Closed form fuzzy interpolation with interval type-2 fuzzy sets

Fuzzy rule interpolation enables fuzzy inference with sparse rule bases by interpolating inference results, and may help to reduce system complexity by removing similar (often redundant) neighbouring rules. In particular, the recently proposed closed form fuzzy interpolation offers a unique approach which guarantees convex interpolated results in a closed form. However, the difficulty in defining the required precise-valued membership functions still poses significant restrictions over the applicability of this approach. Such limitations can be alleviated by employing type-2 fuzzy sets as their membership functions are themselves fuzzy. This paper extends the closed form fuzzy rule interpolation using interval type-2 fuzzy sets. In this way, as illustrated in the experiments, closed form fuzzy interpolation is able to deal with uncertainty in data and knowledge with more flexibility.