Preference Representation by the Choquet Integral: The Commensurability Hypothesis

Until now, decision under uncertainty and multicriteria decision making have been investigated separately and almost independently, although there is a close link between both fields. Decision theory is also closely related to measurement theory. Besides, it is well known that additive representations in decision making are not sufficient to avoid paradoxes such as Ellsberg’s paradox. Therefore, we investigate the links between the two paradigms of decision and measurement theory in order to propose a Choquet representation theorem in multicriteria decision making. A key concept for this is a commensurability assumption between the values of attributes. We show that this hypothesis, under a very general structural property on the sets of values of attributes is not restrictive. This implies that our method to translate results from decision under uncertainty to multicriteria decision making is very general.