Defasification in informational technologies of fuzzy control on the basis of membership functions of several arguments

DOI №________________

Abstract

Using the information technologies for the fuzzy control of complex systems with depended characteristics and restrictions on control variables requires the applying of fuzzy logic with the membership functions of several arguments. It requires developing the implementation of fuzzy conclusion phases. The formalization of fuzzy control problem based on the membership functions of several arguments is presented. A generalized view of the knowledge base rules for fuzzy conclusion is presented. Formulas for computing at all stages of fuzzy conclusion for calculating the values of control variables are described. One of the most difficult stages of fuzzy conclusion is defuzzification. Existing approaches to realization of defuzzification in systems of fuzzy conclusion are considered. Among them the methods of the center of gravity, the median, the largest of the maxima, the smallest of the maxima, the center of the maxima could be single out. The most popular among the existing methods of defuzzification is the method of the center of gravity. Classical methods of defuzzification in general case is very difficult to use in the case of membership functions of several arguments. Based on the idea of the center of gravity method, a new defuzzification method is proposed for the membership functions of several arguments, using the Monte Carlo method to calculate the integrals. The use of the numerical method makes it possible to carry out defuzzification with a certain error, depending on the number of points chosen at random. This method of defuzzification can be used in the development of information technologies that implement fuzzy logical conclusion based on the membership functions of several arguments in control tasks.

Keywords: complex system, fuzzy control, information technology, membership function of several arguments, defuzzification.

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