基于模糊结构元的最小生成树问题的求解算法

Algorithm of Minimum Spanning Tree Problem Based on Fuzzy Structured Element

针对梯形模糊数,定义了一种梯形模糊结构元.研究了边权值为梯形模糊数的模糊权值网络,建立了其最小生成树问题的数学模型,并利用梯形模糊结构元加权排序思想和Kruskal算法,设计了一种该问题的求解算法,给出了算法的复杂度分析和应用实例.文中的模型和算法对于边权值为其他类型模糊数的模糊权值网络同样有效.

A trapezoidal fuzzy structured element is defined for the trapezoidal fuzzy number. The minimum spanning tree problem is addressed in the fuzzy weighted network whose weight is trapezoidal fuzzy number, and a mathematical model is established for it. By adopting the idea of weighted priority of the trapezoidal fuzzy structured element and the classical kruskal algorithm, a new algorithm is designed to solve the minimum spanning tree problem in fuzzy weighted network whose weight is trapezoidal fuzzy number; the complexity analysis and practical examples of the new algorithm are also given. In addition, the mathematical model and new algorithm in the paper are as effective to other fuzzy weighted network with other fuzzy number.