A Novel Approach to Generating an Interval Type-2 Fuzzy Neural Network Based on a Well-Behaving Type-1 Fuzzy TSK System

摘要

This paper presents a novel approach to automatically creating an interval type-2 fuzzy neural network (IT2-FNN) from a type-1 fuzzy TSK system (Tl-TSK). The IT2-FNN is constructed in such a way that it takes advantage of the well-behaving Tl-TSK. Our approach makes designing the IT2-FNN more efficient and the resulting system is expected to perform better than the Tl-TSK due to the footprint of uncertainty of the IT2 fuzzy sets, especially when the system is subject to heavy external or internal uncertainties. There are two automated procedures in the IT2-FNN formation: (1) antecedent structure construction, and (2) learning of the parameters in both the antecedent and consequent. The structure construction is based on antecedent structure of the Tl-TSK and consists of three steps - IT2 fuzzy set creation, similarity categorization, and mergence. The IT2 fuzzy sets are directly initialized from the fuzzy sets of the Tl-TSK. Then, the IT2 fuzzy sets are classified into different groups based on their similarities. Finally, the IT2 fuzzy sets in each group are merged to create a representative IT2 fuzzy set for each group. The parameter learning procedure uses a hybrid learning algorithm to attain the optimal values for all the parameters. The learning algorithm adopts a new adaptive steepest descent algorithm and a linear least-squares method to adjust the antecedent parameters and consequent parameters, respectively. One benchmark modelling problem is utilized to compare our approach with the Tl-TSK systems in the literature under various scenarios. The comparison results show our IT2-FNN performs better than the Tl-TSK systems, especially when there are strong uncertainties. In summary, the IT2-FNN can not only achieve better performance but its structure is simpler than that of the similar type-2 fuzzy neural networks in the literature.