Symmetry, Volume 13, Issue 12
December 2021 - 221 articles
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Cover Story: Laws of large numbers (LLNs) are theorems of great importance for probability and chance theory. Within chance theory the notion of an uncertain random variable was defined to model phenomena where both uncertainty and randomness are present. This work considers uncertain random variables as functions of random variables and uncertain variables, introduced within uncertainty theory. Sequences of uncertain random variables are defined for a fixed continuous function, strictly monotone with respect to its second argument, as are sequences of pairwise independent or independent, identically distributed random variables and regular, independent, and identically distributed uncertain variables. Some LLNs for such defined sequences of uncertain random variables are formulated and proven. Two of their counterparts for uncertain variables are also discussed. View this paper