SQLf

SQLf is a SQL extended with fuzzy set theory application for expressing flexible (fuzzy) queries to Regular Relational Databases. Between the known extensions proposed to SQL, at the present time, this is the most complete, because it allows the use of diverse fuzzy elements in all the constructions of the language SQL.^[1][2]

SQLf is the only known proposal of flexible query system allowing linguistic quantification over set of rows in queries throw the extension of SQL nesting and partitioning structures with fuzzy quantifiers. It also allows the use of quantifiers to qualify the quantity of search criteria satisfied by single rows. For query evaluation, they have intended several mechanisms.^[3] The more important is the one based on the derivation principle ^[4] that consists in deriving classic queries that produce, given a threshold t, the t-cut of the result of the fuzzy query, so that the additional processing cost of using a fuzzy language is diminished.

Basic block

The fundamental querying structure of SQLf is the multi-relational block. The conception of this structure is based on the three basic operations of the Relational Algebra: Projection, Cartesian Product and Selection, and the application of fuzzy sets’ concepts. The result of a SQLf query is a fuzzy set of rows that is a fuzzy relation instead of a regular relation. A basic block in SQLf consists of a SELECT clause, a FROM clause and a WHERE clause, that is optional. The semantic of this query structure is:

The SELECT clause corresponds to the projection. It specifies the relations’ attributes (or attribute expressions) that will be selected. The resulting table is a fuzzy set and the resulting table is in decreasing ordered of satisfaction degree. For shake of simplicity in presentation of query semantic we will assume, without loss of generality, single attribute in SELECT clause.

The SELECT clause specifies also a calibration that is intended to restrict the set of rows retrieved. There are two kinds of calibrations: the quantitative and the qualitative. In quantitative calibration the user specifies the number of answer to be retrieved. The query is intended to retrieve the rows with highest membership degrees up to the number of required answers. In qualitative calibration the user specifies a minim level of satisfaction that must have any retrieved row.

The FROM clause corresponds to the Cartesian Product. The consult is made on the Cartesian Product of the relations that are specified in this clause. For shake of simplicity in presentation of query semantic we will assume, without loss of generality, single relation FROM clause.

The WHERE clause corresponds to the selection. It specifies the condition for which the satisfaction degree will be calculated. Rows that do not satisfy at all the condition are rejected. This condition is a fuzzy predicate that may involve any attribute of the relations.

The following is an example of a SELECT query that returns a list of hotels that are cheap. The query retrieves all rows from the Hotels table that satisfice the fuzzy predicate cheap defined by the fuzzy set μ=(∞, ∞, 25, 30). The result is sorted in descending order by the membership degree of the query. The asterisk (*) in the select list indicates that all columns of the Hotels table should be included in the result set.

SELECT *
 FROM  Hotels
 WHERE price = cheap;

References