Fuzzy Functional Dependency and a Series of Design Issues of Fuzzy Relational Databases

Abstract

Fuzzy functional dependencies (FFDs) reflect a kind of semantic knowledge about the real world and are considered as integrity constraints of fuzzy database models. This paper first reviews various efforts made on fuzzy extensions of classical databases with respect to different frameworks of fuzzy data representation. Primary attention is then paid to a series of fundamental issues towards building a theory of fuzzy relational database design. A general overview is provided to show our attempts that have been made to tackle these issues. These issues include FFD inference rules, the soundness and completeness of the FFD axiomatic system, the equivalence of FFD sets, lossless-join and dependency-preservation decompositions, θ-keys, and fuzzy normal forms. The elimination or reduction of data redundancy and update anomalies is the main concern of database design. A proper settlement of these issues enables us to tell what a “good” design is and how it can be obtained.Keywordsfuzzy relational databasescloseness relationsfuzzy functional dependency (FFD)FFD transitive closureArmstrong axiomsrelation scheme decompositionfuzzy normal forms