Generalized Modus Ponens Reasoning for Rules with Partial Overlapping Between Premise and Observation

Using Generalized Modus Ponens reasoning, we examine the values of inferred conclusion when the premise of the rule and the observed fact have a partial overlapping. We work with fuzzy if-then rules with a single input single output and the t-norm t(x, y) = max((1+λ)(x+y−1)−λxy, 0), λ ≥ −1, for composition operation. This t-norm is important to use because for λ = −1 and λ = 0 it gives the very used t-norms t1(x, y) = xy and t2(x, y) = max(0, x + y− 1), respectively. A set of eight implication operators are used, completing some of our previous results, where the method were used analyzing the possible inclusion relations between the premise and the observation. Key–Words: Fuzzy set, Fuzzy implication, Generalized modus ponens, t-norm