Graduality and Databases: Some Contributions of Fuzzy Sets

Current commercial database management systems (DBMSs) are based solely on Boolean conditions which are used both for data retrieval and the expression of properties (or constraints). Possible contributions of fuzzy set theory are examined along these two lines. From a retrieval point of view, usual DBMSs do not allow for expressing preferences at the level of elementary conditions (over the acceptable values) and/or between the various conditions, and then to obtain discriminated answers. The concept of flexible (or gradual) query aims at compensating for this type of limitation. The characteristics of two query languages supporting flexible queries are presented. As to integrity constraints (ICs), one of the major roles of a DBMS is to guarantee that any visible state of the database agrees with the ICs that are declared. Among ICs are functional dependencies (FDs) which play a key role in capturing some forms of redundancy in the data. Regular FDs are extended by relaxing the strict equality, which enables to capture a new type of constraint interpreted as a gradual rule whose antecedent and consequent parts are fuzzy components.