Fuzzy clustering based weighted principal component analysis for interval-valued data considering uniqueness of clusters

We have proposed a weighted principal component analysis for interval-valued data which is a hybrid method of fuzzy clustering and principal component analysis. However, in this method, we need to assume the relationship between minimum values and maximum values of the interval-valued data. That is, if the assumption is not adaptable, then the transformed matrix cannot show the exact situation of the interval-valued data. In order to avoid the wrong assumption, this paper proposes another weighted principal component analysis using the fuzzy clustering solutions of minimum and maximum data under unique clusters. From the uniqueness of the clusters, we can obtain two comparable results of principal components for the minimum and maximum data.