Abstarct: Using H-differentiability of a fuzzy-valued function and a parametric total order relation on set of fuzzy numbers, we prove the necessary and sufficient optimality condition for unconstrained single and multi variable fuzzy optimization problems. The following, we solve the unconstrained and constrained fuzzy ptimization problems using partial order relation-fuzzy max order on the set of fuzzy numbers. Under the concepts of convexity and generalized convexity of fuzzy-valued functions, we derive sufficient optimality conditions for constrained fuzzy optimization problems. Eventully, we propose the Newton’s method for solving unconstrained single and multi variable fuzzy optimization problems.