Fuzzy Reasoning Method Based On The Similarity Of Characteristic Parameters Of Membership Functions

People often use the fuzzy reasoning method to deal with everyday issues and problems. For a certain problem and phenomena, people will firstly compressed all aspects of its information effectively, forming a series of useful basic rules and memory it.By using these basic rules and through the fuzzy reasoning method, the brain can reproduce the original information or get some speculated results, the brain may achieve the purpose of solving problems and interpreting various phenomenon. Therefore, the fuzzy reasoning is the inherent thinking mode of human beings, and a good fuzzy reasoning method is to express the thinking mode of human beings in a brief way which could be implemented conveniently.Fuzzy reasoning is the core of fuzzy logic system, reasoning method and rule bases are closely related. When the rule bases are completed, that is to say, all the rules in the rule bases completely are covered the input of fuzzy logic system domain; the reasoning method being used most is compositional rule of inference rules put forward by professor Zadeh. However, if the rule bases are sparse, that is, there is a gap between the two rules and the observed values exactly fall into the gap and there is no rule to match. Even though we get a conclusion, it's meaningless.So far, there are many ways to solve these reasoning problems under conditions of sparse rule bases in different degrees, but these methods all have some disadvantages to some extent such as:Complex reasoning, high calculations, narrow scope, convexity and normality which are difficult to guaranteed, resulting in very poor circumstances during multi-dimensional.This paper firstly combines the graphics features of membership functions of fuzzy sets, its support sets for a limited appropriate segmentation, and gets some characteristic nodes to indicate some important graphics features of membership functions which are in the rule bases. When all the membership functions of fuzzy sets are triangular, take the left and right endpoints of support sets and peak point as the graphics features of membership functions; When all the membership functions of fuzzy sets are trapezoidal, take the left and right endpoints of support sets and the supremum and infimum of peak points as the graphics features of membership functions; When the membership functions of fuzzy sets in the rule bases are not the same type or do not have the obvious graphics features, firstly calculate the supremum and infimum of peak points and the supremum and infimum of support sets of membership functions. Then do a limited division between the infimum of support sets and the infimum of peak points, also do a limited division between the supremum of peak points and the supremum of support sets. And the number of division points in the two respective intervals of all membership functions is the same. All of these division points which are contained the key information of membership functions construct a group characteristic nodes. We referred the arithmetic mean of these points to as the mean of the characteristic nodes. Then given the characteristic nodes and the mean of the characteristic nodes of each premise fuzzy sets and input fuzzy set, by their relative ratio expressed the relative position, we can get a new premise fuzzy sets which has the same mean of the characteristic nodes with the input fuzzy set. The same way, we can get a new conclusion fuzzy set. As a result, the two known rules can be simplified as a new rule. And the premise fuzzy set of the new rule has the same mean of the characteristic nodes and the graphic similarity of membership functions between the division points with the input fuzzy set. So the conclusion that we need has the same mean of the characteristic nodes and the graphic similarity of membership functions between the division points with the conclusion of the new rule. As a result, we can get an equation. For the equation, we can get the characteristic nodes of the conclusion that we need.The results show that the method applied in the complete rule bases, especially in the sparse rule bases, it still works; and the method is simple, and convexity, normality, monotone voice, intermediate value property and reduction can be guaranteed, and wide range of application, not subject to the restrictions under the shape of the membership functions, you can select a appropriate number of segmentation and method to improve the similar reasonability of reasoning conclusion.The reasoning algorithm for fuzzy controller for a general sense of control in different plant model simulation, the results shows that:the stronger the anti-interference, stability robustness of selected control system, the more suitable, reasonable and privileged will the controlled object be.