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The problem of extracting knowledge from decision tables in terms of functional dependencies is one of the important problems in knowledge discovery and data mining. Based on some results in relational database, in this paper we propose two algorithms. The first one is to find all reducts of a consistent decision table. The second is to infer functional dependencies from a consistent decision table. The second algorithm is based on the result of the first. We show that the time complexity of the two algorithms proposed is exponential in the number of attributes in the worst case.

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Mining High Utility Sequential Patterns (HUSP) is an emerging topic in data mining which attracts many researchers. The HUSP mining algorithms can extract sequential patterns having high utility (importance) in a quantitative sequence database. In real world applications, the time intervals between elements are also very important. However, recent HUSP mining algorithms cannot extract sequential patterns with time intervals between elements. Thus, in this paper, we propose an algorithm for mining high utility sequential patterns with the time interval problem. We consider not only sequential patterns' utilities, but also their time intervals. The sequence weight utility value is used to ensure the important downward closure property. Besides that, we use four time constraints for dealing with time interval in the sequence to extract more meaningful patterns. Experimental results show that our proposed method is efficient and effective in mining high utility sequential pattern with time intervals.

Reduct of decision systems is the topic that has been attracting the interest of many researchers in data mining and machine learning for more than two decades. So far, many algorithms for finding reduct of decision systems by rough set theory have been proposed. However, most of the proposed algorithms are heuristic algorithms that find one reduct with the best classification quality. The complete study of properties of reduct of decision systems is limited. In this paper, we discover equivalence properties of reduct of consistent decision systems related to a Sperner-system. As the result, the study of the family of reducts in a consistent decision system is the study of Sperner-systems.