Possibility theory and data fusion in poorly informed environments

Some data fusion problems seem to be naturally handled in the framework of possibility theory. As an example, the problem of modelling expert knowledge about numerical parameters in the field of reliability is reconsidered in that framework. Usually expert opinions about quantities such as failure rates are modelled, assessed and pooled in the setting of probability theory. In this paper, we formulate a model of expert opinion by means of possibility distributions that are thought to better reflect the imprecision pervading expert judgments. They are weak substitutes to unreachable subjective probabilities. Assessment evaluation is carried out in terms of accurateness and level of precision, respectively measured by membership grades and fuzzy cardinality indices. Lastly, elaborating from previous works on data fusion using possibility theory, we present various pooling modes with their formal model under various assumptions concerning the sources of information. This framework is particularly suitable when sources are heterogeneous and statistical data are not available.