Double Fuzzy Dot Extension of the FRIPOC fuzzy rule interpolation method

Classical Fuzzy Rule Interpolation (FRI) methods can not correctly describe the change of the fuzziness of the interpolated fuzzy function. They can not 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 yield less fuzziness in the conclusion. This problem is mainly inherited from the deficiency of the classical fuzzy dot rule representation. To improve the fuzzy dot concept to describe the change of fuzziness in a given rule position the “double fuzzy dot” rule representation is suggested. Essential problem of the double fuzzy dot rule representation, that it requires the extension of the existing FRI methods to be able to handle the novel rule format. The goal of this paper is to demonstrate a possible way for such a FRI method extension by rewriting the FRIPOC FRI method. Some numerical examples of handling the change of the fuzziness by the rewritten FRIPOC FRI method are also briefly introduced in this paper.