On the equivalence of some approaches to the OWA operator and RIM quantifier determination

The ordered weighted averaging (OWA) operator is a widely used aggregation method, and its determination is usually a prerequisite step in many related applications. The regular increasing monotone (RIM) quantifier can be seen as the continuous case of the OWA operator with the quantifier aggregation method. Some approaches with optimization criteria for the determination of OWA operator and RIM quantifier were proposed. Although these problems look different at the first sight, a deeper investigation can reveal the equivalence of solutions between them. Inspired by the solution equivalence of minimum variance problems and minimax disparity problem for OWA operator, we propose the minimax disparity RIM quantifier problem and two minimax ratio problems for OWA operator and RIM quantifier, respectively. We investigate the equivalence of solutions for the maximum entropy and minimax ratio problems, and solutions for the minimum variance and minimax disparity problems of OWA operator and RIM quantifier, respectively, by a theoretical point of view.