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Aggregation on Bipolar Scales

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Theory and Applications of Relational Structures as Knowledge Instruments II

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 4342))

Abstract

The paper addresses the problem of extending aggregation operators typically defined on [0,1] to the symmetric interval [−1,1], where the “0” value plays a particular role (neutral value). We distinguish the cases where aggregation operators are associative or not. In the former case, the “0” value may play the role of neutral or absorbant element, leading to pseudo-addition and pseudo-multiplication. We address also in this category the special case of minimum and maximum defined on some finite ordinal scale. In the latter case, we find that a general class of extended operators can be defined using an interpolation approach, supposing the value of the aggregation to be known for ternary vectors.

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Author information

Authors and Affiliations

  1. Université Paris I – Panthéon-Sorbonne, CERMSEM, 110-116 Bd de l’Hôpital, 75013, Paris, France

    Michel Grabisch

Authors
  1. Michel Grabisch
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Editor information

Editors and Affiliations

  1. Faculty of Philosophy, Tilburg University, P.O. Box 90153, 5000, Tilburg, LE, The Netherlands

    Harrie de Swart

  2. National Institute of Telecommunications, Warsaw,  

    Ewa Orłowska

  3. Institute for Software Technology, Department of Computing Science, Universität der Bundeswehr München, 85577, Neubiberg, Germany

    Gunther Schmidt

  4. Faculté Polytechnique de Mons, Rue de Houdain 9, B-7000, Mons, Belgium

    Marc Roubens

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© 2006 Springer-Verlag Berlin Heidelberg

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Grabisch, M. (2006). Aggregation on Bipolar Scales. In: de Swart, H., Orłowska, E., Schmidt, G., Roubens, M. (eds) Theory and Applications of Relational Structures as Knowledge Instruments II. Lecture Notes in Computer Science(), vol 4342. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11964810_17

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  • DOI: https://doi.org/10.1007/11964810_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-69223-2

  • Online ISBN: 978-3-540-69224-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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