Management of Ignorance by Interval Probability

Interval probabilities have been proposed as one of non-additive measures. The frame of interval probabilities is similar to evidence theory proposed by Dempster and Shafer and they can be regarded as evidences on a finite set. The interval probability is suitable to represent ignorance on the given phenomenon so that it can be used as a kind of subjective probability. We show how to obtain the evidence by a pairwise comparison matrix on a finite set. The pariwise comparisons are usually inconsistent each other since they are given based on human judgements. The interval probabilities from them are determined so as to include such inconsistency. In case of two evidences whose prior and conditional probabilities are obtained as intervals, the marginal and posterior probabilities are also calculated as interval probabilities from the view of possibility. The illustrative numerical example is given in this paper.