Multicriteria Choice Functions Based on Binary Relations

This paper discusses methods of determining choices from sets of alternatives on the basis of one or more binary relations defined on the alternatives. Although the binary relations will be ordering relations in many practical contexts, most of the methods for determining choices do not assume that the relations are transitive. Choices based on a single binary relation are discussed first, followed by choices based on a set of binary relations. The latter methods are divided into post-choice methods, pre-choice methods, and hybrids. Post-choice methods determine choice sets for the several relations and then aggregate these choice sets. Pre-choice methods first combine the relations into one aggregate relation and then determine choices on the basis of the aggregate relation.