| Affiliation: | (1) Faculty of Law, Economics, and Finance, University of Luxembourg, 162A, avenue de la Faïencerie, L-1511 Luxembourg, G.D. Luxembourg;(2) Department of Mathematics, Faculty of Civil Engineering, Slovak Technical University, Radlinskeho 11, SK-81368 Bratislava, Slovakia |
| Abstract: | We define and investigate the scale independent aggregation functions that are meaningful to aggregate finite ordinal numerical scales. Here scale independence means that the functions always have discrete representatives when the ordinal scales are considered as totally ordered finite sets. We also show that those scale independent functions identify with the so-called order invariant functions, which have been described recently. In particular, this identification allows us to justify the continuity property for certain order invariant functions in a natural way.Mathematics Subject Classifications (2000) Primary: 91C05, 91E45; Secondary: 06A99, 39A12.Jean-Luc Marichal: Partially supported by a grant from the David M. Kennedy Center for International Studies, Brigham Young University.Radko Mesiar: Partially supported by grants VEGA 1/0273/03 and APVT-20-023402. |
