ANSWER SET PROGRAMMING AND COMBINATORIAL MULTICRITERIA DECISION MAKING

Abstract

The majority of approaches to multicriteria optimization are based on quantitative representations of preferences of a decision maker, in which numerical procedures of multicriteria analysis are used for aggregation purposes. However, very often qualitative data cannot be known in terms of absolute values so that a qualitative approach is needed. Moreover, the multicriteria methods are directly applicable when alternatives are individuals-then they may be explicitly listed and ordered by an agent. However, sometimes the set of alternatives has combinatorial structure and it must be selected from the set of Cartesian products of value domains of attributes satisfying certain constraints. Then, the space of possible alternatives has a size exponential in the number of variables and ranking all alternatives explicitly is a complex and tedious task. In this paper we propose logic programming with ordered disjunction as a qualitative approach to combinatorial multicriteria decision making, allowing a concise representation of the preference structures, and a human-like form of expressions, being close to natural language, hence providing a good readability and simplicity. A combinatorial multicriteria decision making problem is encoded as a logic program, in which preferences of the decision maker are represented qualitatively. The optimal decision corresponds exactly to the preferred answer set of the program, obtained via the well-known methods of multicriteria analysis.