Center of Gravity Fuzzy Systems and the Probability Distributions Based on the Circle Operators
Xue Yang, Xiao Tian Wang, Xue Hai Yuan · Advanced materials research · 2012
In the paper, the center of gravity fuzzy systems and probability representation theory based on two circle operators of the regular implications(Godel, Goguen) are studied. Firstly, based on CRI algorithm and the center of gravity defuzzification method, the joint probability density functions of two-dimensional random variables, the marginal probability density functions and numerical characteristics of these two circle operators are obtained. Then it is pointed out that the fuzzy systems based on these two circle operators are regression functions with the joint probability density function. Finally, we prove these two fuzzy systems not only have the universal approximation but possess the first-order approximation accuracy. By comparing with the center-average defuzzification method, it is found that the center of gravity defuzzification method is better than the center-average defuzzification method.