Nonstationary fuzzy neural network based on FCMnet clustering and a modified CG method with Armijo-type rule

Abstract

Nonstationary fuzzy inference systems (NFISs) model the variation in opinions of individual experts and expert groups. They have the capability similar to type-2 fuzzy systems in some regards with less computational costs. This paper presents a nonstationary fuzzy neural network (NFNN) model by combining NFISs and neural networks (NNs). The proposed model synthesizes the logical inference and language expression abilities of NFIS with the learning mechanism of NNs. Hence, it makes NNs more translatable and also achieves self-learning of fuzzy rules. Besides, a fuzzy c-means network (FCMnet) clustering and a modified conjugate gradient method with constrained Armijo-type rule (MCGA) are proposed to initialize and train NFNN, respectively. The proposed FCMnet first combines the fuzzy c-means (FCM) algorithm with NNs. Thus, it not only improves the performance of FCM, but also makes NNs more interpretable. For MCGA, we construct a specific conjugate coefficient to ensure the sufficient descent property and propose a constrained Armijo-type rule to search a suitable learning rate in each iteration. By adopting these two techniques, MCGA achieves a fast convergence speed. In addition, both weak and strong convergence results are proven rigorously. Experiments on 14 datasets are carried out to illustrate the competitive performance of our models.