We characterize Łukasiewicz tribes, i.e., collections of fuzzy sets that are closed under the standard fuzzy complementation and the Łukasiewicz t-norm with countably many arguments. As a tool, we introduce σ-McNaughton functions as the closure of McNaughton functions under countable MV-algebraic operations. We give a measure-theoretical characterization of σ-complete MV-algebras which are isomorphic to Łukasiewicz tribes.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm103-1-13,
author = {Antonio Di Nola and Mirko Navara},
title = {The $\sigma$-complete MV-algebras which have enough states},
journal = {Colloquium Mathematicae},
volume = {103},
year = {2005},
pages = {121-130},
zbl = {1081.06011},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm103-1-13}
}
Antonio Di Nola; Mirko Navara. The σ-complete MV-algebras which have enough states. Colloquium Mathematicae, Tome 103 (2005) pp. 121-130. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm103-1-13/