基于矩阵半张量积的模糊逻辑研究进展

Recent Development of Fuzzy Logic Based on Semi-Tensor Product

模糊逻辑是一种在不确定性条件下建模和控制复杂过程的革命性方法,在系统建模与控制领域得到了广泛的应用。基于矩阵半张量积理论可以将模糊逻辑表达式转化为代数表达式,借鉴代数系统的经典控制理论与方法来进一步研究模糊逻辑。首先介绍了以矩阵半张量积理论为框架的模糊逻辑的理论研究进展,如模糊关系矩阵、模糊关系方程、模糊关系不等式与分层模糊控制等,其次介绍了基于矩阵半张量积框架下的模糊控制理论的应用,最后给出了基于矩阵半张量积理论的模糊逻辑研究前景。

Fuzzy logic is a revolutionary method for modeling and control of uncertain complex process,which has been widely used in the field of system modeling and control.Fuzzy logic expressions can be converted to algebraic expressions by using semi-tensor product of matrices,and the classical control theory and method of algebraic systems can be used for the further study of fuzzy logic system.This paper firstly introduces the research progress of fuzzy logic based on semi-tensor product of matrices,such as fuzzy relation matrices,fuzzy relation equations,fuzzy relation inequalities,and hierarchical fuzzy system.Then,the applications of fuzzy control theory based on semi-tensor product framework is introduced.Finally,the research prospect of fuzzy logic based on semi-tensor product of matrices is given.