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On Defuzzyfication of Ordered Fuzzy Numbers

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Book cover Artificial Intelligence and Soft Computing - ICAISC 2004 (ICAISC 2004)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 3070))

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Abstract

Ordered fuzzy number is an ordered pair of continuous real functions defined on the interval [0, 1]. Such numbers have been introduced by the author and his co-workers as an enlargement of classical fuzzy numbers by requiring a membership relation. It was done in order to define four algebraic operations between them, i.e. addition, subtraction, multiplication and division, in a way that renders them an algebra. Further, a normed topology is introduced which makes them a Banach space, and even more, a Banach algebra with unity. General form of linear functional on this space is presented which makes possible to define a large family of defuzzification methods of that class of numbers.

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Author information

Authors and Affiliations

  1. Polish-Japanese Institute of Information Technology, Research Center, ul. Koszykowa 86, 02-008, Warszawa, Poland

    Witold Kosiński

Authors
  1. Witold Kosiński
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Editor information

Editors and Affiliations

  1. Department of Artificial Intelligence, Academy of Humanities and Economics, Poland

    Leszek Rutkowski

  2. German Research Center of Artificial Intelligence (DFKI), Germany

    Jörg H. Siekmann

  3. Institute of Automatics, AGH University of Science and Technology, Al. Mickiewicza 30, PL-30-059, Kraków, Poland

    Ryszard Tadeusiewicz

  4. Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, Initiative in Soft Computing (BISC), 94720-1776, Berkeley, CA

    Lotfi A. Zadeh

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© 2004 Springer-Verlag Berlin Heidelberg

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Kosiński, W. (2004). On Defuzzyfication of Ordered Fuzzy Numbers. In: Rutkowski, L., Siekmann, J.H., Tadeusiewicz, R., Zadeh, L.A. (eds) Artificial Intelligence and Soft Computing - ICAISC 2004. ICAISC 2004. Lecture Notes in Computer Science(), vol 3070. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24844-6_46

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  • DOI: https://doi.org/10.1007/978-3-540-24844-6_46

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-22123-4

  • Online ISBN: 978-3-540-24844-6

  • eBook Packages: Springer Book Archive

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