1Department of Mathematics and Informatics University of Salerno via S. Allende 84081 Baronissi, Salerno, Italy 2Center for Machine Perception Department of Cybernetics Faculty of Electrical Engineering Czech Technical University Technická 2 166 27 Praha 6, Czech Republic
Colloquium Mathematicum, Tome 103 (2005) no. 1, pp. 121-130
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 $\sigma $-McNaughton functions as the closure of
McNaughton functions under countable MV-algebraic operations. We give a
measure-theoretical characterization of $\sigma $-complete
MV-algebras which are isomorphic to Łukasiewicz tribes.
Keywords:
characterize ukasiewicz tribes collections fuzzy sets closed under standard fuzzy complementation ukasiewicz t norm countably many arguments tool introduce sigma mcnaughton functions closure mcnaughton functions under countable mv algebraic operations measure theoretical characterization sigma complete mv algebras which isomorphic ukasiewicz tribes
Affiliations des auteurs :
Antonio Di Nola
1
;
Mirko Navara
2
1
Department of Mathematics and Informatics University of Salerno via S. Allende 84081 Baronissi, Salerno, Italy
2
Center for Machine Perception Department of Cybernetics Faculty of Electrical Engineering Czech Technical University Technická 2 166 27 Praha 6, Czech Republic
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Antonio Di Nola; Mirko Navara. The $\sigma$-complete MV-algebras which have enough states. Colloquium Mathematicum, Tome 103 (2005) no. 1, pp. 121-130. doi: 10.4064/cm103-1-13
