Interval Type-2 Fuzzy Membership Function Design and its Application to Radial Basis Function Neural Networks

Abstract

Type-2 fuzzy sets has been shown to manage uncertainty more effectively than type-1 fuzzy sets in several pattern recognition applications [1]-[10]. However, computing with type-2 fuzzy sets can require high computational complexity since it involves numerous embedded type-2 fuzzy sets. To reduce the complexity, interval type-2 fuzzy sets can be used. In this paper, an interval type-2 fuzzy membership design method and its application to radial basis function (RBF) neural networks is proposed. Type-1 fuzzy memberships which are computed from the centroid of the interval type-2 fuzzy memberships are incorporated into the RBF neural network. The proposed membership assignment is shown to improve the classification performance of the RBF neural network since the uncertainty of pattern data are desirably controlled by interval type-2 fuzzy memberships. Experimental results for several data sets are given.