@Article{DiNolaNavara:CollMath05, IS = { zkontrolovano 30 Dec 2005 }, UPDATE = { 2005-12-14 }, author = {Di~Nola, Antonio and Navara, Mirko}, title = { The $\sigma$-complete {MV}-algebras which have enough states }, year = {2005}, pages = {121--130}, journal = {Colloquium Mathematicum}, publisher = {Polish Academy of Sciences}, address = {Warsaw, Poland}, issn = {0010-1354}, volume = {103}, number = {1}, importance = {1}, authorship = {50-50}, annote = { We characterize Lukasiewicz tribes, i.e., collections of fuzzy sets that are closed under the standard fuzzy complementation and the Lukasiewicz 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 Lukasiewicz tribes. }, keywords = {MV-algebra, $\sigma$-complete MV-algebra, McNaughton function, tribe }, project = {GACR 201/02/1540}, psurl = {[PDF] }, }