The supremum and infimum of the set of fuzzy numbers and its application

Abstract

In this paper, we prove that the bounded set of fuzzy numbers must exist supremum and infimum and give the concrete representation of supremum and infimum. As an application, we obtain that the continuous fuzzy-valued function on a closed interval exists supremum and infimum and give the precise representation. We also show that the bounded fuzzy-valued function on a closed interval can define the lower and upper sums and the lower and upper integrals of Riemann and Riemann-Stieltjes by the usual way. © 1997 Academic Press.