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The \(\sigma\)-complete MV-algebras which have enough states. (English) Zbl 1081.06011
The authors characterize Łukasiewicz tribes, special sets of fuzzy sets forming \(\sigma\)-complete MV-algebras closed under pointwise limits of monotone functions. To have this characterization, they generalize the concept of McNaughton functions to \(\sigma\)-McNaughton functions as the closure of McNaughton functions under countable MV-algebraic operations. In addition, the authors characterize \(\sigma\)-complete MV-algebras to be isomorphic to Łukasiewicz tribes as those having a separating system of pure states.

06D35 MV-algebras
03E72 Theory of fuzzy sets, etc.
28E10 Fuzzy measure theory
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