Extending the concept of Fuzzy Rule Interpolation with the interpolation of fuzziness

Fuzzy Rule Interpolation (FRI) methods are not always suitable for describing changes in the conclusion fuzziness. For example, it is difficult to describe cases in which the conclusion for a crisp observation must be fuzzy, or in which an increase in the fuzziness of an observation yields less fuzziness in the conclusion. This problem is mainly inherited from a lack of information in the model, and originates from the deficiency of the fuzzy rule representation. In this paper, a novel rule representation concept called “double fuzzy dot” is suggested, which helps the elaboration of FRI methods in order to be able to better handle the fuzziness of the conclusion. Two simple examples of such FRI methods are also briefly introduced in this paper.