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Optimistic Arithmetic Operators for Fuzzy and Gradual Intervals - Part I: Interval Approach

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Information Processing and Management of Uncertainty in Knowledge-Based Systems. Applications (IPMU 2010)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 81))

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Abstract

This two part paper proposes new and exact arithmetic operations for intervals and their extension to fuzzy and gradual ones. Indeed, it is well known that the practical use of interval and fuzzy arithmetic operators gives results more imprecise than necessary or in some cases, even incorrect. This problem is due to the overestimation effect induced by computing interval arithmetic operations. In this part, the Midpoint-Radius (MR) representation is considered to define new exact and optimistic subtraction and division operators. These operators are extended to fuzzy and gradual intervals in the Part II.

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Author information

Authors and Affiliations

  1. LISTIC, Laboratoire d’Informatique, Systems, Traitement de l’Information et de la Connaissance, Université de Savoie, BP. 80439, 74944, 1nnecy le vieux Cedex, France

    Reda Boukezzoula & Sylvie Galichet

Authors
  1. Reda Boukezzoula
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  2. Sylvie Galichet
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Editor information

Editors and Affiliations

  1. Fachbereich Mathematik und Informatik, Philipps-Universität Marburg, Marburg, Germany

    Eyke Hüllermeier

  2. Department of Knowledge Processing and Language Engineering, Otto-von-Guericke University of Magdeburg, Universitätsplatz 2, 39106, Magdeburg, Germany

    Rudolf Kruse

  3. Fakultät für Elektrotechnik und Informationstechnik, Technische Universität Dortmund, 44221, Dortmund, (Germany)

    Frank Hoffmann

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Boukezzoula, R., Galichet, S. (2010). Optimistic Arithmetic Operators for Fuzzy and Gradual Intervals - Part I: Interval Approach. In: Hüllermeier, E., Kruse, R., Hoffmann, F. (eds) Information Processing and Management of Uncertainty in Knowledge-Based Systems. Applications. IPMU 2010. Communications in Computer and Information Science, vol 81. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14058-7_46

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  • DOI: https://doi.org/10.1007/978-3-642-14058-7_46

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14057-0

  • Online ISBN: 978-3-642-14058-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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