A Research On Independence Of Fuzzy Systems

The concept of Fuzzy Sets was proposed by Zadeh in 1965. Afterwards, many scholars have dealed with a series of research on it, and have established the systematic fuzzy systems theory. As we known, fuzzy sets theroy is mostly used in fuzzy systems. And because it is important to discuss the independence of fuzzy rules for the expression and understanding of fuzzy systems, so what we studied as followed are significant.In this paper, we firstly introduce the independent definition about two fuzzy sets, after that we give the independent definition between the fuzzy relationship. Then presents a new definition of fuzzy rules independence based on fuzzy relationship, at the same time, we discuss the relevant properties of rules independence. In what follows, the equivalent condition between Mamdani compositional inference and independent inference of sum composition are also obtained, and getting the conclusion that Minimum Inference Engine will not be influenced if using the above result. All these concepts have played a major role in the discussion of the independence of fuzzy systems.Secondly, by contrast with the independent definition of fuzzy rules, we present the correlated notion of fuzzy sets; it can reflect the correlated possibility of fuzzy sets. And we will confirm the relations between the fuzzy sets. In this perspective, the correlated conception of fuzzy rules is also described. Using the fuzzy rules' correlated degree target, may carry on optimized processing to the fuzzy rule base. This has given the concrete example in the paper, and has made the anticipated good result. Then proposes a classification method of fuzzy rules. So, the fuzzy rule base can be divided into the independent fuzzy rules and the correlated fuzzy rules through the definition of fuzzy rules independence. For the independent part, we apply the Mamdani compositional inference, but for the correlated part, we use the Godel combination inference, then the inference formula of fuzzy rules base is obtained.Finally, a real fuzzy system is established and the detailed division of fuzzy rules base is given. Validity of the division to the real fuzzy system is obtained by computing, and has made better approximation effects.