Recurrent Interval Type-2 Fuzzy Neural Network Using Asymmetric Membership Functions

The fuzzy systems and control are regarded as the most widely used application of fuzzy logic systems in recent years (Jang, 1993; John & Coupland, 2007; Lin & Lee, 1006; Mendel, 2001; Wang, 1994). The structure of traditional fuzzy system models that is characterized by using type 1 fuzzy sets, which are defined on a universe of discourse, map an element of the universe of discourse onto a precise number in the unit interval [0, 1]. The concept of type-2 fuzzy sets was initially proposed by Zadeh as an extension of typical fuzzy sets (called type1) (Zadeh, 1975). Mendel and Karnik developed a complete theory of interval type-2 fuzzy logic systems (iT2FLSs) (Karnik et al, 1999; Liang & Mendel, 2000; Mendel, 2001). Recently, T2FLSs have attracted more attention in many literatures and special issue of IEEE Transactions on Fuzzy systems (Baldwin & Karake, 2003; John & Coupland, 2007; Lee & Lin, 2005; Liang & Mendel, 2000; Mendel, 2001, Hagras, 2007; Ozen & Garibaldi, 2004; Pan et al, 2007; Wang et al, 2004). T2FLSs are more complex than type-1 ones, the major difference being the present of typeis their antecedent and consequent sets. T2FLSs result better performance than type-1 Fuzzy Logic Systems (T1FLSs) on the applications of function approximation, modeling, and control. In addition, neural networks have found numerous practical applications, especially in the areas of prediction, classification, and control (Lee & Teng, 2000; Lin & Lee, 1996; Narendra & Parthasarathy, 1990). The main aspect of neural networks lies in the connection weights which are obtained by training process. Based on the advantages of T2FLSs and neural networks, the type-2 neural fuzzy systems are presented to handle the system uncertainty and reduce the rule number and computation (Castillo & Melin, 2004; Lee & Lin, 2005; Mendel, 2001; Pan et al, 2007; Wang et al, 2004). Besides, recurrent neural network has the advantages of store past information and speed up convergence (Lee & Teng, 2000). The design of a fuzzy partition and rules engine normally affects system performance. To simplify the design procedure, we usually use the symmetric and fixed membership functions (MFs), such as Gaussian, triangular. However, a large rule number should be used to achieve the specified approximation accuracy (or result larger approximated error) (Lee & Teng, 2001; Lotfi & Tsoi, 1996). Several approaches have been introduced to optimize fuzzy MFs and choose an efficient scheme for structure and parameter learning. Nevertheless, asymmetric fuzzy MFs (AFMFs) has been discussed and analyzed for this problem (Baldwin O pe n A cc es s D at ab as e w w w .ite ch on lin e. co m