Reconstruction of additive phylogenetic tree

In the construction of phylogenetic tree, the choice of a metric for measuring the distance of pairs of objects, and linkages for measuring distance between groups are both crucial. For stepwise methods, different linkages usually produce different trees, and for exhaustive methods, the computation is time-consuming when the number of objects to be classified is large. In this paper, we propose an ultrametric fuzzy distance, and show that under this distance, the correspondent distance tree is additive and linkage-free, and therefore has a one-to-one correspondence between the distance matrix and trees. The algorithm is easy to implement even for a large sample of objects; however, it may mildly increase the chance of misclassification due to the loss of information.