Algebraic Formulation and Application of Multi-Input Single-Output Hierarchical Fuzzy Systems With Correction Factors

Abstract

Hierarchical fuzzy systems (HFSs) are successfully applied to control systems and computer networks. Particularly, correction factor is introduced to regulate fuzzy rules and alleviate the problems of memory usage and real-time performance of systems. This paper considers the multi-input single-output HFSs with correction factors, and proposes an algebraic framework by using the semi-tensor product of matrices. Firstly, a kind of fuzzy correction factor matrix (FCFM) is constructed to realize the fuzzification of correction factor, based on which, an algebraic form is developed for two-input single-output fuzzy systems. Secondly, the structure diagram of HFSs is decomposed into several fuzzy logic units, which have the form of two-input singleoutput fuzzy systems with FCFM. Based on this operation, the algebraic formulation of serial, parallel and hybrid HFSs with correction factors is proposed. Finally, the effectiveness of HFSs with FCFM is verified by studying the on-ramp metering of freeway.