Discovering functional dependencies from similarity-based fuzzy relational databases

We present here a data mining technique for discovering all minimal non-trivial coarsest functional dependencies (FD) based on equivalence classes from similarity-based fuzzy relational databases. The similarity-based fuzzy data model has been recognized as most suitable for describing imprecise data that are analogical over discrete domains. Various searching techniques for discovering functional dependencies on crisp relational databases have been proposed recently. However, they have not been fully explored on the similarity-based fuzzy relational data model. In this work, we present a form of functional dependency based on equivalence classes on the similarity-based fuzzy relational database and a method to test the validity of such dependency. In addition, a data mining technique based on top-down level-wise searching is proposed. The time and space complexities of the proposed algorithm are analyzed. Experimental results showing the behaviors of these functional dependencies are discussed. The dependencies discovered contain not only the conventional functional dependencies when similarity relations are reduced to identity relations but also semantic dependencies that describe the conceptual relationships between attributes. The results developed here can be applied to fuzzy database design, query optimization and database reverse engineering.