Design of Reinforced Interval Type-2 Fuzzy C-Means-Based Fuzzy Classifier

This paper is concerned with a new design methodology of a reinforced interval type-2 fuzzy c-means (FCM) based fuzzy classifier (FC). The key point of this study is to reduce the computational complexity of type-2 fuzzy set-based models and to alleviate the deterioration of its generalization abilities through the synergistic effect of two algorithms: First, interval type-2 FCM (IT2FCM) is used in the hidden layer of the network and connections (weights) are adjusted by invoking the least squares error estimation method. Second, an L2-norm regularization is considered in the cost function to avoid the construction of the network suffering from overfitting. In more detail, the hidden layer of the proposed FC is realized by interval type-2 FCM clustering to deal with the factor of uncertainty involved in the problem. This type of clustering is realized by using two values of the fuzzification coefficient resulting in the interval type-2 membership functions. Once completing type reduction, the membership grades of IT2FCM are used as the outputs of the hidden layer. Instead of the backpropagation training, least squares estimator based learning is applied to adjust the functional connection being regarded as linear functions mapping the hidden layer to the output layer. In order to reduce potential overfitting, L2-norm regularization is taken into account. The effectiveness of the proposed classifier is analyzed with the aid of a number of machine learning datasets as well as face image datasets. Thorough comparative studies are also included.

I. Introduction

Fuzzy neural networks (FNNs) have emerged as one of the most visible areas of research in synergy of fuzzy logic and neural networks. Fuzzy neurocomputing is concerned with the integration of the two fields in which significant advances have been made during the past two decades [1], [2]. There have been many successful ways to synthesize FNNs. The essential advantage of neural networks lies in their adaptive nature and learning abilities. In order to create and exploit a synergy effect between these two areas, FNN combines fuzzy if-then rules with neural networks that are developed by means of the standard backpropagation (BP) learning algorithm [3]– [5]. Through the combination of neural networks and fuzzy logic, a concept of FNNs was proposed by Jang [6]. The variety of fuzzy inference systems and clustering-based neural networks were proposed by Oh and Pedrycz by applying clustering and evolutionary algorithms to neural network or fuzzy logic system (FLS) [7]– [10].