Convergence, Strong Law of Large Numbers, and Measurement Theory in the Language of Fuzzy Variables

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dc.creatorBzowski, Adam
dc.creatorUrbanski, Michal K.
dc.date2009-03-05
dc.date2009-04-06
dc.date.accessioned2026-07-07T13:00:09Z
dc.date.available2026-07-07T13:00:09Z
dc.descriptionIn the paper we define the convergence of compact fuzzy sets as a convergence of alpha-cuts in the topology of compact subsets of a metric space. Furthermore we define typical convergences of fuzzy variables and show relations with convergence of their fuzzy distributions. In this context we prove a general formulation of the Strong Law of Large Numbers for fuzzy sets and fuzzy variables with Archimedean t-norms. Next we dispute a structure of fuzzy logics and postulate a new definition of necessity measures. Finally, we prove fuzzy version of the Glivenko-Cantelli theorem and use it for a construction of a complete fuzzy measurement theory.
dc.identifierhttps://arxiv.org/abs/0903.0959
dc.identifierhttp://arxiv.org/abs/0903.0959
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/225772
dc.subjectProbability
dc.subjectStatistics Theory
dc.subject03E72; 03E75; 28E10; 60F15
dc.titleConvergence, Strong Law of Large Numbers, and Measurement Theory in the Language of Fuzzy Variables
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