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The ordered weighted averaging (OWA) determination method with stress function was proposed by Yager, and it makes the OWA operator elements scatter in the shape of the stress function. In this paper, we extend the OWA determination with the stress function method using an optimization model. The proposed method transforms the OWA optimal solution elements into the interpolation points of the stress function. The proposed method extends the basic form of the stress function method with both scale and vertical shift transformations. We also explore a number of properties of this optimization-based stress function method. The OWA operator optimal solution elements can distribute as the shape of the given stress function in a parameterized way, in which case, the solution always possesses the arithmetic average operator as a special case.