The controlled convergence theorems for the strong Henstock integrals of fuzzy-number-valued functions

Authors:
Zengtai Gong;Yabin Shao
Affiliations:
College of Mathematics and Information Science, Northwest Normal University, Lanzhou, Gansu 730070, China;College of Mathematics and Information Science, Northwest Normal University, Lanzhou, Gansu 730070, China
Venue:
Fuzzy Sets and Systems
Year:
2009

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Abstract

In this paper, we discuss the properties of the strong Henstock integrals of the fuzzy-number-valued functions using the notion of generalized derivatives, and prove the controlled convergence theorem for such integrals. Also, we present the concept of equi-integrability of a sequence for fuzzy-number-valued functions. Under this concept, we prove another controlled convergence theorem and establish the relationships between the above two controlled convergence theorems.