【摘要】 为进一步研究分析多变量模糊系统以及分层模糊系统的数学机理,解决多变量模糊系统的"维数灾"问题,该文对一类广泛应用的多输入单输出模糊系统(MISO-FS)进行了解析分析,提出了一类二叉树型分层模糊系统(HFS),并推导了其解析表达式。从而证明了HFS和MISO-FS具有等效性。在此基础上分析了HFS的规则数,证明了HFS的规则数随输入变量数线性增长,因此HFS是解决模糊多变量系统"维数灾"问题的一个很好的实用方案。更多还原

【Abstract】 This paper analyzes multiple-input-single-output fuzzy systems (MISO-FS) with unequally spaced, fully-overlapped, triangular membership functions for the input variables and equally spaced, singleton membership functions for the output variable. The Sum-Product inference method, linearization rules and the center of gravity method are used for defuzzification. Explicit analytical expressions are given for the MISO-FS along with explicit analytical expressions for binary-tree-type hierarchical fuzzy systems (HFS) to prove the equivalence between MISO-FS and HFS. Since the number of rules in HFS linearly increases with the number of input variables, HFS can be used to replace MISO-FS to solve the "dimensional disaster" problem in fuzzy multi-variable systems with large numbers of input variables.更多还原