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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 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.

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