Multiattribute decision aid with extended ISMAUT

Multiattribute decision-making problems with imprecise data refer to a situation in which at least one of the parameters such as attribute weights and value scores is not specified in precise numerical values. Often the imprecision of preference information, on one hand, may give a decision maker chances that are enhanced freedom of choice and comforts of specification and, on the other hand, may cause decision analysts difficulties in establishing dominance relations among alternatives. The model, imprecisely specified multiattribute utility theory (ISMAUT), developed by Sage and White in 1984, is a generalization of the standard multiattribute decision-analysis paradigm in that they extend the types of preference specifications and provide a novel approach to resolve the complication of a problem caused by imprecision on both attribute weights and value scores. This paper is intended to extend the ISMAUT in several aspects. For the first part, we present the properties of decision rules and their relationships in the presence of imprecise weight and value information in a systematical way though many research efforts, differing by respective problem domains considered, have been devoted to deal with them. Further, methods for resolving a nonlinearity inherent in the formulation while cutting into the number of linear programs to be solved are also presented. For the second part, a method for determining multiattribute weights is presented when paired comparison judgments on alternatives are articulated. The attribute weights are to be estimated in the direction of minimizing the amount of violations and thus to be as consistent as possible with a decision maker's a priori ordered pairs of alternatives. The derived multiattribute weights can be utilized for prioritizing the other alternatives that are not included in a set of a priori ordered pairs of alternatives. For the third part, the paper deals with a prescriptive group decision-making method by aggregating group members' imprecise preference judgments. The imprecise additive group value function can be decomposed into the individual decision maker's imprecise decision-making problems, which are finally aggregated to identify a group's preferred alternative. The group decision rules, analogous to the rules dealt in a single decision-making context, are presented as well.