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Abstract

In imprecise domains the preference order of the alternatives is not straightforward to establish, due to possible overlapping of expected values among the alternatives. Nevertheless, such rankings are useful in decision analysis applications, as obtaining a ranking of alternatives is a way to gain an overview of the situation. The rankings presented in this paper represent overviews of a preference order of the alternatives based on their respective expected utility. The ranking can be either ordinal, focusing only on the ordering, or cardinal, also taking the differences in expected utility into account. The first set of procedures discussed is a cardinal ranking, which provides the user with expected utility intervals of the evaluated alternatives. This yields a more extensive overview with more detailed information. The second set of procedures discussed ordinal rankings of the alternatives based on three different approaches; 1) contraction based ranking, 2) intersection based ranking, and 3) focal point based ranking with indifference level. Finally, we show that regardless of ranking method their respective maximal elements all conform to the maximal element of the ordinal ranking. Hence, if the intention is to find a maximal element, it is sufficient to use either pointwise cardinal ranking or ordinal ranking with zero as indifference level.

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