A method based on crisp possibilistic mean value for solving fuzzy random bilevel programming problem

DOI：10.7511/dllgxb201802016

 作者 单位 任爱红

针对目标函数和约束函数中系数均为模糊随机变量的双层规划问题，基于模糊随机变量的期望值概念，将原模糊随机双层规划问题变形为一个模糊双层规划问题．采用模糊数的确定可能性均值对上下层目标函数进行去模糊化，利用基于可能性测度的模糊机会约束方法处理模糊约束函数，提出模糊随机双层确定可能性均值-机会约束规划模型，并给出其确定等价模型，再运用K次最好算法求解最终确定模型．最后通过数值例子验证了所提方法的可行性．

A kind of bilevel programming problem involving fuzzy random variable coefficients in both objective functions and constraint functions is considered. Based on the notion of the expectation of a fuzzy random variable, the fuzzy random bilevel programming problem is converted into a fuzzy bilevel programming problem. Subsequently, the crisp possibilistic mean value of a fuzzy number is used to defuzzy the upper and lower level objective functions and fuzzy chance constrained method based on possibility is applied to handle fuzzy constraint functions, and then a fuzzy random bilevel crisp possibilistic mean value-chance constrained programming model is developed. Then the crisp equivalent model is given and the Kth-best algorithm is employed to deal with it. Finally, numerical examples testify the feasibility of the proposed method.