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Abstract This paper proposes a new mathematical programming method—grey fuzzy linear programming (GFLP)—as a means for optimization analysis under uncertainty. The method improves upon previous grey linear programming (GLP) and flexible fuzzy linear programming (FLP) methods by allowing uncertainty in both the model coefficients and stipulations to be effectively communicated into the optimization process, and thus provide more satisfactory solutions for an optimization problem under uncertainty. Compared with the ordinary GLP method, grey solutions with smaller variations are provided, which may be useful when model inputs are very uncertain. Compared with existing flexible FLP methods, more uncertain information is incorporated within the GFLP model, and the tolerance interval of the objective function value can be determined quantitatively. The modelling approach is applied to a hypothetical problem in the municipal solid waste management planning area. The results indicate that, compared with the solutions from a GLP model, the ranges of values for the objective function and the majority of the decision variables are decreased. Therefore, the developed GFLP method can be considered as a feasible approach for increasing system certainty and achieving more applicable and satisfactory grey solutions.
Huang et al. (Sat,) studied this question.