Approximation Performance And Localization Algorithm Of Generalized Mamdani Fuzzy Systems Constructed Based On Fuzzy Similarity

Fuzzy similarity degree is a measure of describing the similar level of a fuzzy set by local information,it plays an important role in the design of fuzzy systems and fuzzy controllers.The essence of fuzzy system is a mapping relationship from the input domain to the output domain,the characteristic of fuzzy system is that it can process data information and language information at the same time,usually.The input-output relationship that reflecting the system is obtained through measurement data or digital sensors,and it has the ability of logical reasoning,numerical calculation and approximation of nonlinear functions.Especially,the approximation determines whether it can approximate any continuous nonlinear dynamic model when the fuzzy system is used for modeling and discrimination,so the approximation of the fuzzy system is very important.In the first chapter:The background of selecting topic and the research status of the topics is introduced.In the second chapter:Preparatory knowledge,in order to construct a fuzzy system,we first introduce some related concepts,for example,similar degree,fuzzy similarity and fuzzification etc.In the third chapter:The calculation formula of the fuzzy set which is rely on fuzzy similarity and Gauss fuzzifier(or single fuzzifier)is first given,then,according to Gauss fuzzifier(or single fuzzifier),product inference engine and center-averaged fuzzification,we can get the mathematic model and its analytical representation of multi-input single output generalized Mamdani fuzzy system.Secondly,the approximation of a generalized Mamdani fuzzy system based on fuzzy simi-larity is proved.In the four chapter:The positioning algorithm of the fuzzy system which is constructed in Chapter 3 is given by using the spatial positioning model of the input variables,making the al-gorithm suitable for any given input variable that we can get a specific output value.In the end,by calculating and comparing the actual output values of the sample points,it is proved that the approximation effect of the Mamdani fuzzy system based on Gauss fuzzification is better than that of the single point model gelatinization.