Choice Rules with Size Constraints for Multiple Criteria Decision Making

Abstract

In outranking methods for Multiple Criteria Decision Making (MCDM), pair-wise comparisons of alternatives are often summarized through a fuzzy preference relation. In this paper, the binary preference relation is extended to pairs of subsets of alternatives in order to define on this basis a scoring function over subsets. A choice rule based on maximizing score under size constraint is studied, which turns to formulate as solving a sequence of classical location problems. For comparison with the kernel approach, the interior stability property of the selected subset is discussed and analyzed.Combinatorial optimization; Fuzzy preferences; Integer Programming; Location; Multiple Criteria Decision Aid