A new indirect approach to the type-2 fuzzy systems modeling and design

This paper proposes a new method for designing Interval Type-2 Fuzzy Logic Systems (IT2 FLSs) considering two issues: first, quality of clustering the output space and secondly, approximating the output of the IT2 FLS based on a new output processing method. Based on these two issues, we present a new cluster validity index capable of being used for type-1 Fuzzy C-Means (FCMs), Interval Type-2 FCM (IT2 FCM), and Possibilistic C-Means (PCMs) clustering algorithms. This validity index is highly efficient in determining clusters with the least similarity between them and the highest similarity between data vectors in each cluster. Then, a new definition for uncertainty bounds is presented in order to eliminate the type-reduction process in IT2 FLSs and to increase accuracy of the existing uncertainty bounds in the literature. Finally, effectiveness of the proposed approaches compared to several well-known existing methods has been investigated. Computational results have verified accuracy and effectiveness of the proposed method.