METRIC STRUCTURES ON POSSIBILITY DISTRIBUTIONS

Higashi and Klir have defined a metric on the set of possibility distr ibutions, based on the U-uncertainty: We show here that similar metric s can be defined based on Yager's measure of (non) specificity and the imprecision measure of Lamata and Moral. These metrics satisfy almost all properties of the earlier metric, indicating some invariant chara cteristics of these three measures of (non) specificity. We also dispr ove some results present in the literature. Finally, we argue in favor of defining these metrics on ordered possibility distributions.