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

摘要

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.