Clustering observations using fuzzy similarities between ordered categorical data

In general, we use cluster analysis or factor analysis to cluster or position observations having multivariate continuous variables. Those methods are based on measurements or correlation coefficients between continuous variables. Therefore, there are many problems in applying those techniques to a dataset where ordered categorical data are collected. At first, we propose a fuzzy similarity between ordered categorical variables. Next, we propose techniques of clustering and positioning observations of statistical 2 or 3 dimensional dataset where ordered categorical data are collected. The effectiveness of the fuzzy similarity and our techniques is discussed through two examples of image datasets in marketing research.