Comparison of Two Approaches to Approximated Reasoning

P.M. van den Broek

    Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

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    Abstract

    A comparison is made of two approaches to approximate reasoning: Mamdani's interpolation method and the implication method. Both approaches are variants of Zadeh's compositional rule of inference. It is shown that the approaches are not equivalent. A correspondence between the approaches is established via the inverse of the implied fuzzy relation. The interpolation method has the lowest time-complexity, provided the minimum operator is chosen as t-norm. Otherwise, the time-complexity of both methods is the same. It is more efficient to first compile a set of fuzzy rules into a fuzzy relation, instead of aggregating inference results for each fuzzy rule separately.
    Original languageUndefined
    Title of host publicationEUSFLAT 2003
    EditorsMichael Wagenknecht, Rainer Hampel
    Place of PublicationZittau/Goerlitz, Germany
    PublisherEuropean Society for Fuzzy Logic and Technology
    Pages512-516
    Number of pages5
    ISBN (Print)3-9808089-4-7
    Publication statusPublished - Sep 2003

    Publication series

    Name
    PublisherEuropean Society for Fuzzy Logic and Technology

    Keywords

    • Approximate reasoning
    • IR-64088
    • EWI-10085
    • time-complexity
    • compositional rule of inference
    • SE-SC: Soft Computing applied to Software Engineering
    • METIS-215015

    Cite this

    van den Broek, P. M. (2003). Comparison of Two Approaches to Approximated Reasoning. In M. Wagenknecht, & R. Hampel (Eds.), EUSFLAT 2003 (pp. 512-516). Zittau/Goerlitz, Germany: European Society for Fuzzy Logic and Technology.
    van den Broek, P.M. / Comparison of Two Approaches to Approximated Reasoning. EUSFLAT 2003. editor / Michael Wagenknecht ; Rainer Hampel. Zittau/Goerlitz, Germany : European Society for Fuzzy Logic and Technology, 2003. pp. 512-516
    @inproceedings{b7068ce2da0f40c4b10a3a7bc0b5d1d3,
    title = "Comparison of Two Approaches to Approximated Reasoning",
    abstract = "A comparison is made of two approaches to approximate reasoning: Mamdani's interpolation method and the implication method. Both approaches are variants of Zadeh's compositional rule of inference. It is shown that the approaches are not equivalent. A correspondence between the approaches is established via the inverse of the implied fuzzy relation. The interpolation method has the lowest time-complexity, provided the minimum operator is chosen as t-norm. Otherwise, the time-complexity of both methods is the same. It is more efficient to first compile a set of fuzzy rules into a fuzzy relation, instead of aggregating inference results for each fuzzy rule separately.",
    keywords = "Approximate reasoning, IR-64088, EWI-10085, time-complexity, compositional rule of inference, SE-SC: Soft Computing applied to Software Engineering, METIS-215015",
    author = "{van den Broek}, P.M.",
    year = "2003",
    month = "9",
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    van den Broek, PM 2003, Comparison of Two Approaches to Approximated Reasoning. in M Wagenknecht & R Hampel (eds), EUSFLAT 2003. European Society for Fuzzy Logic and Technology, Zittau/Goerlitz, Germany, pp. 512-516.

    Comparison of Two Approaches to Approximated Reasoning. / van den Broek, P.M.

    EUSFLAT 2003. ed. / Michael Wagenknecht; Rainer Hampel. Zittau/Goerlitz, Germany : European Society for Fuzzy Logic and Technology, 2003. p. 512-516.

    Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

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    AB - A comparison is made of two approaches to approximate reasoning: Mamdani's interpolation method and the implication method. Both approaches are variants of Zadeh's compositional rule of inference. It is shown that the approaches are not equivalent. A correspondence between the approaches is established via the inverse of the implied fuzzy relation. The interpolation method has the lowest time-complexity, provided the minimum operator is chosen as t-norm. Otherwise, the time-complexity of both methods is the same. It is more efficient to first compile a set of fuzzy rules into a fuzzy relation, instead of aggregating inference results for each fuzzy rule separately.

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    KW - EWI-10085

    KW - time-complexity

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    van den Broek PM. Comparison of Two Approaches to Approximated Reasoning. In Wagenknecht M, Hampel R, editors, EUSFLAT 2003. Zittau/Goerlitz, Germany: European Society for Fuzzy Logic and Technology. 2003. p. 512-516