Cauchy criterion for the Henstock-Kurzweil integrability of fuzzy number-valued functions

In this paper, Cauchy criterion, the necessary and sufficient conditions for Henstock integrability of fuzzy number-valued functions defined on a compact interval in the real line is presented. The results can be used to characterize the integrability of a fuzzy number valued function without calculation the value of the integral. In addition, the notion, the elementary properties and the relation of R and R* integrals of fuzzy number-valued function defined on a compact interval in the real line are also presented.