Combination of Uncertain Class Membership Degrees with Probabilistic, Belief, and Possibilistic Measures

One important issue of uncertain or fuzzy object-oriented models is that uncertain membership degrees of an object to the classes in a class hierarchy may be obtained from different sources while they are actually constrained by the subclass relation. In this paper we present the notion of admissible combination functions and an algorithm to propagate and combine prior uncertain membership degrees on a class hierarchy, which are possibly conflicting, in order to produce a tightly consistent uncertain membership assignment. We assume uncertain membership degrees to be measured by support pairs represented by sub-intervals of [0, 1]. The usual probabilistic interval intersection, Dempster-Shafer, and possibilistic combination rules are examined and proved to be admissible ones.