On the FM_α-Integral of Fuzzy-Number-Valued Functions

摘要

In this paper, we define the FM_α integrals of fuzzy-number-valued functions and discuss its properties. Especially, we give two examples which show that the FM_α integrable function is not fuzzy McShane integrable, and the fuzzy Henstock integrable function is not FM_α integrable function. As the main outcomes, we prove that a fuzzy-number-valued function f : I_0 → E~n is FM_α integrable on I_0 if and only if there exists an ACG_α function F such that F' = f almost everywhere on I_0.