By fuzzy optimization we here mean optimization in a fuzzy environment, i.e., optimization with fuzzy constraints. Such a problem can be reduced to a family of ordinary optimization problems by using the representation theorem which states that a fuzzy set is a family of ordinary sets. Since it is difficult to work with a family of sets, in this paper a fuzzy set is approximated by an ordinary set. The Chebyshev norm is introduced into the set of all fuzzy sets, and a set is said to approximate a fuzzy set if the norm of a difference of its characteristic functions is smaller than a given number.