Abstract
Functional dependency is the basis of database normalization. Various types of fuzzy functional dependencies have been proposed for fuzzy relational database and applied to the process of database normalization. However, the problem of achieving lossless join decomposition occurs when employing the fuzzy functional dependencies to database normalization in an extended possibility-based fuzzy data models. To resolve the problem, this study defined fuzzy functional dependency based on a notion of approximate equality for extended possibility-based fuzzy relational databases. Examples show that the notion is more applicable than other similarity concept to the research related to the extended possibility-based data model. We provide a decomposition method of using the proposed fuzzy functional dependency for database normalization and prove the lossless join property of the decomposition method.
Highlights
Database normalization plays a crucial role in the design theory of relational database to avoid insertion and deletion and update anomalies in a database
The contribution of this work is threefold. It highlights the problem of relation decomposition when tuple elimination is order sensitive. It proposes the notion of approximate equality for the tuples or relations in the fuzzy databases and provides the measure of the approximate equality
It proposes approximate lossless join decomposition for the fuzzy databases and defines two operations projection and equal join for the decomposition, all of which are based on the approximate equality
Summary
Database normalization plays a crucial role in the design theory of relational database to avoid insertion and deletion and update anomalies in a database. Applying the similarity-based FFDs on relation decomposition prompts the difficulty for lossless join decomposition on two facets: (i) redundancy removal: how to eliminate redundant tuples that are not identical from the Journal of Applied Mathematics decomposed results so that the results can be, later on, used to produce the original relation without losing information and (ii) tuple merging: how to combine two relations via merging their tuples of which attribute values are similar but not identical Complicating this problem further, most similarity measures [7, 13, 14] of values in the form of possibility distribution are not transitive. This study first proposes a notion of approximate equality which represents the transitive equivalent relation among tuples It provides new definition of FFD and lossless join decomposition based on approximate equality for the fuzzy databases.
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