Approximate Reasoning with Fuzzy Booleans

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

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    Abstract

    This paper introduces, in analogy to the concept of fuzzy numbers, the concept of fuzzy booleans, and examines approximate reasoning with the compositional rule of inference using fuzzy booleans. It is shown that each set of fuzzy rules is equivalent to a set of fuzzy rules with singleton crisp antecedents; in case of fuzzy booleans this set contains only two rules. It is shown that Zadeh's extension principle is equivalent to the compositional rule of inference using a complete set of fuzzy rules with singleton crisp antecedents. The results are applied to describe the use of approximate reasoning with fuzzy booleans to object-oriented design methods.
    Original languageUndefined
    Title of host publicationInformation Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU 2004)
    Place of PublicationLa Sapienza
    PublisherUniversity of Rome
    Pages1429-1434
    Number of pages6
    ISBN (Print)8887242542
    Publication statusPublished - Jul 2004
    EventInformation Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU 2004 - Perugia, Italy
    Duration: 4 Jul 20049 Jul 2004

    Publication series

    Name
    PublisherEditrice Universita La Sapienza, Italy
    Volume2

    Conference

    ConferenceInformation Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU 2004
    Abbreviated titleIPMU
    CountryItaly
    CityPerugia
    Period4/07/049/07/04

    Keywords

    • METIS-220503
    • Approximate reasoning
    • Fuzzy booleans
    • object-oriented design methods
    • EWI-10046
    • IR-64067

    Cite this

    van den Broek, P. M., & Noppen, J. A. R. (2004). Approximate Reasoning with Fuzzy Booleans. In Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU 2004) (pp. 1429-1434). La Sapienza: University of Rome.