Interpolative fuzzy reasoning method based on the incircle of a generalized triangular fuzzy number

Fuzzy Rule Interpolation (FRI) is an important technique for implementing inference with sparse fuzzy rulebases. Even if a given observation has no overlap with the antecedent of any rule from the rule-base, FRI may still conclude a conclusion. This paper introduces a new method called "Incircle FRI" for fuzzy interpolation which is based on the incircle of a triangular fuzzy number. The suggested method is defined for triangular CNF fuzzy sets, for a single antecedent universe and two surrounding rules from the rule-base. The paper also extends the suggested "Incircle FRI" to trapezoidal, and hexagonal shaped fuzzy sets by decomposing their shapes to multiple triangulars. The generated conclusion is also a CNF fuzzy set. The performance of the suggested method is evaluated based on numerical examples and a comprehensive comparison to other current FRI methods.