Type-2 FLS Modeling Capability Analysis

There has been an increasing amount of research on type-2 fuzzy logic systems (FLSs) recently. The interest is fueled by results demonstrating that type-2 fuzzy sets offer a framework for effectively solving problems where uncertainties are present A concept, known as the footprint of uncertainty (FOU), is mainly responsible for the improved modeling capability of type-2 FLSs. This paper aims at providing insight into how the extra mathematical dimension provided by the FOU differentiates type-2 FLSs from type-1 FLSs. Since the input-output relationships of both types of FLS are fixed once the parameters are selected, the analysis is performed by finding a set of equivalent type-1 sets (ET1Ss) that re-produces the input-output map of a type-2 FLS. Results are presented to demonstrate that a type-2 fuzzy system is able to model more complex input-output relationship because the ET1S changes as the input varies. The technique for converting a type-2 fuzzy set into a group of type-1 sets is also useful as it provides a framework for extending the entire wealth of type-1 fuzzy control/identification/design/analysis techniques to type-2 systems