Algebraic Aspects of Families of Fuzzy Languages

Peter R.J. Asveld

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    Abstract

    We study operations on fuzzy languages such as union, concatenation, Kleene $\star$, intersection with regular fuzzy languages, and several kinds of (iterated) fuzzy substitution. Then we consider families of fuzzy languages, closed under a fixed collection of these operations, which results in the concept of full Abstract Family of Fuzzy Languages or full AFFL. This algebraic structure is the fuzzy counterpart of the notion of full Abstract Family of Languages that has been encountered frequently in investigating families of crisp (i.e., non-fuzzy) languages. Some simpler and more complicated algebraic structures (such as full substitution-closed AFFL, full super-AFFL, full hyper-AFFL) will be considered as well. In the second part of the paper we focus our attention to full AFFL's closed under iterated parallel fuzzy substitution, where the iterating process is prescribed by given crisp control languages. Proceeding inductively over the family of these control languages, yields an infinite sequence of full AFFL-structures with increasingly stronger closure properties.
    Original languageEnglish
    Place of PublicationEnschede
    PublisherCentre for Telematics and Information Technology (CTIT)
    Number of pages24
    Publication statusPublished - Feb 2001

    Publication series

    NameCTIT Technical Report Series
    PublisherUniverisity of Twente, CTIT
    No.01-05
    ISSN (Print)1381-3625

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    Keywords

    • Fuzzy languages
    • Closure properties
    • Full Abstract Family of Fuzzy Languages (Full AFFL)
    • Controlled iterated fuzzy substitution
    • Infinite hierarchy

    Cite this

    Asveld, P. R. J. (2001). Algebraic Aspects of Families of Fuzzy Languages. (CTIT Technical Report Series; No. 01-05). Enschede: Centre for Telematics and Information Technology (CTIT).