Preference Representation by Means of Conjoint Measurement and Decision Rule Model

We investigate the equivalence of preference representation by numerical functions and by “if ..., then...” decision rules in multicriteria choice and ranking problems. The numerical function is a general non-additive and non-transitive model of conjoint measurement. The decision rules concern pairs of actions and conclude either presence or absence of a comprehensive preference relation; conditions for the presence are expressed in “at least” terms, and for the absence in “at most” terms, on particular criteria. Moreover, we consider representation of hesitation in preference modeling. Within this context, two approaches are considered: dominance-based rough set approach—handling inconsistencies in expression of preferences through examples, and four-valued logic—modeling the presence of positive and negative reasons for preference. Equivalent representation by numerical functions and by decision rules is proposed and a specific axiomatic foundation is given for preference structure based on the presence of positive and negative reasons. Finally, the following well known multicriteria aggregation procedures are represented in terms of the decision rule model: lexicographic aggregation, majority aggregation, ELECTRE I and TACTIC.