Toward General Type-2 Fuzzy Logic Systems Based on zSlices

Abstract

Abstract-Higher order fuzzy logic systems (FLSs), such as interval type-2 FLSs, have been shown to be very well suited to deal with the high levels of uncertainties present in the majority of real-world applications. General type-2 FLSs are expected to further extend this capability. However, the immense computational complexities associated with general type-2 FLSs have, until recently, prevented their application to real-world control problems. This paper aims to address this problem by the introduction of a complete representation framework, which is referred to as zSlicesbased 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 FLSs, while it offers the capability to represent complex general type-2 fuzzy sets. As a proof-of-concept application, we have implemented a zSlicesbased general type-2 FLS for a two-wheeled mobile robot, which operates in a real-world outdoor environment. We have evaluated the computational performance of the zSlices-based general type-2 FLS, which is suitable for multiprocessor execution. Finally, we have compared the performance of the zSlices-based general type-2 FLS against type-1 and interval type-2 FLSs, and a series of results is presented which is related to the different levels of uncertainty handled by the different types of FLSs.Index Terms-General type-2 fuzzy logic systems (FLSs), type-2 FLSs, zSlices.

Type-2 fuzzy sets applied to multivariable self-organizing fuzzy logic controllers for regulating anesthesia

“…zSlices based general type-2 fuzzy sets as proposed in [24] provides a framework for extending the capabilities of interval type-2 sets to model the unequal uncertainty distribution in the third dimension. This should result in the potential for a superior control performance in comparison to type-1 and interval type-2 based fuzzy systems.…”

“…In the case of z-slices based general type-2 fuzzy sets the interval type-2 control operations previously M a n u s c r i p t 23 described are computed independently on the input and output interval type-2 fuzzy sets for each level i z . A centre of sets type-reducer is then used to combine all the type reduced sets for each zlevel i z to create an overall type reduced set [24]. The centroid defuzzifier is finally applied to obtain a final crisp output value as described in [24].…”

“…A centre of sets type-reducer is then used to combine all the type reduced sets for each zlevel i z to create an overall type reduced set [24]. The centroid defuzzifier is finally applied to obtain a final crisp output value as described in [24].…”

“…Type-2 SOFLC's are based on interval and z-slices based type-2 fuzzy sets [24] which are used for modeling the uncertainties associated with the input / output parameters. We evaluate the performance of the type-2 SOFLCs for the automatic control of anesthesia during single stage surgical procedures in which we use a non-fixed patient model and add signal noise to account for environmental and patient drug interaction uncertainties.…”

EEG Analysis for Cognitive Failure Detection in Driving Using Type-2 Fuzzy Classifiers

“…The computation of secondary membership is done offline to reduce run-time complexity of the classifiers. It may be noted that in traditional z-sliced based GT2 system [40], the GT2MF is presumed to have a specific geometry, such as triangle. The proposed method, on the other hand, computes secondary MF from the primary MF and thus is more accurate.…”