A Kemeny Distance-Based Robust Fuzzy Clustering for Preference Data

Abstract

We propose two robust fuzzy clustering techniques in the context of preference rankings to group judges into homogeneous clusters even in the case of contamination due to outliers or, more generally, noisy data. The two fuzzy C-Medoids clustering methods, based on the same suitable exponential transformation of the Kemeny distance, belong to two different approaches and differ in the way they introduce the fuzziness in the membership matrix, the one based on the “m” exponent and the other on the Shannon entropy. As far as the Kemeny distance is concerned, it is equivalent to the Kendall distance in the case of complete rankings but differs from the latter in the way of handling tied rankings. Simulations prove that our methods are able to recover the natural structure of the groups neutralizing the effect of possible noises and outliers. Two applications to real datasets are also provided.