Scale and Move Transformation-Based Fuzzy Rule Interpolation with Interval Type-2 Fuzzy Sets

Fuzzy rule interpolation (FRI) is an important technique for performing inference with sparse rule bases. Even when a given observation has no overlap with the antecedent values of any existing rules, FRI may still derive a conclusion. In particular, the scale and move transformation-based approach can handle interpolation and extrapolation with multiple multi-antecedent rules. However, the difficulty in defining the required precise-valued membership functions significantly restricts the application of FRI. Type-2 fuzzy sets help to alleviate such limitations because their membership functions are themselves fuzzy. This paper extends the existing transformation-based approach of FRI by using interval type-2 fuzzy sets. The proposed approach not only facilitates the definition of representative values of interval type-2 fuzzy sets, but also modifies the underlying FRI technique to ensure intuitive interpolated conclusions. The experimentation demonstrates that the proposed approach can deal with uncertainty in FRI in a more flexible way, extending the potential of conventional FRI techniques.