Algebraic Aspects of Families of Fuzzy Languages

P.R.J. Asveld, Dirk K.J. Heylen (Editor), Antinus Nijholt (Editor), Giuseppe Scollo (Editor)

Research output: Contribution to conferencePaperAcademicpeer-review

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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 full Abstract Family of Languages that has been encountered frequently in investigating families of crisp (i.e., non-fuzzy) languages. 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 languageUndefined
Pages1-16
Number of pages16
Publication statusPublished - 2000
EventAlgebraic Methods in Language Processing, AMiLP 2000: 2nd AMAST Workshop - Iowa City, United States
Duration: 20 May 200022 May 2000

Workshop

WorkshopAlgebraic Methods in Language Processing, AMiLP 2000
Abbreviated titleAMiLP
CountryUnited States
CityIowa City
Period20/05/0022/05/00

Keywords

  • EWI-6777
  • IR-63394

Cite this

Asveld, P. R. J., Heylen, D. K. J. (Ed.), Nijholt, A. (Ed.), & Scollo, G. (Ed.) (2000). Algebraic Aspects of Families of Fuzzy Languages. 1-16. Paper presented at Algebraic Methods in Language Processing, AMiLP 2000, Iowa City, United States.
Asveld, P.R.J. ; Heylen, Dirk K.J. (Editor) ; Nijholt, Antinus (Editor) ; Scollo, Giuseppe (Editor). / Algebraic Aspects of Families of Fuzzy Languages. Paper presented at Algebraic Methods in Language Processing, AMiLP 2000, Iowa City, United States.16 p.
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author = "P.R.J. Asveld and Heylen, {Dirk K.J.} and Antinus Nijholt and Giuseppe Scollo",
note = "A revised and extended version appeared as http://dx.doi.org/10.1016/S0304-3975(01)00354-1, i.e. as Theoretical Computer Science 293 (2003) 417-445.; null ; Conference date: 20-05-2000 Through 22-05-2000",
year = "2000",
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}

Asveld, PRJ, Heylen, DKJ (ed.), Nijholt, A (ed.) & Scollo, G (ed.) 2000, 'Algebraic Aspects of Families of Fuzzy Languages' Paper presented at Algebraic Methods in Language Processing, AMiLP 2000, Iowa City, United States, 20/05/00 - 22/05/00, pp. 1-16.

Algebraic Aspects of Families of Fuzzy Languages. / Asveld, P.R.J.; Heylen, Dirk K.J. (Editor); Nijholt, Antinus (Editor); Scollo, Giuseppe (Editor).

2000. 1-16 Paper presented at Algebraic Methods in Language Processing, AMiLP 2000, Iowa City, United States.

Research output: Contribution to conferencePaperAcademicpeer-review

TY - CONF

T1 - Algebraic Aspects of Families of Fuzzy Languages

AU - Asveld, P.R.J.

A2 - Heylen, Dirk K.J.

A2 - Nijholt, Antinus

A2 - Scollo, Giuseppe

N1 - A revised and extended version appeared as http://dx.doi.org/10.1016/S0304-3975(01)00354-1, i.e. as Theoretical Computer Science 293 (2003) 417-445.

PY - 2000

Y1 - 2000

N2 - 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 full Abstract Family of Languages that has been encountered frequently in investigating families of crisp (i.e., non-fuzzy) languages. 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.

AB - 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 full Abstract Family of Languages that has been encountered frequently in investigating families of crisp (i.e., non-fuzzy) languages. 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.

KW - EWI-6777

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M3 - Paper

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ER -

Asveld PRJ, Heylen DKJ, (ed.), Nijholt A, (ed.), Scollo G, (ed.). Algebraic Aspects of Families of Fuzzy Languages. 2000. Paper presented at Algebraic Methods in Language Processing, AMiLP 2000, Iowa City, United States.