Alternative α-level-cuts methods for optimum structural design with fuzzy resources

Three alternative α-level-cuts approaches: single-cut, double-cuts, and multiple-cuts, for solving nonlinear programming design problems of structuring engineering with fuzzy resources were developed and proposed in this paper. The conventional standard α-cuts method of fuzzy linear programming (FLP) inspired presenting development of innovative fuzzy nonlinear programming (FNLP) solution method. This paper also presents the inter-relations between the standard α-cuts approaches and the proposed novel formulation. The illustration of structural design example generally indicates that the multiple-cuts approach can achieve a better final design than that of double-cuts approach. The final design of double-cuts approach is better than that of single-cut approach. The approaches presented perform better than that of conventional α-level-cuts method. It is shown in double and multiple level-cuts approaches that direct minimization of α of the objective function and maximization of the constraints simultaneously yield the most effective formulation. Additionally, linear or nonlinear membership functions of objective functions can be selected by designer depending on the practical requirements of design objectives. The presented alternative α-level-cuts approaches guarantees to obtain the unique optimum design on nonlinear engineering problems with fuzzy resources.