Fuzzy Confirmation Measures (a)symmetry Properties

While Bayesian Confirmation Measures assess the degree to which an antecedent E supports a conclusion H in a rule by means of probabilities, Fuzzy Confirmation Measures evaluate the quality of fuzzy association rules between the fuzzy antecedent A and fuzzy consequence B. Fuzzy Confirmation Measures defined in terms of confidence can be compared in different ways, among them symmetry properties evaluations play an important role. We first focus on symmetry properties for Fuzzy Confirmation Measures and then on the evaluation of possible levels of asymmetry. We suggest a way to measure the level of asymmetry and we also provide some examples to illustrate its possible use.