Generalization of the expectation for a unified description of random and indefinite factors

In this paper we demonstrate the possibility of a general description of random, indefinite and (some kinds of) fuzzy factors by weakening the additivity axiom for the probability and considering a measurable space of elementary events with a subadditive functional defined on the space of measurable functions. This functional (sublinear expectation) is a generalization of the expectation. Some properties of sublinear expectations are studied and some examples of constructing spaces with sublinear expectations of interest for applications are considered, in particular, the direct product of given spaces. The references consist of 9 titles.