Convergence, Strong Law of Large Numbers, and Measurement Theory in the Language of Fuzzy Variables
Adam Bzowski,
Michal K. Urbanski
Abstract:In the paper we define the convergence of compact fuzzy sets as a convergence of α-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. Fina… Show more
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