A Research On Partition Of Fuzzy Systems And Its Approximation Accuracy

The concept of Fuzzy Sets was proposed firstly by Zadeh in 1965. Afterwards, many scholars have dealed with a series of research on it, and has established the systematic fuzzy systems theory. Fuzzy system has been widely applied in practical production activities, scientific experiments and daily life, Which promotes the development of fuzzy system further. A fuzzy system is comprised of fuzzifier, fuzzy rule base, fuzzy inference engine and defuzzifier. And the fuzzy rule base is core. So the researching for the fuzzy rule base is very important for fuzzy system.In the first chapter of this paper mainly introduces the basic concept of fuzzy mathematics, the second chapter basically introduces fuzzy system and its relevant knowledge, and the problem of its approximation accuracy, The third chapter basically introduces the definition of independence and coupling of the fuzzy system. So we will study fuzzy system based on the definition of independence and coupling of the fuzzy rule. Firstly, based on the definition of independence and coupling, we can divided fuzzy rule base into independent rules, coupling rules and surplus rules. For the part of independent rules, we adopt Mamdani combination inference, for the part of coupling rules, we adopt Godel combination inference, for the part of surplus rules, we adopt the incompatibility of rules for calculation. Secondly, for the part of independent rules, we get its expression by the singletom Fuzzifier and center average Defuzzifier. Similarly, we also get the expression of the part of coupling rules. For the part of surplus rules, we also adopt center average Defuzzifier and get its expression. So we get the analytical expression of the whole fuzzy system. Finally, with a concrete fuzzy system for example, we divide it into three parts, and analyse approximation accuracy of the fuzzy system. And we analyse the absolute error and relative error. Then We show that the method is reasonable.