Some properties of sequences of generalized fuzzy integrable functions

Authors:
Jin-xuan Fang
Affiliations:
Department of Mathematics, Nanjing Normal University, Nanjing, Jiangsu 210097, China
Venue:
Fuzzy Sets and Systems
Year:
2007

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Abstract

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.