An Efficient High-Order α-Plane Aggregation in General Type-2 Fuzzy Systems Using Newton–Cotes Rules

Abstract

Nowadays, general type-2 fuzzy systems are an attractive alternative for non-linear control problems because they provide good robustness in real-world environments, where there exist many noise sources. This kind of fuzzy systems can have better performance in comparison to type-1 fuzzy systems as they offer uncertainty handling capabilities. However, one of the main problems in implementing general type-2 fuzzy systems is their elevated computational cost. The computational cost of a general type-2 fuzzy system depends on the representation that is used, for example, the α-planes representation consists on a discretization of general type-2 fuzzy systems into several horizontal slices called α-planes, then solving every α-plane as an interval type-2 fuzzy system and after that the integration of the results to approximate a general type-2 fuzzy system. The main contribution of this work is the proposed computational cost reduction of the α-planes representation by optimizing the α-planes integration process based on the composite Newton–Cotes rules. In this way, the number of α-planes required for a good approximation is reduced, and the computational cost is also reduced by introducing new equations for the α-planes aggregation. Finally, a systematic comparative analysis of the improvement offered by the proposed method with respect to the conventional approach is presented.