Endographic approach on supremum and infimum of fuzzy numbers

In this paper it is shown that supremum and infimum of fuzzy numbers can be characterized by membership function method via endograph metric more directly than by using the levelwise metric, it is proved that the endograph metric is approximative with respect to orders on fuzzy number spaces, also, the endograph metric is computable. The result in this paper shows that the fuzzy-number-valued integrals of the kind based on concept like Riemann sum in calculus are computable.