Gravity-based Boolean Fuzzy Systems And Their Representation Theory Of Probability

Fuzzy control is the method using fuzzy mathematics idea to achieve control purpose. In the traditional control areas, the precision of control system's dynamic model effects control result. However, for complex systems, because of too many variables, it's difficult to accurately describe the dynamic, so engineers have used various methods to simplify the system dynamics, but this method is less than ideal. In other words, if the system is too complex or difficult to accurately describe, it appears that they do nothing to help, so people try to deal with these problems using fuzzy control.Construction of fuzzy systems is divided into the following four processes: (1) Fuzzy input variables;(2) Construct fuzzy reasoning;(3) Fuzzy reasoning;(4) Defuzzy the output fuzzy sets. In this paper, major elements are as follow:Part one, it gives brief introduction of fuzzy control system.This part explains what is fuzzy control systems and its advantages and disadvantages.Part two, it structures single input-single output data's joint probability density function and fuzzy system. Firstly, input variables fuzzy using single point, then we structure fuzzy reasoning of the given five fuzzy implication operators, and calculated joint probability density function using the fuzzy reasoning. This part also examins the marginal distribution and digital features of this probability distribution. Finally, we calculate its center-of-gravity fuzzy system and the universal approximation using the probability distribution.Part three, it solves the function's joint probability density function and structures fuzzy systems. This part introduces the concept of a single point fuzzy method of input variables and adaptive universe of output fuzzy sets. Appling of these two methods, we successfully resolve the problem that Boolean-type implication operator can not be constructed fuzzy system using CRI method.Part four, it compares fuzzy systems which constructe by center-of-gravity method and maximum defuzzifier method. The result is that the fuzzy system's approximation accuracy of maximum defuzzification is higher than the other. Fuzzy systems of center-of-gravity method reveal the significance of the probability theory.