 基于LR-梯形模糊数的模糊线性系统解问题及其数值计算[J]. 云南大学学报(自然科学版), 2018, 40(5): 836-847. |
| [16] | Ghanbari, M., Allahviranloo, T. and Pedrycz, W. (2022) A Straightforward Approach for Solving Dual
Fuzzy Linear Systems. Fuzzy Sets and Systems, 435, 89-106. https://doi.org/10.1016/j.fss.2021.04.007 |
| [17] | Gong, Z., Wu, J. and Liu, K. (2023) The Dual Fuzzy Matrix Equations: Extended Solution, Algebraic
Solution and Solution. AIMS Mathematics, 8, 7310-7328. https://doi.org/10.3934/math.2023368 |
| [18] | Congxin, W. and Ming, M. (1992) Embedding Problem of Fuzzy Number Space: Part II. Fuzzy Sets and
Systems, 45, 189-202. https://doi.org/10.1016/0165-0114(92)90118-n |
| [19] | Kaleva, O. and Seikkala, S. (1984) On Fuzzy Metric Spaces. Fuzzy Sets and Systems, 12, 215-229.
https://doi.org/10.1016/0165-0114(84)90069-1 |
