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

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• 作者：Yongyi Yan (1) (2)
  Zengqiang Chen (1) (2)
  Zhongxin Liu (1) (2)
  
• 关键词：Fuzzy control system ; Type ; 2 fuzzy logic system ; Type ; 2 fuzzy relation ; Type ; 2 fuzzy relation equation ; Semitensor product of matrices
• 刊名：Journal of Control Theory and Applications
• 出版年：2014
• 出版时间：May 2014
• 年：2014
• 卷：12
• 期：2
• 页码：173-186
• 全文大小：
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• 作者单位：Yongyi Yan (1) (2)
  Zengqiang Chen (1) (2)
  Zhongxin Liu (1) (2)
  
  1. College of Computer and Control Engineering, Nankai University, Tianjin, 300071, China
  2. Tianjin Key Laboratory of Intelligent Robotics, Nankai University, Tianjin, 300071, China
  
• ISSN：1993-0623

文摘

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.