A theory of three-way decisions is formulated based on the notions of three regions and associated actions for processing the three regions. Inspired by the theory of three-way decisions, some researchers have further investigated the theory of three-way decisions and applied it in different domains. After reviewing the recent studies on three-way decisions, this paper introduces the three-way cluster analysis. In order to address the problem of the uncertain relationship between an object and a cluster, a three-way clustering representation is proposed to reflect the three types of relationships between an object and a cluster, namely, belong-to definitely, uncertain and not belong-to definitely. Furthermore, this paper reviews some three-way clustering approaches and discusses some future perspectives and potential research topics based on the three-way cluster analysis.
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