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Solving type-2 fuzzy relation equations via semi-tensor product of matrices
Y.Yan,Z.Chen,Z.Liu
0
(College of Computer and Control Engineering, Nankai University; Tianjin Key Laboratory of Intelligent Robotics, Nankai University)
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.
关键词:  Fuzzy control system  Type-2 fuzzy logic system  Type-2 fuzzy relation  Type-2 fuzzy relation equation  Semitensor product of matrices
DOI:
Received:August 22, 2013Revised:February 21, 2014
基金项目:
Solving type-2 fuzzy relation equations via semi-tensor product of matrices
Y. Yan,Z. Chen,Z. Liu
(College of Computer and Control Engineering, Nankai University; Tianjin Key Laboratory of Intelligent Robotics, Nankai University)
Abstract:
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.
Key words:  Fuzzy control system  Type-2 fuzzy logic system  Type-2 fuzzy relation  Type-2 fuzzy relation equation  Semitensor product of matrices