Optimum design using fuzzy numbers as design variables (3rd Report, Determinations of fuzzy sets and discussion)

In the previous papers, we proposed a formulation of optimization using fuzzy numbers as design variables, developed a new concept of simple fuzzy number operation and examined their effectiveness. In those papers, however, we did not pay enough attention to the determination of fuzzy sets of design variables. In this paper, we focus our attention on the determination of leeways of fuzzy numbers in design variables. We propose 3 types of formulation based mainly on leeways of design variables (formulation 2), leeways of objective function (formulation 3) and robustness of structure (formulation 4), all 3 of which were proposed by one of the authors. We applied the proposed formulation to the same rather simple optimization problem and compared the results from each formulation. Through these applications, we could easily understand the relationships between fuzziness of objective function and constraints and design variables in formulations 2 and 4, and we could also clarify fuzziness of design variables in formulations 3 and 4.