Abstract
The paper is concerned with a logic-based expansion of the standard FCM clustering. The proposed algorithm captures the logic fabric of the structure in a dataset by describing it in the form of a union of the clusters (that is fuzzy relations) determined by the clustering algorithm. In contrast to the standard FCM, the elements (clusters) are combined together as a union of such fuzzy relations—clusters and this form of combination arises as a constraint in the clustering method. In this sense, the introduced clustering environment gives rise to the clustering that is regarded as a logic-driven data decomposition. A detailed algorithm is presented along with some illustrative examples.