# 基于参数单点模糊化的重心法模糊系统及其概率表示理论The Center-of-Gravity Fuzzy System and Its Probability Representation Theory Based on the Parameter Singleton Fuzzifier

Abstract:
The constructed fuzzy systems are not universal approximators when the normal fuzzy implications such as Lukasiewicz implication is chosen and the union operation is taken to aggregate fuzzy inference rela- tions. It is pointed in this paper that one can dissolve the problem if the parameter singleton fuzzifier is used in the construction of fuzzy system. In this paper, the center-of-gravity fuzzy systems based on Lukasiewicz implication are first constructed by use of the parameter singleton fuzzifier, then the universal approximations of the fuzzy systems are proved and the sufficient conditions for the fuzzy system as universal approximator are given. In the end, the joint probability density functions, the marginal density functions and numerical characteristics such as mathematical expectations, variances and covariances for the fuzzy system are ob- tained.

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