2009/03/05 by Adam Bzowski, Bzowski, Adam, Michał K. Urbański +2
Computer Science · Decision Sciences · Mathematics · #03E72 #03E75 #28E10 #60F15 #FOS: Mathematics #Fuzzy Logic and Control Systems #Fuzzy Systems and Optimization #Multi-Criteria Decision Making #Probability (math.PR) #Statistics Theory (math.ST) #math.PR #math.ST #msc:03E72 #msc:03E75 #msc:28E10 #msc:60F15 #stat.TH
paper · pdf · doi:10.48550/arxiv.0903.0959
openalex publication_date 2009/03/05 · arxiv created 2009/04/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In 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.