Building an Intelligent Controller using Simple Genetic Type-2 Fuzzy Logic System

Despite the advantages offered by type-2 fuzzy systems (T2FS) in handling uncertainties in control applications, one major problem that hinders its wide-spread implementation in real-time applications is its high computational cost (Hameed, 2010). In order to reduce the computational burden of T2FS, a simplified T2FS based on a hybrid structure of four type-1 fuzzy systems (T1FS) and a genetic algorithm (GA) is introduced (Hameed, 2009). In addition to its rule in providing the system with adaptability to cope with changing conditions, a GA provides the system with a tool to detect and illustrate the amount of uncertainty incorporated in the system. In order to show the robustness and reliability of the new implementation, the developed approach is applied to: (a) control a nonlinear multiinput multi-output (MIMO) system equipped with various types of uncertainties as an example of using T2FS in industrial applications, and (b) evaluate students’ learning achievement as an example of using T2FS in decision support systems. The new implementation of T2FS showed a superior response compared to the very complex and computational costly type-reduction approach. In addition, the ease of using the new implementation, which does not require more than the basic knowledge of T1FS and GA, is expected to help advancing the application of T2FS in multiple different areas of applications. FLS constructed based on type-1 fuzzy systems (T1FS), referred to as T1FLS, have demonstrated their ability in many applications, especially for the control of complex nonlinear systems that are difficult to model analytically (Zadeh, 1973; King & Mamdani, 1997). However, researchers have shown that T1FLS have difficulty in modeling and minimizing the effect of uncertainties (Mendel, 2001). A reason being that, T1FS are certain in the sense that for each input there is a crisp membership grade. T2FS, characterized by membership grades that are themselves fuzzy, were first introduced by Zadeh in 1975 to account for this problem (Zadeh, 1975a). As it is illustrated in Fig. 1, the MF of a T2FS has a footprint of uncertainty (FOU), which represents the uncertainties in the shape and position of T1FS (Wu & Tan, 2004). The FOU is bounded up by an upper MF (UMF) and lower by a lower MF (LMF), both of which are T1MF. Since the FOU of T2FS provides an extra mathematical dimension, they are very useful in circumstances where it is difficult to determine an exact membership grade for FS. Therefore, the amount of uncertainty in a system could be reduced by using T2FLS since it offers better capabilities to handle