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Erschienen in:
2016 | OriginalPaper | Buchkapitel
Decomposition Integral Based Generalizations of OWA Operators
verfasst von : Radko Mesiar, Andrea Stupňanová
Erschienen in: Information Processing and Management of Uncertainty in Knowledge-Based Systems
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Abstract
Based on the representation of OWA operators as Choquet integrals with respect to symmetric capacities, a new kind of OWA generalizations based on decomposition integrals is proposed and discussed. The symmetry of the underlying capacity is not sufficient to guarantee the symmetry of the resulting operator, and thus we deal with symmetric saturated decomposition systems only. All possible generalized OWA operators on \(X = \{1,2\}\) are introduced. Similarly, when considering the maximal decomposition system on \(X = \{1,2,3\},\) all generalized OWA operators are shown, based on the ordinal structure of the normed weighting vector \({\mathbf w} = (w_1,w_2,w_3).\)