Fuzzy Group By

On a Fuzzy Group-by Clause in SQLf
Patrick Bosc, Member, IEEE, and Olivier Pivert

Abstract— Group-by is a core database operation that is used
extensively in data analysis and decision support systems. In
many application scenarios, it appears useful to group values
according to their compliance with a certain concept instead
of founding the grouping on value equality. In this paper, wepropose a new SQLf construct that supports fuzzy-partitionbased group-by (FGB). We show that FGB can be used to
generate fuzzy summaries as well as to mine fuzzy association
rules in a practical and efficient way.

I. I NTRODUCTION
The relationships between databases and fuzzy sets have
been studied for a long time. Among the very first works is
that launched by L.A. Zadeh while supervisingV. Tahani’s
Ph.D thesis in the early 70s. The core of this study was
about the design of new querying capabilities for relational
databases. The basic idea was to use fuzzy sets in order
to devise new predicates intended for representing a graded
satisfaction instead of the “all-or-nothing” behavior conveyed
by Boolean conditions. If this type of issue was quite
innovative at that time, itturns out that it has gained more and
more acceptance for some years in the database community.
Many fuzzy querying approaches have been proposed in the
last decades, among which a fuzzy extension of the SQL
language, called SQLf [1]). This language has the same
general philosophy as SQL (as to querying features and
syntax in particular) and offers new possibilities regarding
flexiblequerying. The underlying principle was to introduce
graduality wherever it appeared meaningful (by using fuzzy
predicates in the where clause of a base block, of course, but
also by introducing fuzzy nesting operators, fuzzy quantifiers
and so on). However, the group-by clause in SQLf remained
unchanged with respect to SQL. As noted in [2], grouping
capabilities have been extensively studied andimplemented
in data management systems. The standard group-by operator
has relatively good execution time and scalability properties.
However, while its semantics is simple, it is also limited
because it is based only on equality, i.e., all the tuples
in a group have exactly the same values of the grouping
attributes. In this paper, we aim to extend this core database
operation by defining a“fuzzy grouping” mechanism. The
contributions of this paper are as follows:
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we introduce the fuzzy group-by (FGB) operator which
extends standard group-by to allow the formation of
groups based on predefined fuzzy partitions of the
attribute domains rather than equality of data,
we show how this mechanism makes it possible to
perform some kind of data summarization “on demand”,Patrick Bosc and Olivier Pivert are with IRISA–ENSSAT, Lannion,
France (email: {bosc, pivert}@irisa.fr)

we point out the interest of the FGB operator for the
purpose of fuzzy association rule mining.
The remainder of the paper is organized as follows.
Section II presents the general framework of the SQLf
language. Section III introduces the definition of the FGB
operator and shows how fuzzysummaries can be obtained by
means of appropriate aggregates applied to the fuzzy groups
that are produced by this operator. Section IV discusses
different forms that the complementary having clause can
take. Section V deals with the way FGB can be used for
mining fuzzy association rules. Section VI briefly tackles
implementation aspects. Related work is presented in Section
VII, and SectionVIII presents the conclusions and directions
for future research.
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II. R EMINDER A BOUT SQL F
The language called SQLf described in [1] extends SQL so
as to support fuzzy queries. The general principle consists in
introducing gradual predicates wherever it makes sense. The
three clauses select, from and where of the base block of SQL
are kept in SQLf and the “from” clause remains...