Fuzzy Knowledge Discovery Based on Statistical Implication Indexes

We describe one application of statistical implication indexes to fuzzy knowledge discovery. After recalling principles of fuzzy logics, we explain how we have adapted statistical indexes to fuzzy knowledge: the support, the confidence and a less common index, the intensity of implication. These indexes highlight statistical links between conjunctions of fuzzy attributes and fuzzy conclusions, but do not evaluate the associated fuzzy rules, which depend of the chosen fuzzy operators. Since fuzzy operators are numerous, we evaluate their sets by applying the generalized modus ponens on the database and by comparing its results to the effective conclusions. We give a summary of the results on several databases, and we present the sets of fuzzy operators that appear to be the best. Studying methods to aggregate fuzzy rules, we show that in order to keep classical reduction schemes, fuzzy operators must be chosen differently. However, one of these possible operator sets is also one of the best for processing the generalized modus ponens.