To find genetic association between complex diseases and phenotypic traits, one important procedure is conducting a joint analysis. Multifactor dimensionality reduction (MDR) is an efficient method of examining the interactions between genes in genetic association studies. It commonly assumes a dichotomous classification of the binary phenotypes. Its usual approach to determining the genomic association is to construct a confusion matrix to estimate a classification error, where a binary risk status is determined and assigned to each genotypic multifactor class. While multi-class phenotypes are commonly observed, the current MDR approach does not handle these phenotypes appropriately because the thresholds for the risk statuses may not be clear. In this study, we suggest a new method for estimating gene-gene interactions for multi-class phenotypes. Our approach adopts the index of dissimilarity (IDS) as an evaluation measure. This is analytically equivalent to the common association measure of balanced accuracy (BA) for the binary traits, while it is not required to determine the risk status for the estimation. Moreover, it is easily expandable to the generalized index of dissimilarity (GIDS), which has an explicit form that can handle any number of categories. The performance of the proposed method was compared with those of other approaches via simulation studies in which fifteen genetic models were generated with three class outcomes. A consistently better performance was observed using the proposed method. The effect of a varying number of categories was examined. The proposed method was also illustrated using real genome-wide association studies (GWAS) data from the Korean Association Resource (KARE) project.