The Compositional Rule of Inference and Zadeh’s Extension Principle for Non-normal Fuzzy Sets

P.M. van den Broek, J.A.R. Noppen

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    Abstract

    Defining the standard Boolean operations on fuzzy Booleans with the compositional rule of inference (CRI) or Zadeh's extension principle gives counter-intuitive results. We introduce and motivate a slight adaptation of the CRI, which only effects the results for non-normal fuzzy sets. It is shown that the adapted CRI gives the expected results for the standard Boolean operations on fuzzy Booleans. As a second application, we show that the adapted CRI enables a don't-care value in approximate reasoning. From the close connection between the CRI and Zadeh's extension principle, we derive an adaptation of the extension principle, which, like the modified CRI, also gives the expected Boolean operations on fuzzy Booleans.
    Original languageUndefined
    Title of host publicationTheoretical Advances and Applications of Fuzzy Logic and Soft Computing
    EditorsOscar Castillo
    Place of PublicationBerlin Heidelberg, Germany
    PublisherSpringer
    Pages621-628
    Number of pages8
    ISBN (Print)978-3-540-72433-9
    DOIs
    Publication statusPublished - 2007

    Publication series

    NameAdvances in Soft Computing
    PublisherSpringer
    Number7/42
    Volume42
    ISSN (Print)1615-3871

    Keywords

    • SE-SC: Soft Computing applied to Software Engineering
    • METIS-246020
    • IR-62172
    • EWI-11918

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