Multiple Criteria Ranking and Choice with All Compatible Minimal Cover Sets of Decision Rules

We introduce a new multiple criteria ranking/choice method that applies Dominance-based Rough Set Approach (DRSA) and represents the Decision Maker's (DM's) preferences with decision rules. The DM provides a set of pairwise comparisons indicating whether an outranking (weak preference) relation should hold for some pairs of reference alternatives. This preference information is structured using the lower and upper approximations of outranking (S) and non-outranking (S c ) relations. Then, all minimal-cover (MC) sets of decision rules being compatible with this preference information are induced. Each of these sets is supported by some positive examples (pairs of reference alternatives from the lower approximation of a preference relation) and it does not cover any negative example (pair of alternatives from the upper approximation of an opposite preference relation). The recommendations obtained by all MC sets of rules are analyzed to describe pairwise outranking and non-outranking relations, using probabilistic indices (estimates of probabilities that one alternative outranks or does not outrank the other). Furthermore, given the preference relations obtained in result of application of each MC set of rules on a considered set of alternatives, we exploit them using some scoring procedures. From this, we derive the distribution of ranks attained by the alternatives. We also extend the basic approach in several ways. The practical usefulness of the method is demonstrated on a problem of ranking Polish cities according to their innovativeness

Reduct-based ranking of attributes

The paper is dedicated to the area of feature selection, in particular a notion of attribute rankings that allow to estimate importance of variables. In the research presented for ranking construction a new weighting factor was defined, based on relative reducts. A reduct constitutes an embedded mechanism of feature selection, specific to rough set theory. The proposed factor takes into account the number of reducts in which a given attribute exists, as well as lengths of reducts. Two approaches for reduct generation were employed and compared, with search executed by a genetic algorithm. To validate the usefulness of the reduct-based rankings in the process of feature reduction, for gradually decreasing subsets of attributes, selected through rankings, sets of decision rules were induced in classical rough set approach. The performance of all rule classifiers was evaluated, and experimental results showed that the proposed rankings led to at least the same, or even increased classification accuracy for reduced sets of features than in the case of operating on the entire set of condition attributes. The experiments were performed on datasets from stylometry domain, with treating authorship attribution as a classification task, and stylometric descriptors as characteristic features defining writing styles

Analysis of the potentials of multi criteria decision analysis methods to conduct sustainability assessment

Sustainability assessments require the management of a wide variety of information types, parameters and uncertainties. Multi criteria decision analysis (MCDA) has been regarded as a suitable set of methods to perform sustainability evaluations as a result of its flexibility and the possibility of facilitating the dialogue between stakeholders, analysts and scientists. However, it has been reported that researchers do not usually properly define the reasons for choosing a certain MCDA method instead of another. Familiarity and affinity with a certain approach seem to be the drivers for the choice of a certain procedure. This review paper presents the performance of five MCDA methods (i.e. MAUT, AHP, PROMETHEE, ELECTRE and DRSA) in respect to ten crucial criteria that sustainability assessments tools should satisfy, among which are a life cycle perspective, thresholds and uncertainty management, software support and ease of use. The review shows that MAUT and AHP are fairly simple to understand and have good software support, but they are cognitively demanding for the decision makers, and can only embrace a weak sustainability perspective as trade-offs are the norm. Mixed information and uncertainty can be managed by all the methods, while robust results can only be obtained with MAUT. ELECTRE, PROMETHEE and DRSA are non-compensatory approaches which consent to use a strong sustainability concept, accept a variety of thresholds, but suffer from rank reversal. DRSA is less demanding in terms of preference elicitation, is very easy to understand and provides a straightforward set of decision rules expressed in the form of elementary “if … then …” conditions. Dedicated software is available for all the approaches with a medium to wide range of results capability representation. DRSA emerges as the easiest method, followed by AHP, PROMETHEE and MAUT, while ELECTRE is regarded as fairly difficult. Overall, the analysis has shown that most of the requirements are satisfied by the MCDA methods (although to different extents) with the exclusion of management of mixed data types and adoption of life cycle perspective which are covered by all the considered approaches

Incorporating stakeholders’ knowledge in group decision-making

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