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

作　　者：任爱红 

机构地区：[1]宝鸡文理学院数学与信息科学学院,陕西宝鸡721013

出　　处：《大连理工大学学报》2018年第2期213-220,共8页Journal of Dalian University of Technology

基　　金：国家自然科学基金资助项目(61602010);陕西省自然科学基础研究计划项目(2017JQ6046);陕西省教育厅专项科研计划项目(17JK0047)

摘　　要：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.

关 键 词：双层规划 模糊随机变量 模糊数 K次最好算法 

分 类 号：O221[理学—运筹学与控制论]