Combination of anti‐optimization and fuzzy‐set‐based analysis for structural optimization under uncertainty

An approach to the optimum design of structures, in which uncertainties with a fuzzy nature in the magnitude of the loads are considered, is proposed in this study. The optimization process under fuzzy loads is transformed into a fuzzy optimization problem based on the notion of Werners′ maximizing set by defining membership functions of the objective function and constraints. In this paper, Werner′s maximizing set is defined using the results obtained by first conducting an optimization through anti‐optimization modeling of the uncertain loads. An example of a ten‐bar truss is used to illustrate the present optimization process. The results are compared with those yielded by other optimization methods.