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In this paper, we present an extension of the rough set theory based on similarity relation, called Φ-Rough Set Theory, where the indiscernibility relation of the crisp rough set theory is replaced by the notion of Φ-approximate equivalence relation. Many of the related concepts of crisp rough set theory are redefined, e.g., equivalence class, lower and upper approximations, Φ-reduction, etc. After that, we give an adequate interpretation of approximate dependencies(ADs) and partial approximate 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 the ADs and PADs, on relational or fuzzy relational schema database. Finally, a numeric example is given to illustrate the process of mining the ADs and PADs in decision system database with similarity relation. [ABSTRACT FROM AUTHOR]