Best approximation of OWA Olympic weights under predefined level of orness.

An ideal type of OWA aggregation operator is the one constructed on the so-called Olympic weights. The orness of this operator is 1/2. Therefore, sometimes we need a trade-off between the desire of having an OWA aggregation operator with weights as close as possible to the Olympic ones and the desire of having a predefined level of orness. In this paper, we choose these optimal weights by minimizing the Euclidean distance to the Olympic weights vector under the constraint of preserving a given level of orness. First, in the case n = 4 , we propose an iterative algorithm where the optimal solution is given for all possible values of the orness, values that are grouped along a partition of the unit interval. This iterative algorithm will inspire us to deduce the optimal weights in the general case. Consequently, we will obtain the analytical solution of the optimal weights as a function depending on the orness level. [ABSTRACT FROM AUTHOR]