Lecture Notes in Artificial Intelligence
Conflictness is an important a priori characteristic of combining rules in the belief functions theory. A new approach to the estimation of internal conflict offered in this article. This approach is based on the idea of decomposition of the initial body of evidence on the set of bodies of evidence by means of some combining rule. Then the (external) conflict of this set of beliefs is estimated. The dependence of change of internal conflict from the choice of the combining rules is analyzed in this study.
In the paper we argue that aggregation rules in the theory of belief functions should be in accordance with underlying decision models, i.e. aggregation produced in conjunctive manner has to produce the order embedded to the union of partial orders constructed in each source of information; and if we take models based on imprecise probabilities, then such aggregation exists if the intersection of underlying credal sets is not empty. In the opposite case there is contradiction in information and the justifiable functional to measure it is the functional giving the smallest contradiction by applying all possible conjunctive rules. We give also the axiomatics of this contradiction measure.