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Aggregation on Finite Ordinal Scales by Scale Independent Functions

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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.

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Authors and Affiliations

  1. Faculty of Law, Economics, and Finance, University of Luxembourg, 162A, avenue de la Faïencerie, L-1511, Luxembourg, G.D. Luxembourg

    Jean-Luc Marichal

  2. Department of Mathematics, Faculty of Civil Engineering, Slovak Technical University, Radlinskeho 11, SK-81368, Bratislava, Slovakia

    Radko Mesiar

Authors
  1. Jean-Luc Marichal
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  2. Radko Mesiar
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Correspondence to Jean-Luc Marichal.

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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.

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Marichal, JL., Mesiar, R. Aggregation on Finite Ordinal Scales by Scale Independent Functions. Order 21, 155–180 (2004). https://doi.org/10.1007/s11083-004-3409-x

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