On fuzzy classification indices and their variability assessment

Y. Melnykov${}^a$, V. Melnykov${}^a$ and M. Nai Ruscone${}^b$

${}^a$University of Alabama, ${}^b$University of Genoa

In the area of cluster analysis, the comparison of obtained partitions is a task of primary importance. It is standard to compare the partitions based on one of available classification indices. The vast majority of such indices assume crisp membership assignments and their direct application to fuzzy procedures may yield biased results. While several attempts have been made to develop classification indices applicable in the fuzzy framework, all current approaches focus on providing a point value without taking the variability in membership assignments into consideration. We propose several novel variants of fuzzy classification indices and present an approach to derive their distributions. This allows to develop confidence intervals and hypothesis testing procedures for the introduced indices.

Keywords: Classification Index, Cluster Analysis, Fuzzy Classification.