A priori identification of preferred alternatives of OWA operators by relational analysis of arguments

We present a reverse decision-aiding method that is distinct from previously reported ordered weighted averaging (OWA) aggregation methods. The proposed method is implemented in two phases. In the first phase, potentially best alternative, defined as one having any weighting vector that enables it to be at least as good as the others, is identified. In the second phase, the maximum and the minimum attitudinal characters for such an alternative are computed as the highest and the lowest values which it can attain under the weights-set identified in the first phase. These two phases are governed only by the relational analysis of input arguments, without soliciting the decision-maker to supply a specific attitudinal character. The proposed method can be applied to cases when it is difficult to obtain a precise attitudinal character and when, even if a precise one is obtained, the OWA operator weights are different, depending on the weights generating methods adopted. Further, if uncertain attitudinal character in the form of the interval number is available, its projection into the results of the proposed method yields less alternatives of consideration, in some cases, a single best alternative. The proposed method also allows for a priori identification of alternatives prone to change at a particular range of attitudinal character.