Some properties of sequences of generalized fuzzy integrable functions

In this paper, we continue with the investigation of the generalized fuzzy integral (for short, (G) fuzzy integral), which is introduced by Wu et al. in 1993 [Generalized fuzzy integrals: part 1. Fundamental concepts, Fuzzy Sets and Systems 57 (1993) 219–226]. Some properties of (G) fuzzy integrable functions are obtained. The relations between convergence in fuzzy measure and mean convergence in (G) fuzzy integral for a sequence of non-negative measurable functions are discussed. Moreover, we also study the uniform integrability of a sequence of (G) fuzzy integrable functions, the uniformly absolute continuity and the uniform boundedness of a sequence of (G) fuzzy integrals.