Computationally efficient type-reduction strategies for a type-2 fuzzy logic controller

A type-2 fuzzy set is characterized by a concept called footprint of uncertainty (FOU). It provides the extra mathematical dimension that equips type-2 fuzzy logic systems (FLSs) with the potential to outperform their type-1 counterparts. While a type-2 FLS has the capability to model more complex relationships, the output of a type-2 fuzzy inference engine needs to be type-reduced. As type-reduction is very computationally intensive, type-2 FLSs may not be suitable for certain real-time applications. This paper aims at developing more computationally efficient type-reducers. The proposed type-reducer is based on the concept known as equivalent type-1 sets (ET1Ss), a collection of type-1 sets that replicates the input-output map of a type-2 FLS. Simulations are presented to demonstrate that the proposed type-reducing algorithms have lower computational cost and better performances than the Karnik-Mendel type-reducer.