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
Wemers' 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.