A New Model for Complete Ranking Problems in MCDA Based on Multi-graded Dominance Relations

After Greco et al. introduce PCT (Pairwise Comparison Table) into rough sets, with this extension rough sets method can resolve ranking and choice problems in MCDA. But there are still two problems: one is how to change decision table into PCT, meanwhile to avoid losing information; the other is how to get complete ranking of alternatives, as different alternatives have the same net flow value in some new instances. Due to both PROMETHEE II and dominance-based rough sets based on binary preference relations between objects on particular attribute, this paper introduces PROMETHEE II into dominance-based rough sets to get a new synergic P2DRS model. The new model can easily obtain PCT and resolve the problem of some alternatives having indistinguishable ranking for getting the complete ranking of all alternatives. Finally an example illustrates the model is scientific and validity.