Sorted-Pareto Dominance: an extension to the Pareto Dominance relation and its application in Soft Constraints

The Pareto dominance relation, widely used in a number of decision making areas, can suffer from a lack of discriminatory power, which may result in a large number of undominated or optimal solutions. By strengthening this relation, we can narrow down this optimal set further, which is desirable e.g., for presenting a smaller number of more interesting solutions to a decision maker. This paper looks at a particular strengthening of the Pareto dominance relation, called Sorted-Pareto dominance, giving a semantics for the relation, and explores some possible usages within a Soft Constraints setting for providing a set of optimal solutions to a Soft Constraints problem. We also look at some further possible usages of the relation, with a view to future work and providing some empirical results.