Theory And Application Of Type-Ⅱ Fuzzy Systems

In1975, Professor Zadeh introduced the type-2fuzzy set to expand the traditionalfuzzy set (type-1fuzzy set). Compared with the type-1fuzzy set, the most advantage ofthe type-2fuzzy set is to use three-dimensional membership functions, so themembership degree of the element becomes a fuzzy number in [01]. The type-2fuzzysets theory is more applicable to the case of the multi-uncertainty. For example, theshape or parameters of membership functions are uncertain. When an element can notbe entirely part of a set (the membership of the element that belongs to a set is between0and1), we choose type-1fuzzy sets. When the "membership" of an element belongsto a set is uncertain (the membership degree of an element is uncertain), we can choosethe type-2fuzzy sets.Now, fuzzy systems have become most successful in the applications of fuzzy setstheory. The core of a fuzzy system is the knowledge database formed by fuzzyIF-THEN rules, which is based on the fuzzy sets theory. The same as the type-1fuzzysystem, type-2fuzzy system is also constructed by the combination of fuzzy IF-THENrules. However, the type-2fuzzy system is based on type-2fuzzy sets. Compared withthe type-1fuzzy system, the type-2fuzzy system can handle the multi-uncertaintydirectly. Because the high computational complexity of the type-2fuzzy sets, most ofthe applications of type-2fuzzy sets theory focus on the interval type-2fuzzy sets.Through constructing the model of interval type-2fuzzy systems, this PhD thesisstudies the applications of type-2fuzzy system in the field of automatic control andpattern recognition. The main contents are as follows:1. Based on the discrete interval type-2T-S fuzzy model, a fuzzy control system isdesigned by using the parallel distributed compensation. By using the Lyapunovmethod, the stabilization of the control system is analyzed, and the results arepresented in terms of linear matrix inequalities. The effectiveness of the resultsis illustrated by numerical simulations. Finally, the type-2fuzzy controllerdesign for autonomous parallel parking on bumpy road is applied to detail the design processes. The simulation results have showed the advantages of type-2fuzzy control systems on handling the information of multi-uncertainty.2. Based on the continued interval type-2T-S fuzzy model with time-varing delay,a fuzzy control system is designed by using the parallel distributedcompensation. By using the Lyapunov method, the stabilization of the controlsystem is analyzed, the results are presented in terms of linear matrixinequalities. The effectiveness of the control system is verified by numericalsimulations. Finally, the type-2fuzzy controller design for the continuous stirredtank reactor is discussed to detail the design process. The results of thesimulations further illustrate the advantages of type-2fuzzy control systems onhandling the information of multi-uncertainty.3. Chinese automatic summarization method is discussed based on the type-2fuzzy C-means clustering. In order to use the cluster analysis method, it isnecessary to represent Chinese sentences as vectors of features. These featuresinclude sentence centrality, title feature, high frequency words feature, firstsentence feature, sentence length, sentence position, and numerical data feature.Based on the text clustering analysis, the key sentences of the text can be foundout to construct the summary. Finally, the experiments have showed that theChinese automatic summarization result is more accurate to adopt the type-2fuzzy system than to adopt the type-1fuzzy system.4. Type-2fuzzy c-means clustering algorithm is applied to solve the digital audiosignal classification problem, and jumping genes genetic algorithm is used tooptimize the initial fuzzy model which is obtained by the clustering algorithm.At last, the optimized fuzzy rule base is simplified by the vector similaritymeasure, and the final fuzzy classifier model is obtained. Compared to theconventional type-1fuzzy sets, type-2fuzzy sets can handle more uncertaininformation. Especially for sample sets whose samples distribute uneven andstructures are irregular. The experiment results are more precise when the type-2fuzzy c-means clustering algorithm is adopted.