Measuring Conflict Between Possibilistic Uncertain Information Through Belief Function Theory

Dempster Shafer theory of evidence (DS theory) and possibility theory are two main formalisms in modelling and reasoning with uncertain information. These two theories are inter-related as already observed and discussed in many papers (e.g. [DP82,DP88b]). One aspect that is common to the two theories is how to quantitatively measure the degree of conflict (or inconsistency) between pieces of uncertain information. In DS theory, traditionally this is judged by the combined mass value assigned to the emptyset. Recently, two new approaches to measuring the conflict among belief functions are proposed in [JGB01,Liu06]. The former provides a distance-based method to quantify how close a pair of beliefs is while the latter deploys a pair of values to reveal the degree of conflict of two belief functions. On the other hand, in possibility theory, this is done through measuring the degree of inconsistency of merged information. However, this measure is not sufficient when pairs of uncertain information have the same degree of inconsistency. At present, there are no other alternatives that can further differentiate them, except an initiative based on coherence-intervals ([HL05a,HL05b]). In this paper, we investigate how the two new approaches developed in DS theory can be used to measure the conflict among possibilistic uncertain information. We also examine how the reliability of a source can be assessed in order to weaken a source when a conflict arises.