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

摘要: 在模糊系统的构造中，如果使用Lukasiewicz蕴涵且推理关系取并运算，则所构造的模糊系统没有泛逼近性。针对这一问题，本文指出：通过应用参数单点模糊化方法可解决此问题。本文首先应用参数单点模糊化方法，成功地构造出了基于Lukasiewicz蕴涵的重心法模糊系统，然后证明了所构造的模糊系统具有泛逼近性，并给出了这种模糊系统具有泛逼近性的充分条件。最后给出了所构造重心法模糊系统对应的联合概率密度函数和边缘概率密度函数，给出了这些概率分布的数学期望、方差和协方差等数字特征。

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.