METRIC STRUCTURES ON POSSIBILITY DISTRIBUTIONS

Abstract

Higashi and Klir have defined a metric on the set of possibility distributions, based on the U-uncertainty. We show here that similar metrics 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 characteristics of these three measures of (non) specificity. We also disprove some results present in the literature. Finally, we argue in favor of defining these metrics on ordered possibility distributions.

INDEX TERMS:

• Possibility distributions
• uncertainty
• nonspecificity metrics