Self-Organizing Interval Type-2 Fuzzy Neural Network With Adaptive Discriminative Strategy

Covariate shift is a critical issue of interval type-2 fuzzy neural networks (IT2FNNs) due to the distribution discrepancy between training and testing samples. In this situation, IT2FNNs usually struggle to identify potential features from samples with explicit inductive biases. To address this problem, a self-organizing IT2FNN with an adaptive discriminative strategy (ADS-SOIT2FNN) is developed to maintain the identification performance in the presence of covariate shift. First, a granularity-based metric (GM), using higher order statistics of local samples, is designed to distinguish the distribution discrepancy caused by covariate shift. The multiple kernels incorporated into GM are able to cover the sample features of the whole Hilbert space. Second, a self-organizing strategy, associated with GM-based discriminative information, is presented to alleviate the structural bias by growing and pruning fuzzy rules. Then, a compact structure of ADS-SOIT2FNN is achieved to adapt to the covariate shift of samples and further strengthen its inductive ability. Third, an adaptive risk mitigation learning algorithm (RMLA) is introduced to update the parameters of ADS-SOIT2FNN. RMLA can regulate the derivatives of parameters with arbitrary distribution samples, which is beneficial for maintaining the global accuracy by relieving the risk of parameter biases. Finally, the effectiveness of ADS-SOIT2FNN is verified by some experiments for identifying nonlinear systems with covariate shift.

I. Introduction

The interval type-2 fuzzy neural network (IT2FNN) with powerful fuzzy reasoning capability and learning capability has been increasingly used in nonlinear dynamical systems [1], [2], [3]. It is essential for modeling IT2FNN with high-quality training samples that match the target task [4], [5], [6]. Nevertheless, the distribution discrepancy between training and testing samples results in few testing samples in the regions of interest, which is referred to as covariate shift [7], [8]. Once a covariate shift occurs, the distribution of training samples reflected onto the local regulation may cause the biasedness of IT2FNN.