Using Preference Information in Multistep Methods for Solving Multiple Criteria Decision Problems

Abstract

This paper deals with principles of using information about the decision maker’s preferences in multistep techniques for solving multiple criteria decision problems. A connection is investigated between relationships built after two successive steps of a multistep procedure. It is proved that the existence of the transitive closure of the union of the preference-indifference relationships obtained after the ith and at the (i+1) steps is the necessary condition of the existence of a preference-indifference relationship elaborated after the (i+1) step. An example is given of decison-rule construction for specific sorts of preference information. The decision rule which ensures the identification of the efficient frontier of the set of consequences is used in this example at the first step. The preferenceindifference relationship is defined on the second step by means of an additional decision rule. This rule uses the information about a change in amounts for one attribute, from the most desirable to some other amount, such that this change is preferable to a similar change in amounts for another attribute. A new decision rule is constructed after the second step which uses all the information available and leads to a new preference-indifference relationship which is the transitive closure of the union of the previous relationships.