A Brief Survey on Fuzzy Set Interpolation Methods

Fuzzy systems working with classical compositional rule based reasoning methods require the existence of applicable rules for all the possible observations, i.e. an ε>0 covering rule base. In several cases this demand cannot be fulfilled either due to lack of proper rules or the limited storing and processing possibilities. In such circumstances the application of FRI based inference techniques offer the best solution. FRI methods can be divided into two groups depending on whether they produce the conclusion directly or a new auxiliary rule is interpolated first. The members of the second group, the so-called two-step methods essentially follow the concepts of the Generalized Methodology of fuzzy rule interpolation (GM) introduced by Baranyi et al in [1]. The rest of this paper is organized as follows. Section 2 recalls the basic ideas of GM. A condition set for the evaluation and comparison of the FSI techniques is introduced in section 3. Sections 4-6 present the FSI methods FEAT-p, FEAT-LS and VESI.