Φ-Rough Sets Theory and Its Usage on Mining Approximate Dependencies

Authors:
Yiyong Xiao;Ikou Kaku;Wenbing Chang
Affiliations:
Department of System Engineering of Engineering Technology, Beihang University, China;Department of Management Science and Engineering, Akita Prefectural University, Honjo, Japan 015-0055;Department of System Engineering of Engineering Technology, Beihang University, China
Venue:
ICIC '08 Proceedings of the 4th international conference on Intelligent Computing: Advanced Intelligent Computing Theories and Applications - with Aspects of Artificial Intelligence
Year:
2008

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Abstract

In this paper, we present an extension of the rough set theorybased on similarity relation, called Φ-Rough Set Theory, wherethe indiscernibility relation of the crisp rough set theory isreplaced by the notion of Φ-approximate equivalence relation.Many of the related concepts of crisp rough set theory areredefined, e.g., equivalence class, lower and upper approximations,Φ-reduction, etc. After that, we give an adequateinterpretation of approximate dependencies(ADs) and partialapproximate dependencies(PADs) from the point of view of Φ-RST,which sheds a new light on the functional dependency(FD) theories.The methodologies of Φ-Rough Set Theory are used on mining theADs and PADs, on relational or fuzzy relational schema database.Finally, a numeric example is given to illustrate the process ofmining the ADs and PADs in decision system database with similarityrelation.