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We recall the OWA operator and discuss some of the features used to characterize these operators. In passing we introduce an new characterizing attribute called the divergence. We then consider two cases of information fusion and use these as motivation to generalize the OWA operator with the introduction of the Heavy OWA operator. These HOWA operators differ from the ordinary OWA operators by relaxing the constraints on the associated weighting vector. We consider some applications of these HOWA operators and provide some examples of weighting vectors associated with these HOWA operators.