Mathematical Problems in Engineering
Volume 4 (1998), Issue 3, Pages 187-200

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

J. Fang,1 S. M. Smith,2 and I. Elishakoff1

1Department of Mechanical Engineering, Florida Atlantic University, Boca Raton 33431–0991, FL, USA
2Department of Ocean Engineering, Florida Atlantic University, Boca Raton 33431–0991, FL, USA

Received 10 March 1995; Revised 11 April 1996

Copyright © 1998 J. Fang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.