Multigranulation rough-fuzzy clustering based on shadowed sets

Abstract

In this study, a new technique of rough-fuzzy clustering based on multigranulation approximation regions is developed to tackle the uncertainty associated with the fuzzifier parameter m. According to shadowed set theory, the multigranulation approximation regions for each cluster can be formed based on fuzzy membership degrees under the multiple values of fuzzifier parameter with a partially ordered relation. The uncertainty generated by the fuzzifier parameter m can be captured and interpreted through the variations in approximation regions among different levels of granularity, rather than at a single level of granularity under a specific fuzzifier value. An ensemble strategy for updating prototypes is then presented based on the constructed multigranulation approximation regions, in which the prototype calculations that may be spoiled due to the uncertainty caused by a single fuzzifier value can be modified. Finally, a multilevel degranulation mechanism is introduced to evaluate the validity of clustering methods. By integrating the notions of shadowed sets and multigranulation into rough-fuzzy clustering approaches, the overall topology of data can be captured well and the uncertain information implicated in data can be effectively addressed, including the uncertainty generated by fuzzification coefficient, the vagueness arising in boundary regions and overlapping partitions. The essence of the proposed method is illustrated by comparative experiments in terms of several validity indices.