Importance-based multicriteria decision making with interval valued criteria satisfactions

Multiple-criteria decision problems involve selecting an alternative that best satisfies a collection of criteria as quantified by a scalar corresponding to an aggregation of the alternatives satisfaction to the individual criteria. A fundamental issue is the formulation of decision maker's aggregation function based upon the decision maker's perceived relationship between the criteria. Here, we allow the decision maker to express their perceived relationship between the criteria in terms of information about the criteria importances by providing a fuzzy measure over the criteria such that the measure of any subset of criteria is its importance. With the aid of the Choquet integral, we use this fuzzy measure of importances to construct an aggregation function. As the Choquet integral requires an ordering of an alternatives individual criteria satisfactions, special handling is required in the case when criteria satisfactions are interval valued rather then scalar. Here we use the golden rule representative value in the case of interval values.