Conflict Analysis and Merging Operators Selection in Possibility Theory

In possibility theory, the degree of inconsistency is commonly used to measure the level of conflict in information from multiple sources after merging, especially conjunctive merging. However, as shown in [HL05,Liu06b], this measure alone is not enough when pairs of uncertain information have the same degree of inconsistency, since it is not possible to tell which pair contains information that is actually better, in the sense that the two pieces of information in one pair agree with each other more than the information does in other pairs. In this paper, we investigate what additional measures can be used to judge the closeness between two pieces of uncertain information. We deploy the concept of distance between betting commitments developed in DS theory in [Liu06a], since possibility theory can be viewed as a special case of DS theory. We present properties that reveal the interconnections and differences between the degree of inconsistency and the distance between betting commitments. We also discuss how to use these two measures together to guide the possible selection of various merging operators in possibility theory.