Nonlinear membership functions in multiobjective fuzzy optimization of mechanical and structural systems

Abstract

An application of fuzzy mathematical programming techniques to multiple objective design problems is presented. Two examples dealing with the multiobjective design of mechanical and structural systems are considered. The concept of a Pareto-optimal and fuzzy Pareto-optimal solution is discussed, and it is shown that the resulting formulation yields Pareto-optimal solutions. The fundamental assumption in fuzzy mathematical programming applications involving the use of linear membership functions is critically examined. Several nonlinear shapes for the membership functions of the fuzzy sets are proposed, consistent with varying perceptions of the designer, and are analyzed to determine their impact on the overall design process. These shapes correspond to what we define as the coefficient of membership satiation. It is seen that optimum designs for both examples are strongly influenced by the sign of the membership satiation coefficient.