Weak approximation in the lattice of fuzzy number space

In this paper, first it is observed that the fuzzy number lattice satisfies the two infinite distributive laws for bounded set of fuzzy numbers, then it is shown that the lattice is not continuous. To overcome the deficiency of discontinuity the concept of weak below relation is introduced into the fuzzy number lattice in contrast to the way below relation in continuous lattices. It turns out that, though the lattice of all fuzzy numbers is not continuous, the weak below relation behaves well as that of way below relation in continuous lattices.