Extended methods for identifying dominance and potential optimality in multi-criteria analysis with imprecise information

Many of the recent prescriptive approaches to multi-attribute decision analysis have dealt with situations in which trade-off weights are known imprecisely while (marginal) values are known exactly. A way to handle such problems is to utilize a linear programming technique from which non-dominated and/or potentially optimal score vectors can be obtained. In some attributes, however, it is not easy for decision makers to provide the marginal value functions that are explicit and exact. The purpose of this paper is to address problems such that both attribute weights and marginal values are known imprecisely. We then assume, without loss of generality, that this imprecise information on both weights and values is in the form if inequalities and/or equalities such as rankings and bounds. The first formulations for checking dominance and potential optimality become non-linear programming problems hard to be solved generally. We thus present how these non-linear problems are reduced to linear programming equivalents.