On generalized versions of central limit theorems for IF-events

Abstract

IF-sets were introduced by Atanassov to model imprecision, which can be often met in real-world applications. IF-sets were also used for definition of IF-events, for which probability theories were considered, including IF-probability theory and M-probability theory. Within these theories IF-observables and M-observables were introduced and their properties have been studied. In this paper we consider limit behavior of the row sums of triangular arrays of independent IF-observables and M-observables. We prove generalized versions of the central limit theorem (CLT for short) for both types of observables, i.e., the Lindeberg CLT and the Lyapounov CLT. Furthermore, we prove the Feller theorem for null arrays of IF-observables and M-observables. Finally, we illustrate our theoretical results by examples.