Shadowed sets in the characterization of rough-fuzzy clustering

In this study, we develop a technique of an automatic selection of a threshold parameter, which determines approximation regions in rough set-based clustering. The proposed approach exploits a concept of shadowed sets. All patterns (data) to be clustered are placed into three categories assuming a certain perspective established by an optimization process. As a result, a lack of knowledge about global relationships among objects caused by the individual absolute distance in rough C-means clustering or individual membership degree in rough-fuzzy C-means clustering can be circumvented. Subsequently, relative approximation regions of each cluster are detected and described. By integrating several technologies of Granular Computing including fuzzy sets, rough sets, and shadowed sets, we show that the resulting characterization leads to an efficient description of information granules obtained through the process of clustering including their overlap regions, outliers, and boundary regions. Comparative experimental results reported for synthetic and real-world data illustrate the essence of the proposed idea.