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Abstract
In this thesis, type-1 and type-2 Takagi-Sugeno-Kang (TSK) inference engines are presented. The uncertainties in type-1 TSK fuzzy logic systems (FLSs) using subtractive clustering is analyzed. A new subtractive clustering based type-2 TSK fuzzy system identification algorithm [1] and fuzzy model evaluation is proposed. Experimental result shows the effectiveness of our method. Furthermore, a comparison of these two TSK FLSs is given. Finally, the importance and limitation of the results are discussed.
Our new subtractive clustering algorithm [1] is designed to identify type-2 TSK FLSs. This algorithm is an extension of the type-1 TSK modeling algorithm proposed by Chiu [2, 3]. In our proposed method, the subtractive clustering method is combined with least-square estimation algorithm to pre-identify a type-1 fuzzy model from input/output data. Then with type-2 TSK fuzzy logic theory [4], considering the type-1 membership functions as principal membership functions (MFs) of type-2 FLS, the antecedent MFs are extended as interval type-2 fuzzy memberships by assigning uncertainty to cluster centers, and the consequent parameters are extended as fuzzy numbers (type-1 fuzzy subsets) by assigning uncertainty to consequent parameter values. Minimum error model is obtained through enumerative search of optimum values for spreading percentage of cluster centers and consequent parameters. By doing so, fuzzy modeling result of type-2 TSK FLS is found to be more appropriate than the one of type-1 TSK FLS.
