POSSIBILISTIC INFORMATION METRICS AND DISTANCES: CHARACTERIZATIONS OF STRUCTURE

Abstract

Axiomatic characterizations of possibilistic distances and measures are studied. The basic distance g(p,q), defined for p≦q, is characterized using axioms of translation invariance, monotonic sum, metric and additivity with respect to cartesian products. To extend this definition to arbitrary pairs p, q one of the latter properties must be relaxed. Retaining the additive property gives H(p,q), while retaining the metric property leads to a class of metric distances, of which G(p,q) is maximal. A new metric K(p,q) = max(g(p, p ∨ q),g(q,p ∨ q)) is introduced. It is in a certain sense a minimal metric extension of g(p,q).

INDEX TERMS:

• Possibility distribution
• uncertainty measure
• information measure
• U-uncertainty
• information distance
• information metric