模糊线性规划的γ-鲁棒解

γ-robust solutions of fuzzy linear programming problems

对于不确定系统的优化问题,模糊线性规划是一种常用的建模方法,但得到的最优解或满意解,往往对参数的变动缺少"免疫"能力,即参数受到扰动后,最初的最优解会变得不再最优甚至不可行.首先针对λ-截集水平下的模糊线性规划,给出了λ-鲁棒解的定义.利用模糊结构元理论对λ-鲁棒解的定义进行表示,得到了求解模型.由于决策者的不同,对解的可实现程度要求不同.故在模型中加入了能够反映决策者风险偏好的测度约束,该模型的解即为γ-鲁棒解,该解既有鲁棒性、优化性,又能体现决策者的风险偏好程度.通过算例可以看出,γ-鲁棒解对参数的变动具有"免疫"能力,能为决策者提供更为丰富的信息,体现出了更好的实用价值.

Fuzzy linear programming is used widedly for the problems of uncertain system＇s optimization, but the optimization solutions or satisfactory solution are often not ＂immune＂ to parameters, that is if the parameters are changed, initial optimal solution is no longer optimal or even infeasible. First of all, for the λ-cut level of fuzzy linear programming, λ-robust optimization solutions are put forward; then article indicates the definition of λ-robust solution by fuzzy structured element, and obtains the solving model. Solution can achieve the degree requirements are different due to the different decision makers, therefore, the measure constraints which can reflect the decision-makers risk preferences are added to the model, the solution of this model is γ-robust solution, and the solution not only has the robustness and optimization, but also reflects the degree of risk preference of the decision makers. By an example, it is found that the optimization robust solutions with measurement are immune to parameters, which are more useful for decision-makers and reflect a better practical value.