A new method for rule interpolation inspired by rough-fuzzy sets

Abstract

Fuzzy rule interpolation (FRI) is an important technique for performing inference with sparse rule bases. Even when the given observations have no overlap with the antecedent values of any rule, FRI may still derive a conclusion. Nevertheless, little existing work on FRI can handle different types of uncertainty in fuzziness. Whilst membership functions play an important role in defining fuzzy sets, it is sometimes impossible to give a precise crisp value. The uncertainty in fuzzy set membership functions makes the task of FRI more difficult. Rough set theory is a useful tool to deal with incomplete knowledge by the introduction of the concepts of lower and upper approximations. This paper proposes a new extension to conventional FRI by representing uncertain fuzzy set membership functions with a specific type of rough-fuzzy approximation. The proposed method follows the scale and move transformation approach to performing interpolation, and can deal with rule interpolation in a more flexible way.