Solving type-2 fuzzy relation equations via semi-tensor product of matrices

被引：0
作者：
Yan Y. [1 ,2 ]
Chen Z. [1 ,2 ]
Liu Z. [1 ,2 ]
机构：
[1] College of Computer and Control Engineering, Nankai University, Tianjin
[2] Tianjin Key Laboratory of Intelligent Robotics, Nankai University, Tianjin
来源：
Yan, Y. (yyyan@mail.nankai.edu.cn) | 1600年 / South China University of Technology卷 / 12期
基金：
中国国家自然科学基金;
关键词：
Fuzzy control system; Semitensor product of matrices; Type-2 fuzzy logic system; Type-2 fuzzy relation; Type-2 fuzzy relation equation;
D O I：
10.1007/s11768-014-0137-7
中图分类号：
学科分类号：
摘要：
The problem of solving type-2 fuzzy relation equations is investigated. In order to apply semi-tensor product of matrices, a new matrix analysis method and tool, to solve type-2 fuzzy relation equations, a type-2 fuzzy relation is decomposed into two parts as principal sub-matrices and secondary sub-matrices; an r-ary symmetrical-valued type-2 fuzzy relation model and its corresponding symmetrical-valued type-2 fuzzy relation equation model are established. Then, two algorithms are developed for solving type-2 fuzzy relation equations, one of which gives a theoretical description for general type-2 fuzzy relation equations; the other one can find all the solutions to the symmetrical-valued ones. The results can improve designing type-2 fuzzy controllers, because it provides knowledge to search the optimal solutions or to find the reason if there is no solution. Finally some numerical examples verify the correctness of the results/algorithms. © 2014 South China University of Technology, Academy of Mathematics and Systems Science, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg.
引用
收藏
页码：173 / 186
页数：13
相关论文
共 28 条
[1]  
Cheng D., Semi-tensor product of matrices and its application to Morgen's problem, Science in China Series F: Information Sciences, 44, 3, pp. 195-212, (2001)
[2]  
Cheng D., Qi H., Zhao Y., An Introduction to Semi-Tensor Product of Matrices and Its Applications, (2012)
[3]  
Li H., Wang Y., On reachability and controllability of switched Boolean control networks, Automatica, 48, 11, pp. 2917-2922, (2012)
[4]  
Cheng D., Disturbance decoupling of boolean control networks, IEEE Transactions on Automatic Control, 56, 1, pp. 2-10, (2011)
[5]  
Cheng D., Qi H., Zhao Y., Analysis and control of Boolean networks: a semi-tensor product approach, Acta Automatica Sinica, 37, 5, pp. 529-540, (2011)
[6]  
Li H., Wang Y., Boolean derivative calculation with application to fault detection of combinational circuits via the semi-tensor product method, Automatica, 48, 4, pp. 688-693, (2012)
[7]  
Li Z., Qiao Y., Qi H., Et al., Stability of switched polynomial systems, Journal of Systems Science and Complexity, 21, 3, pp. 362-377, (2008)
[8]  
Cheng D., Qi H., Global stability and stabilization of polynomial systems, Proceedings of the 46th IEEE Conference on Decision and Control, pp. 1746-1751, (2007)
[9]  
Wang Y., Zhang C., Liu Z., A matrix approach to graph maximum stable set and coloring problems with application to multi-agent systems, Automatica, 48, 7, pp. 1227-1236, (2012)
[10]  
Ge A., Wang Y., Wei A., Et al., Control design for multi-variable fuzzy systems with application to parallel hybrid electric vehicles, IET Control Theory and Applications, 30, 8, pp. 998-1004, (2013)
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