Abstract
ABSTRACTIn the classical p-median problem, we want to find a set Y containing p points in a given graph G such that the sum of weighted distances from Y to all vertices in V is minimised. In this paper, we consider the 1-median and 2-median problems on a tree with fuzzy weights. We show that the majority property holds for fuzzy 1-median problem on a tree. Then based on a proposed ranking function and the majority property, a fuzzy algorithm is presented to find the median of a fuzzy tree. Finally, the algorithm is extended to solve 2-median problem on fuzzy trees.
Highlights
The p-median problem is an important issue in the location theory
A new method is presented for ranking all triangular fuzzy numbers
The proposed method is a linear ranking method and it is a simple implementation that makes use of the algorithm more effectively to solve fuzzy real-world problems. Based on this ranking, a unique index is assigned to each fuzzy number
Summary
The p-median problem is an important issue in the location theory. In this problem, we want to find p best places for locating facility centers to provide the demands of n customers such that the sum of weighted distances from customers to the nearest facility is minimised. An O(pn2) algorithm for the p-median and related problems on tree graphs was presented by Tamir [3]. Tragantalerngsak et al [4] studied single-source capacitated facility location problem and proposed a Lagrangian relaxation-based branch and bound algorithm for this problem. An uncertain model for single-facility location problems on networks was presented by Gao [6]. Uno et al [14] considered the facility location problem on a network with fuzzy random weights. A fuzzy algorithm for finding the median of fuzzy trees is presented. The algorithm is extended to find 2-median of a fuzzy tree.
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