Fuzzy Control System Based on Wavelet Analysis

In the paper, we discuss the relationship between the membership function of the fuzzy control system and the wavelet basis function. We prove that a wavelet mother function can be described by a membership function of the fuzzy control system and a membership function of the fuzzy control system can also be described by a simple wavelet mother function. The one-to-one corresponding relationship between the membership function of the fuzzy control system and the wavelet basis function is verified. Thus the essence of the fuzzy reasoning and fuzzy control is revealed. This paper presents a new approach to applying wavelet analysis to fuzzy system identification, fuzzy control and fuzzy data analysis, etc.