求解多层线性规划的模糊规划法

Fuzzy Programming Approach for Multilevel Linear Programming

用模糊集理论中的隶属函数描述多层线性规划的各层目标,在第一层给定最小满意水平下,通过求解相应层次的模糊规划来确定各层的最小满意度,从而最终得到问题的一个满意解.提出的方法只需求解一系列线性规划问题,具有较好的计算复杂性和可行性,最后的算例进一步验证了方法的有效性.

In this study,we use the concepts of membership function and multiple objective optimization to develop a fuzzy programming approach for solving the multilevel linear prograjnming problems.The higher level decision maker defines his or her objective which is described by linear membership functions of fuzzy set theory.This information then constrains the lower level decision maker＇s feasible space.After the first decision maker gives a minimum satisfaction level,the fuzzy programming approach will give the minimum satisfaction degree of each level by solving the corresponding fuzzy programming.The proposed approach only needs to solve a series of linear programming problems and will not increase the complexities of original problems.Finally,illustrative numerical example is provided to demonstrate the feasibility of the proposed method.