Interval Type-2 Radial Basis Function Neural Network: A Modeling Framework

Abstract

In this paper, an interval type-2 radial basis function neural network (IT2-RBF-NN) is proposed as a new modeling framework. We take advantage of the functional equivalence of radial basis function neural networks (RBF-NNs) to a class of type-1 fuzzy logic systems (T1-FLS) to propose a new interval type-2 equivalent system; it is systematically shown that the type equivalence (between RBF and FLS) of the new modeling structure is maintained in the case of the IT2 system. The new IT2-RBF-NN incorporates interval type-2 fuzzy sets within the radial basis function layer of the neural network in order to account for linguistic uncertainty in the system's variables. The antecedent part in each rule in the IT2-RBF-NN is an interval type-2 fuzzy set, and the consequent part is of Mamdani type with interval weights, which are used for the Karnik and Mendel type-reduction process in the output layer of the network. The structural and parametric optimization of the IT2-RBF-NN parameters is carried out by a hybrid approach that is based on estimating the initial rule base and footprint of uncertainty (FOU) directly via a granular computing approach and an adaptive back propagation approach. The effectiveness of the new modeling framework is assessed in two parts. First, the IT2-RBF-NN is tested against a number of popular benchmark datasets, and second, it is demonstrated in a real-world industrial application that has particular challenges that are related to the uncertainty of the raw information. Via simulation results, it is shown that the proposed modeling framework performs well as compared with its T1 equivalent system. In addition, a very good computational efficiency is demonstrated as a result of the systematic and automatic creation of IT2 linguistic information and the FOU. Crucially, the proposed modeling framework opens up a host of opportunities for the academic community that already uses the popular T1-RBF-NN-based structure to try the new IT2-RBF-NN and take advantage of the numerous existing RBF-based adaptive learning algorithms, RBF-based multiobjective optimization techniques, granular computing-based information capture techniques, and real-world FLS implementations, and, in general, take advantage of the computational efficiency of the fusion of IT2-FLS and RBF-NN.