Elicitation, assessment, and pooling of expert judgments using possibility theory

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Abstract
The problem of modeling expert knowledge about numerical parameters in the field of reliability is reconsidered in the framework of possibility theory. Usually expert opinions about quantities such as failure rates are modeled, assessed, and pooled in the setting of probability theory. This approach does not seem to always be natural since probabilistic information looks too rich to be currently supplied by individuals. Indeed, information supplied by individuals is often incomplete, imprecise rather than tainted with randomness. Moreover, the probabilistic framework looks somewhat restrictive to express the variety of possible pooling modes. 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 calibration and level of precision, respectively, measured by membership grades and fuzzy cardinality indexes. Last, drawing from previous works on data fusion using possibility theory, we present various pooling modes with their formal model under various assumptions concerning the experts. A comparative experiment between two computerized systems for expert opinion analysis has been carried out, and its results are presented in this paper.

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