A critical issue when selecting an ordered weighted aggregation (OWA) operator is the determination of the associated weights. For this reason, numerous weight generating methods have appeared in the literature. In this paper, a generalization of the binomial OWA operator on the basis of the Stancu polynomial is proposed and analyzed. We propose a weight function in the parametric form using the Stancu polynomial by which the weights of OWA operators can be generated easily. The proposed Stancu OWA operator provides infinitely many sets of weight vectors for a given level of the orness value. An important property of this kind of OWA operator is its orness, which remains constant, irrespective of the number of objectives aggregated and always equal to one of its parameters. This approach provides a significant advantage for generating the OWA operators’ weights over existing methods. One can choose a set of weight vectors based on his/her own preference. This class of OWA operators can utilize a prejudiced preference to determine the corresponding weight vector. The maximum entropy (Shannon) OWA operator's weights for a given level of orness is calculated by the purposed weight function and compared with the existing maximum entropy OWA operator.