Abstract
The idea of extending the usual Boolean queries with preferences has become a hot topic in the database community. One of the advantages of this approach is to deliver discriminated answers rather than flat sets of elements. Fuzzy sets are a natural means to represent preferences, and many works have been undertaken to define queries where fuzzy predicates can be introduced inside user queries. The objective of this chapter is to illustrate the expressiveness of fuzzy sets with the division operator in the context of regular databases. Like other operators, the regular division is not flexible at all and small variations in the data may lead to totally different results. To counter this behavior, a variety of extended division operators founded on fuzzy sets are suggested. All of them obey a double requirement: to have a clear meaning from a user point of view and to deliver a resulting relation which is a quotient.
Key Terms in this Chapter
Relational Division: Binary operation whose arguments are relations with a common attribute which delivers a result having the property of a quotient.
Fuzzy Querying: Fuzzy set-based querying approach where each element of the result is assigned a degree of satisfaction valued in the unit interval [0, 1].
Regular Relational Database: Database where information is precise and modeled in a relational way
Fuzzy Relation: Relation whose members have a grade of membership expressing the extent to which they comply with the concept conveyed by the relation.
Proximity Relation: Binary relation expressing the extent to which two values are approximately equal.
Approximate Division: Extended version of the division where some idea of tolerance is introduced.
Fuzzy Implication: Operator generalizing the usual material implication, whose arguments and result are valued in the unit interval [0, 1].
Flexible Querying: Approach where users include preferences in their queries so as to get a result made of discriminated elements.