Conjunctive Rules in the Theory of Belief Functions and Their Justification Through Decisions Models

Abstract

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.