A characterization of tribes with respect to the Łukasiewicz t -norm

Erich Peter Klement; Mirko Navara

Czechoslovak Mathematical Journal (1997)

  • Volume: 47, Issue: 4, page 689-700
  • ISSN: 0011-4642

Abstract

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We give a complete characterization of tribes with respect to the Łukasiewicz t -norm, i. e., of systems of fuzzy sets which are closed with respect to the complement of fuzzy sets and with respect to countably many applications of the Łukasiewicz t -norm. We also characterize all operations with respect to which all such tribes are closed. This generalizes the characterizations obtained so far for other fundamental t -norms, e. g., for the product t -norm.

How to cite

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Klement, Erich Peter, and Navara, Mirko. "A characterization of tribes with respect to the Łukasiewicz $t$-norm." Czechoslovak Mathematical Journal 47.4 (1997): 689-700. <http://eudml.org/doc/30392>.

@article{Klement1997,
abstract = {We give a complete characterization of tribes with respect to the Łukasiewicz $t$-norm, i. e., of systems of fuzzy sets which are closed with respect to the complement of fuzzy sets and with respect to countably many applications of the Łukasiewicz $t$-norm. We also characterize all operations with respect to which all such tribes are closed. This generalizes the characterizations obtained so far for other fundamental $t$-norms, e. g., for the product $t$-norm.},
author = {Klement, Erich Peter, Navara, Mirko},
journal = {Czechoslovak Mathematical Journal},
keywords = {fuzzy sets; crisp set; tribe; triangular norm},
language = {eng},
number = {4},
pages = {689-700},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A characterization of tribes with respect to the Łukasiewicz $t$-norm},
url = {http://eudml.org/doc/30392},
volume = {47},
year = {1997},
}

TY - JOUR
AU - Klement, Erich Peter
AU - Navara, Mirko
TI - A characterization of tribes with respect to the Łukasiewicz $t$-norm
JO - Czechoslovak Mathematical Journal
PY - 1997
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 47
IS - 4
SP - 689
EP - 700
AB - We give a complete characterization of tribes with respect to the Łukasiewicz $t$-norm, i. e., of systems of fuzzy sets which are closed with respect to the complement of fuzzy sets and with respect to countably many applications of the Łukasiewicz $t$-norm. We also characterize all operations with respect to which all such tribes are closed. This generalizes the characterizations obtained so far for other fundamental $t$-norms, e. g., for the product $t$-norm.
LA - eng
KW - fuzzy sets; crisp set; tribe; triangular norm
UR - http://eudml.org/doc/30392
ER -

References

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  1. Triangular norm-based measures and games with fuzzy coalitions, Kluwer, Dordrecht, 1993. (1993) 
  2. 10.1007/BF02189866, Aequationes Math. 19 (1979), 194–226. (1979) Zbl0444.39003MR0556722DOI10.1007/BF02189866
  3. 10.1016/0022-247X(82)90015-4, J. Math. Anal Appl. 85 (1982), 543–565. (1982) Zbl0491.28003MR0649189DOI10.1016/0022-247X(82)90015-4
  4. 10.1006/jmaa.1993.1283, J. Math. Anal. Appl. 177 (1993), 633–640. (1993) Zbl0816.28014MR1231507DOI10.1006/jmaa.1993.1283
  5. On the structure of T s -tribes, Tatra Mountains Math. Publ. 3 (1993), 167–172. (1993) MR1278531
  6. T s -tribes and T s -measures, J. Math. Anal. Appl (to appear). (to appear) MR1397888
  7. A characterization of triangular norm based tribes, Tatra Mountains Math Publ. 3 (1993), 161–166. (1993) Zbl0799.28013MR1278530
  8. 10.1007/BF00671785, Int. J. Theor. Physics 31 (1992), 1765–1781. (1992) Zbl0789.03049MR1183522DOI10.1007/BF00671785
  9. Probabilistic Metric Spaces, North-Holland, New York, 1983. (1983) MR0790314

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