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International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems

IPMU 2012: Advances in Computational Intelligence pp 360–369Cite as

The Bipolar Universal Integral

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Part of the Communications in Computer and Information Science book series (CCIS,volume 299)

Abstract

The concept of universal integral, recently proposed, generalizes the Choquet, Shilkret and Sugeno integrals. Those integrals admit a bipolar formulation, useful in those situations where the underlying scale is bipolar. In this paper we propose the bipolar universal integral generalizing the Choquet, Shilkret and Sugeno bipolar integrals. To complete the generalization we also provide the characterization of the bipolar universal integral with respect to a level dependent bi-capacity.

Keywords

  • Choquet
  • Sugeno and Shilkret integrals
  • universal integral
  • bipolar integrals

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Author information

Authors and Affiliations

  1. Department of Economics and Business, University of Catania, Corso Italia 55, 95129, Catania, Italy

    Salvatore Greco & Fabio Rindone

  2. Department of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Slovak University of Technology, Bratislava, Slovakia

    Radko Mesiar

  3. Institute of Theory of Information and Automation, Czech Academy of Sciences, Prague, Czech Republic

    Radko Mesiar

Authors
  1. Salvatore Greco
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  2. Radko Mesiar
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  3. Fabio Rindone
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Editor information

Editors and Affiliations

  1. Faculty of Economics, University of Catania, Corso Italia, 55, 95129, Catania, Italy

    Salvatore Greco & Benedetto Matarazzo & 

  2. CNRS UMR 7606, DAPA, LIP6 8, Université Pierre et Marie Curie - Paris6, rue du Capitaine Scott, F-75015, Paris, France

    Bernadette Bouchon-Meunier

  3. Dip. Matematica e Informatica, Università di Perugia, 06123, Perugia, Italy

    Giulianella Coletti

  4. Department of Computer and Management Science, University of Trento, Via Inama 5, 38122, Trento, Italy

    Mario Fedrizzi

  5. Machine Intelligence Institute — IONA College, 10801, New Rochelle, NY, USA

    Ronald R. Yager

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Greco, S., Mesiar, R., Rindone, F. (2012). The Bipolar Universal Integral. In: Greco, S., Bouchon-Meunier, B., Coletti, G., Fedrizzi, M., Matarazzo, B., Yager, R.R. (eds) Advances in Computational Intelligence. IPMU 2012. Communications in Computer and Information Science, vol 299. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31718-7_38

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  • DOI: https://doi.org/10.1007/978-3-642-31718-7_38

  • Publisher Name: Springer, Berlin, Heidelberg

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