would be better phenotypes. For that reason, the key to selecting an appropriate number of clusters relied on the percentage of variation that the clusters could explain. In the exploratory stage, we observed over 60% variation in the five substance dependence traits could be explained by these two clusters. Second, the goal of implementing fuzzy clustering is to reduce the phenotypic dimensions such that the subsequent linkage analysis could be carried out in a conventional software package. We used the coefficients of fuzzy cluster membership as the trait for the subsequent linkage analysis. The membership coefficients of all clusters sum to one. A pre-selected number of clusters at two results in two membership coefficients such that one coefficient determines the other coefficient due to the constraint of summation to one, and this coefficient was used for the subsequent linkage analysis. Simulation studies showed that fuzzy clustering is more powerful than the principal component approach for multivariate continuous traits and more powerful than the joint linkage method [Mangin et al., 1998] in the presence of pleiotropy [Kaabi and Elston, 2003]. On the other hand, fuzzy clustering could be disadvantageous in studies of very large numbers of clusters because the amount of
