  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.
