| Abstract: | Possibilistic distributions admit both measures of uncertainty and (metric) distances defining their information closeness. For general pairs of distributions these measures and metrics were first introduced in the form of integral expressions. Particularly important are pairs of distributions p and q which have consonant ordering—for any two events x and y in the domain of discourse p(x)⪋ p(y) if and only if q(x) ⪋ q(y). We call such distributions confluent and study their information distances. This paper presents discrete sum form of uncertainty measures of arbitrary distributions, and uses it to obtain similar representations of metrics on the space of confluent distributions. Using these representations, a number of properties like additivity. monotonicity and a form of distributivity are proven. Finally, a branching property is introduced, which will serve (in a separate paper) to characterize axiomatically possibilistic information distances. |
