Geodesic
The $\sigma$-complete MV-algebras which have enough states
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
Colloquium Mathematicum, Tome 103 (2005) no. 1, pp. 121-130 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/cm103-1-13
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

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

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