Geodesic
A characterization of tribes with respect to the Łukasiewicz $t$-norm
Czechoslovak Mathematical Journal, Tome 47 (1997) no. 4, pp. 689-700.

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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.
Classification : 04A72, 28A20, 28E10, 46S10, 46S99 
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     author = {Klement, Erich Peter and Navara, Mirko},
     title = {A characterization of tribes with respect to the {{\L}ukasiewicz} $t$-norm},
     journal = {Czechoslovak Mathematical Journal},
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     number = {4},
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     zbl = {0902.28015},
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     url = {http://geodesic.mathdoc.fr/item/CMJ_1997__47_4_a8/}
}
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Klement, Erich Peter; Navara, Mirko. A characterization of tribes with respect to the Łukasiewicz $t$-norm. Czechoslovak Mathematical Journal, Tome 47 (1997) no. 4, pp. 689-700. http://geodesic.mathdoc.fr/item/CMJ_1997__47_4_a8/