Extension of the rough set approach to multicriteria decision support

The original version of the rough sets theory has proved to be particularly useful in the analysis of multiattribute classification problems under inconsistency following from information granulation, i.e. objects having the same description but belonging to different classes. It fails, however, when attributes with preference-ordered domains (criteria) have to be taken into account. In order to deal with problems of multicriteria decision analysis (MCDA), such as sorting, choice or ranking, the authors have extended the original rough sets theory in a number of directions. The main extension is the substitution of the indiscernibility relation by a dominance relation which permits approximation of ordered decision classes in multicriteria sorting. Second extension was necessary to approximate preference relations in multicriteria choice and ranking problems; it requires substitution of the data table by a pairwise comparison table, where each row corresponds to a pair of actions described by binary relations on particular criteria. In all these MCDA problems, the extended rough set approach ends with a set of "if..., then..." decision rules playing the role of a preference model. It is more general than the classical functional or relational model and more understandable for the users. These rules have a more general syntax than the rules following from the original rough set approach and they are able to handle two kinds of inconsistencies, one with respect to indiscernibility and another with respect to dominance, instead of the first one only. In the extended rough set approach, discretization of quantitative attributes is not necessary and it is possible to consider attributes and criteria within the same decision problem. The paper summarizes these extensions and concentrates on description of the rough set approach to the multicriteria sorting problem, illustrated by a case study of airline company financial ratings.