General Type-2 Fuzzy Inference Systems: Analysis, Design and Computational Aspects

The aim of this work is to handle non-interval type-2 fuzzy logic systems (NIT2 FLS) in a simple manner. We retrieve an alternative representation of Type-2 fuzzy sets (T2 FS) that we call general footprint of uncertainty. Such representation, not only lets us easily visualize T2 FS in two-dimensions but also makes the understanding of basic operations and the inference procedure easier. We introduce the concept of supremum of a T2 FS and translation and cylindric extension for vertical slices to support the adopted inference mechanism, based on the scaled inference mechanism of Type-1 FIS. Finally, we propose a new defuzzification method, the vertical slice centroid type reduction, which requires low computational effort. Some calculations are presented to illustrate that the theory and simplifications proposed in this paper make NIT2 FLS, referred here as general type-2 fuzzy inference systems, much more accessible to FIS designers.