Finding the absolute and vertex center of a fuzzy tree

Abstract

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.