基于确定可能性均值法求解模糊随机双层规划问题

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

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 Kth-best algorithm is employed to deal with it.Finally,numerical examples testify the feasibility of the proposed method.