Interval sets and three-way concept analysis in incomplete contexts

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• 作者：Yiyu Yao
• 关键词：Interval set ; Interval binary relation ; Incomplete formal context ; Partially ; known concept ; Three ; way concept analysis
• 刊名：International Journal of Machine Learning and Cybernetics
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：8
• 期：1
• 页码：3-20
• 全文大小：
• 刊物类别：Engineering
• 刊物主题：Computational Intelligence; Artificial Intelligence (incl. Robotics); Control, Robotics, Mechatronics; Complex Systems; Systems Biology; Pattern Recognition;
• 出版者：Springer Berlin Heidelberg
• ISSN：1868-808X
• 卷排序：8

文摘

In situations with incomplete information, we may have only partial knowledge about a concept. This motivates the introduction of the notion of a partially-known concept represented by a set of known instances, a set of known non-instances, and a set of objects with unknown states. We present a common conceptual framework of the notions of interval sets and incomplete formal contexts for representing partially-known concepts. An interval set is interpreted as a family of sets bounded by a pair of sets, and any one in the family may possibly be the actual set of instances of the concept when the information or knowledge becomes complete. An incomplete formal context is interpreted as a family of complete formal contexts, and any one in the family may possibly be the actual formal context when the information or knowledge becomes complete. While a complete formal context is induced by a binary relation, an incomplete formal context is induced by an interval binary relation that is interpreted as a family of binary relations. Within the proposed framework, we identify four possible forms for representing partially-known concepts. We examine, interpret, and extend existing studies on concept analysis in complete formal contexts.