Abstract
The topic presented in this chapter refers to qualifying objects in some kinds of vague queries sent to relational databases. We want to compute a fulfillment degree in order to measure the quality of objects when we search them in databases. After a discussion on various kinds of object linguistic qualification, with different kinds of fuzzy conditions in a fuzzy query, a new particular situation is proposed to be included in this subject: the relative object qualification as a query selection criterion, that is, queries with two conditions in which the first one depends on the results of the second one. It is another way to express the user’s preferences in a flexible query. In connection with this, a new fuzzy aggregation operator, AMONG, is defined. We also propose an algorithm to evaluate this kind of queries and some definitions to make it applicable and efficient (dynamic modeling of the linguistic values and unified model of the context). We demonstrate these ideas with software already implemented in our lab.
Key Terms in this Chapter
Multiqualification: Including more gradual properties in a query selection criterion. They are independent of each other and they have the same significance for the user’s preferences. The fulfillment degree is computed accordingly to the fuzzy sets describing the meaning of the linguistic qualifiers and to the conjunctive aggregation operator, as model of the connective AND.
Unified Model of the Context: Modeling the context in a uniform style, as a single database, i.e. incorporating the fuzzy model of the linguistic terms or their description, in the target database.
Relative Object Qualification: Two gradual properties, as fuzzy conditions, are combined in a complex selection criterion, such that one of them is applied on a subset of database rows, already selected by the other one; dynamic definition of the linguistic value, corresponding to the secondly evaluated condition, is needed. The fulfillment degree is computed accordingly to the fuzzy sets describing the meaning of the linguistic qualifiers and to the AMONG aggregation operator.
Static Model of the Context: Including in the database the static definitions of the linguistic terms (their fuzzy models) established apriori, before the querying process.
AMONG Operator: Fuzzy aggregation operator used for evaluation of a query selection criterion based on a relative qualification. The algebraic model of the AMONG operator is: µ?AMONGS: R ? [0,1], µ?AMONGS (t) = min (µ? (), µS (t.A2)),where R is a relation, A1 and A2 are two attributes of the R relation, A1 is defined on the interval [a1,b1], t is a tuple, ? and S are two gradual properties corresponding to the attributes A1 and A2,µ? and µS are the membership functions defining the ? and S gradual properties, [a1’, b1’] ? [a1,b1] is the sub-interval of the A1 corresponding to the table QS (R) (obtained by the first selection, on the attribute A2, using property S).
Absolute Object Qualification: Including one gradual property (simple qualification) or a conjunction of gradual properties (multiqualification) in a query selection criterion. The fulfillment degree is computed accordingly to the fuzzy sets describing the meaning of the linguistic qualifiers. A conjunctive aggregation operator is used to model the connective AND (in the case of multi-qualification).
Dynamic Model of the Context: Including in the database only the data necessary to dynamically define the linguistic terms, at the moment of (or during) the querying process.
Context for Fuzzy Querying Interface: The pair: target database and the knowledge base (containing the fuzzy model of the linguistic terms) corresponding to it.
Dynamic Model of the Linguistic Value: Automatic discovering of the linguistic values definitions from the actual content of the database. Appropriate algorithms can be implemented, based on a great advantage: by directly connecting to the database, one can easily obtain details regarding effective attribute domain limits, or distributions of the values. This procedure is generally useful, instead an off-line process of knowledge acquisition from a human expert; but it is mandatory in the relative qualification case.