zSlices — towards bridging the gap between interval and general type-2 fuzzy logic

Higher order fuzzy logic systems such as interval type-2 fuzzy logic systems have been shown to be very well suited to dealing with the large amounts of uncertainties present in the majority of real world applications. General type-2 fuzzy logic systems are expected to further extend this capability. However, the complexity as well as the immense computational requirements have generally prevented a foray into general type-2 fuzzy logic research. This paper introduces an alternative approach termed zSlices for representing general type-2 sets based on interval type-2 sets. Thus, this will lead to a smooth transition from interval to general type-2 fuzzy systems. The proposed approach will lead to a significant reduction in both the complexity and the computational requirements for general type-2 fuzzy logic systems. Hence, this will lead to facilitating the application of general type-2 fuzzy logic to many real world applications.