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

An application of fuzzy mathematical programming techniques to multiple objective design problems is presented. Two examples dealing with multiobjective design of mechanical and structural systems are considered. The fundamental assumption in fuzzy mathematical programming applications dealing with the use of linear membership functions is critically examined. Several nonlinear shapes for membership functions of the fuzzy sets are chosen consistent with varying perceptions of the designer, and are analysed to determine their impact on the overall design process. These shapes correspond to what we define as the coefficient of membership satiation. It is shown that the fuzzy min operator together with linear as well as nonlinear membership functions yield Pareto-optimal solutions to the original multiobjective problem. It is seen that final design for both examples is strongly influenced by the sign of membership satiation coefficient.