Solving type-2 fuzzy relation equations via semi-tensor product of matrices
Yongyi YAN
Zengqiang CHEN
Zhongxin LIU
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.
机标关键词：fuzzy relation equationsoptimal solutionsfuzzy controllersanalysis method
资助基金：This work was partial y supported by the Natural Science Foundation of China(61174094)the Tianjin Natural Science Foundation of China(13JCYBJC17400)the Program for New Century Excel ent Talents in University of China(NCET-10-0506)
论文发表日期：2014-01-01
在线出版日期：2025-08-15（本平台首次上网日期，不代表文献的发表时间）
页数：14( 173-186 )
英文信息