| As the satisfactory performances of fuzzy models,fuzzy logic theory has been widely used in a lot of areas,for example,control,image processing,noise concellation,and so forth.In recent years,type-2 fuzzy models are considered to outperform its counterparts—the type-1 fuzzy models,so the research focusing on type-2 fuzzy logic theory is becoming more and more popular.While,because of the short developemt time,many issues are still under developed for type-2 fuzzy logic theory,for example,there are a lot of shortcomings for the design of type-2 fuzzy sets,for example,the construction is based on interval valued data,the membership function is affected by the fuzzfication coeffieicnets,and so on;the efficient type-reduction and defuzzification methods for general type-2 fuzzy sets is lack,and so forth.In this study,systematic methods for the construction of type-2 fuzzy sets are proposed and a fast type reduction and defuzzification method for general type-2 fuzzy sets is introduced.The main work and innovations are as follows:(1)Based on the principle of justifiable granularity,the interval type-2 fuzzy sets are formulated by extending the type-1 fuzzy sets which is formed based on the data sets or weighted data sets.Compared with IA,EIA,HM,interval type-2 fuzzy C-means clustering based method and several membership function methods,the proposed method is suitable for point sets and weighted point sets;the constructed membership function is not affected by the values of fuzzfier,moreover,the information hidden in the data and the expert knowledge are both involved when the interval type-2 fuzzy set is formed based on the proposed method.(2)Based on the principle of justifiable granularity and least square error method,a method of forming general type-2 fuzzy sets named as a two-phase method is proposed.This process consists of two phases where the construction of general type-2 fuzzy sets is realized by invoking the design at the local and global level.At the local level involving individual points of the universe of discourse,the principle of justifiable granularity is applied to construct secondary membership function.At the global level,the least square error method is invoked to develop the upper and lower membership functions and the principal membership function.Compared with general type-2 fuzzy C means clustering method,the formulated general type-2 fuzzy sets are not affected by the fuzzification coefficients.(3)A type reduction and defuzzficiation method named as the limited embedded type-2fuzzy sets algorithm for general type-2 fuzzy sets is proposed.A limited number of embedded type-2 fuzzy sets are considered in this algorithm.For each embedded type-2 fuzzy set,a fuzzy set made up with the points in the main domain and their associated secondry memberhip is defuzzified.At the same time a weight which is obtained by T norm based on the primary membership degrees corresponding with the points in the main domain.Then all of the defuzzified values and their associated weights are used to form a fuzzy set.At last this fuzzy set is defuzzified.In this way the defuzzification number of the general type-2 fuzzy set could be obtained.Compared with the samping method,the geometric method,the vertical slice centroid type reduction and the monotone centroid flow algorithm,the proposed method develops faster.(4)To compare the performances of interval type-2 fuzzy logic systems and their counterparts thoroughly and fairly,two kinds of interval type-2 fuzzy logic systems based on fuzzy C-means and interval type-2 fuzzy C-means are construted.And they are formulated based on three kinds of type reduction and defuzzification method: q factor method,Nie-Tan method and center of set type reducer without sorting requirement algorithm.In this study,methods for the construction of interval type-2 fuzz sets and general type-2fuzzy sets are proposed;experimental evidence for the selection of type reduction and defuzzification methods for A2C0 and A2C1 are provided;a fast type-reduction and defuzzification method for general type-2 fuzzy sets is introduced,what is more,a thorough comparative analysis is completed for interval type-2 fuzzy logic systems and their counterparts. |
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