17-01-2013, 02:42 PM
Fuzzy Functional Dependency and its Application to Approximate Data Querying
1Fuzzy Functional.pdf (Size: 635.82 KB / Downloads: 20)
Abstract
In this paper, we review a new definition of fuzzy
functional dependency based on conditional probability
and its application to approximate data reduction related
to operation of projection in classical relational
database in order to construct fuzzy integrity constraints
[l]. We introduce the concept of partial fuzzy
functional dependency which expresses the fact that a
given attribute X does not determine Y completely, but
in the partial area of X , it might determine Y. Finally,
we discuss another application of fuzzy functional dependency
an constructing fuzzy query relation for data
querying and approximate join of two or more fuzzy
query relations in the framework of extended query system.
Introduction
The motivation of our work stems from the need to
be able to process and represent imprecise and partially
known (incomplete) information. In our work, we have
constructed and defined a new definition of fuzzy functional
dependency(FFD) where relation between two
attribute domains is based on conditional probability
relation. From the technical point of view, we realized
that this FFD is different from most FFDs [2-71 which
generally started with the definition of classical functional
dependency and weaken the equality relation
into a (gradual) resemblance relation (and then chose
an appropriate implication) [lo]. We also proved that
inference rules (Reflexivity, Augmentation and Transitivity)
which are similar to Armstrong’s Axioms [9]
for the FFD, are both sound and complete. In the
connection with project operator of classical relational
database.
Approximate Data Reduction and
Project ion
In general, based on the type of data value, dornain
attributes can be divided into two categories. Firstly,
domain attributes where their data value can be expressed
in fuzzy sets called fuzzy set domain, i.e.,Age,
Salary, Price, Grade, etc. Secondly, domain attributes
where their data value are crisp data called crisp domain,
i.e., Name, City, etc.
In order to provide relation among appropriate fuzzy
labels, in this section, we provide approximate data reduction
and projection of a given R relation, especially
for its fuzzy set domains. The projection of the relation
R of R(XYZ) over the set of attributes X is obtained
by taking the restriction of the tuples of R to the attributes
in X and eliminating duplicate tuples in what
remains(Raju, Majumdar, 1988 [SI).
Partial FFD
In this section, we introduce partial FFD as one
property which has never been considered before in
classical functional dependency. The fact tells us that
in the real-world data, it might be found that a given
domain attribute X does not determine a given domain
attribute Y completely, but in the partial area of X ,
it might determine Y. i.e., relation between studentname
and ID-number where in general student-name
can not be used to determine ID-number, but it might
happen that there are some unique student names in
the possible values of student-names which can be used
to determine ID-number.
In order to transform the classical relational
database into the fuzzy relational database which is
defined by Buckles and Petry [8], it is necessary to
process every crisp data values in the classical relation
and associate it with a fuzzy membership value of each
partition (this process has been discussed clearly in the
last section). Every partition represents a partial area
of domain attribute which is expressed by a meaningful
fuzzy set. Sometimes, we need to know relation or
partial FFD between two fuzzy sets, as representatives
of two partial areas of two different attributes, that
express which one is stronger or as a determiner.
Conclusion
Our new definition of fuzzy functional dependency(
FFD) based on the concept of conditional probability
and its application of approximate data reduction
[l] were briefly recalled in this paper. Partial FFD
which has never been considered before in the classical
functional dependency was introduced in order to
represent the fact of real-world application. Furthermore,
application of data querying and approximate
join of fuzzy query relations in the framework of extended
query system were also discussed in this paper.
It should be mentioned that this work is not complete
in terms of capturing the capabilities of fuzzy
relational database. However in future work, we need
to consider other properties and applications such as
normalization, fuzzy data mining, and other types of
integrity constraints (e.g. MVDs [ll],JD [12]).