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.
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Klement, E.P., Navara, M. A characterization of tribes with respect to the Łukasiewicz t-norm. Czechoslovak Mathematical Journal 47, 689–700 (1997). https://doi.org/10.1023/A:1022822719086
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DOI: https://doi.org/10.1023/A:1022822719086