模糊权值网络最短路问题的数学模型及算法

Mathematical model and algorithm for shortest path problem in fuzzy weighted network

模糊权值网络的最短路问题是一类重要的网络优化问题.针对边权值为三角模糊数的模糊权值网络的最短路问题,基于模糊数的结构元加权序,将其模糊线性规划模型等价转化为经典的线性规划模型,并提出一种改进的权矩阵算法来求解该问题,算法证明和应用实例表明新算法的正确性和有效性.此外对于边权值为其他形式模糊数的模糊权值网络的最短路问题,文中模型和算法同样有效.

The shortest path problem in fuzzy wejghted network is an important network optimization problem.In view of the shortest path problem in the fuzzy weighted network whose weight is triangular fuzzy number,the fuzzy linear programming model is converted into a classical linear programming model by using the weighted ranking of fuzzy number′s structured element,and an improved weight matrix method is proposed to solve the problem.The new algorithm correctness is proved and its effectiveness is illustrated by an example.In addition,the mathematical model and new algorithm in this paper are as effective as other fuzzy weighted network with other fuzzy number.