ABSTRACT

The p-center problem is the problem of finding p best places on a network to locate facilities for providing customers' demands such that the maximum distance between the demand points and facilities is minimized. If these facilities are located on the edges and vertices of the network, the problem is called the absolute p-center problem. Whereas, if the facilities can just be located on the vertices, the problem is called the vertex p-center problem. In this paper, both absolute and vertex 1-center problems are studied on tree graphs, where the lengths of edges are fuzzy numbers. Based on some presented properties, fuzzy algorithms are proposed for finding absolute and vertex center of a fuzzy tree. The performance of presented algorithms are shown by solving some numerical examples. is considered and the absolute center problem and the vertex center problem are studied, respectively. Also, the weights of all vertices are equal to one and the lengths of edges are fuzzy numbers. Based on some presented properties, fuzzy algorithms are proposed for finding the absolute center and vertex center of a fuzzy tree. The performance of our presented algorithm is shown by solving two numerical examples. Also, to illustrate the applicability and efficiency of the presented algorithm, a real life example is solved.

摘要

p中心问题是在网络上找到 p 个最佳位置来定位设施以满足客户需求的问题，从而使需求点和设施之间的最大距离最小化。如果这些设施位于网络的边缘和顶点，则该问题称为绝对p中心问题。然而，如果设施只能位于顶点上，则该问题称为顶点p中心问题。在本文中，绝对值和顶点1中心问题是在树图上研究的，其中边的长度是模糊数。基于一些提出的性质，提出了模糊算法来寻找模糊树的绝对中心和顶点中心。通过解决一些数值示例来展示所提出算法的性能。分别考虑绝对中心问题和顶点中心问题。此外，所有顶点的权重都等于 1，边的长度是模糊数。基于一些提出的性质，提出了模糊算法来寻找模糊树的绝对中心和顶点中心。我们提出的算法的性能通过解决两个数值例子来展示。此外，为了说明所提出算法的适用性和效率，解决了一个现实生活中的例子。