Kóczy-Hirota Fuzzy Interpolation for Interpolation the Fuzziness in case of Double Fuzzy Dot Rule Representation

The Kóczy-Hirota Fuzzy Interpolation (“KH” method, Kóczy and Hirota, 1991) is the first method adapting the declarative way of fuzzy function definition and the related “fuzzy dot” rule representation by introducing the concept of Fuzzy Rule Interpolation (FRI). The original KH method had many followers. Most of the FRI methods have difficulties in freely defining the relation of the observation and the conclusion fuzziness. E.g. 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 has to lead less fuzziness in the conclusion. One possible solution for this problem is the extension of the “fuzzy dot” rule representation to the “double fuzzy dot” rule representation concept. This case the fuzzy rule description also supports the expression of the antecedentconsequent fuzziness relation. The goal of this paper is to demonstrate that the original KH interpolation method is also suitable for interpolation the fuzziness in case of double fuzzy dot rule representation.