In this study, we will propose a new method of robust design, which is formulated by using fuzzy numbers as design variables and parameters. In the past robust design methodology, especially by considering usage of optimization, its basic formulations have been done by stochastic optimization. In those cases, they could not handle the deviation in design variables of both sides of shape or their index for their width, because they were mainly based on normal distribution. In this study, we will compare the formulation of fuzzy optimization and stochastic optimization and clarify the characteristics of the proposed method from differences between formulations. Through those comparisons, we will explain the benefit and suitability of the proposed method to robust design in settings of objective functions, treatments of constraints and benefit of design variables which can treat both sides of index for its deviation.