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We introduce the basic features of the ordered weighted averaging (OWA) operator. Particular emphasis is put on the task of obtaining the associated weights. We discuss the maximal entropy OWA (MEOWA) approach to obtaining the weights. This approach is based upon the specification of a parameter characterizing the desired type of aggregation and then the solving of a mathematical programming problem whose objective is to maximize the entropy of the weights subject to this parameter. Here, we provide an alternative way of getting these MEOWA weights based upon the use of a weight-generating function. The introduction of this function allows us to obtain the MEOWA weights for the case in which each argument has a distinct degree of importance. The development of this approach allows us to use the OWA operator in decision making under risk. Here, we are able include probabilistic information as well as decision attitude to construct customized decision functions.