Aggregation Operators and Commuting

Commuting is an important property in any two-step information merging procedure where the results should not depend on the order in which the single steps are performed. We investigate the property of commuting for aggregation operators in connection with their relationship to bisymmetry. In case of bisymmetric aggregation operators we show a sufficient condition ensuring that two operators commute, while for bisymmetric aggregation operators with neutral element we even provide a full characterization of commuting n-ary operators by means of unary distributive functions. The case of associative operations, especially uninorms, is considered in detail.