Locally and globally small Riemann sums and Henstock-Stieltjes integral for n-dimensional fuzzy-number-valued functions

摘要

In this paper, we study locally and globally small Riemann sums with respect to α for n-dimensional fuzzy-number-valued functions. And we prove that a fuzzy-number-valued functions in n-dimensional is Henstock-Stieltjes (HS) integrable on [a, b] if and only if it has (LSRS) with respect to α on [a, b]. Also we shall prove that a fuzzy-number-valued functions in n-dimensional is Henstock-Stieltjes (HS) integrable on [a, b] if and only if it has (GSRS) with respect to α on [a, b].