Adapting the scale and move FRI for the fuzziness interpolation of the double fuzzy point rule representation

Fuzzy Rule Interpolation (FRI) methods are following the declarative way of fuzzy function definition and the related “fuzzy point” rule representation concept. Most of the FRI methods have restrictions in the definition of the observation and the conclusion fuzziness relation. In many cases the increase of the observation fuzziness has to lead to higher fuzziness in the conclusion. One possible solution for relaxing this restriction is the introduction of a new dimension for fuzziness expression in FRI by extending the original “fuzzy point” to the “double fuzzy point” rule representation concept. This case the fuzzy rule description also supports the expression of the antecedent-consequent fuzziness relation. For handling the suggested concept the existing FRI methods have to be adapted for the “double fuzzy point” rule representation. The goal of this paper is to demonstrate that the “Scale and Move Transformation”-based FRI method (Huang and Shen, 2003) fits well the requirements of the adaption and can be easily modified for interpolation of the fuzziness in case of double fuzzy point rule representation.