The information entropy of rough relational databases

Authors:
Yuefei Sui;Youming Xia;Ju Wang
Affiliations:
Key Laboratory of Intelligent Information Processing, Institute of Computing Technology, Chinese Academy of Sciences, Beijing, China;Department of Computer Science, Yunnan Normal University, Kunming, China;Institute of Software, Chinese Academy of Sciences, Beijing, China
Venue:
RSFDGrC'03 Proceedings of the 9th international conference on Rough sets, fuzzy sets, data mining, and granular computing
Year:
2003

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Abstract

Beaubouef, Petry and Buckles proposed the generalized rough set database analysis (GRSDA) to discuss rough relational databases. Given any rough relational database (U, A) and an attribute a ∈ A, as in rough set theory, a definition of the lower and upper approximations based on φa is given. The entropy and conditional entropy of similarity relations in a rough relational database are defined. The examples show that the entropy of a similarity relation does not decrease as the similarity relation is refined. It will be proved that given any two similarity relations φ and ψ, defined by a set C of conditional attributes and a decision attribute d, respectively, if d similarly depends on C in a rough relational database then the conditional entropy of φ with respect to ψ is equal to the entropy of φ.