Fuzzy Majority Algorithms for the 1-Median and 2-Median Problems on a Fuzzy Tree

In 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 l-median and 2-median problems on a tree with fuzzy weights. We show that the majority property holds for fuzzy l-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.