An extended Boyce-Codd normal form in fuzzy relational databases

If the relation schemes of any fuzzy database are not properly designed certain anomaly problems may occur when the fuzzy database is updated or maintained. This is because some undesired relationships exist among attributes. Based on the notions of fuzzy functional dependency (FFD) and θ-keys, the Boyce-Codd normal form is extended to cope with the anomaly problems caused by partial and transitive FFDs of θ-prime on some θ-keys, thus resulting in θ-fuzzy Boyce-Codd normal form (θ-FBCNF). Furthermore, the relationship between θ-FBCNF and other existing fuzzy normal forms is analyzed, showing that θ-FBCNF reflects the strongest restriction for attributes. Finally an algorithm is provided that can decompose, in a lossless-join manner, any scheme into a number of θ-FBCNF schemes