Inducing robust decision rules from rough approximations of a preference relation

Given a data set describing a number of pairwise comparisons of reference objects made by a decision maker (DM), we wish to find a set of robust decision rules constituting a preference model of the DM. To accomplish this, we are constructing rough approximations of the comprehensive preference relation, called outranking, known from these pairwise comparisons. The rough approximations of the outranking relation are constructed using the Lorenz dominance relation on degrees of preference on particular criteria for pairs of reference objects being compared. The Lorenz dominance is used for its ability of drawing more robust conclusions from preference ordered data than the Pareto dominance. The rough approximations become a starting point for mining "if ..., then ... " decision rules constituting a logical preference model. Application of the set of decision rules to a new set of objects gives a fuzzy outranking graph. Positive and negative flows are calculated for each object in the graph, giving arguments about its strength and weakness. Aggregation of both arguments by the Net Flow Score procedure leads to a final ranking. The approach can be applied to support multicriteria choice and ranking of objects when the input information is a set of pairwise comparisons of some reference objects.