On proving the extended minimax disparity OWA problem

Determining associated weights in the theory of ordered weighted averaging (OWA) operators is an important issue. Wang and Parkan [Information Sciences 175 (2005) 20–29] proposed a minimax disparity approach for obtaining OWA operator weights, which is based on the solution of a linear program (LP) model for a given degree of orness. Recently, Amin and Emrouznejad [Computers & Industrial Engineering 50 (2006)] proposed an extended minimax disparity model and improved their proposed LP to obtain weights that would be as close as possible. They also left an open problem related to the extended model: For an even number of arguments, there would be an interval for the degree of orness such that the optimal solution of the extended model could be obtained by a compact mathematical form. In this paper, we completely prove this open problem mathematically for all orness levels whatever the number of arguments.