11-05-2012, 02:27 PM
Rough set theory and its applications
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Introduction
Rough set theory can be regarded as a new mathematical
tool for imperfect data analysis. The theory has found
applications in many domains, such as decision support,
engineering, environment, banking, medicine and others.
This paper presents basis of the theory which will be illustrated
by a simple example of churn modeling in telecommunications.
Rough set philosophy is founded on the assumption that
with every object of the universe of discourse some information
(data, knowledge) is associated. Objects characterized
by the same information are indiscernible (similar)
in view of the available information about them. The in-
discernibility relation generated in this way is the mathematical
basis of rough set theory. Any set of all indiscernible
(similar) objects is called an elementary set, and
forms a basic granule (atom) of knowledge about the universe.
Any union of some elementary sets is referred to as
a crisp (precise) set – otherwise the set is rough (impre-
cise, vague).
Illustrative example
Let us start our considerations from a very simple tutorial
example concerning churn modeling in telecommunications,
which is a simplified version of an example given
in [1]. In Table 1, six facts concerning six client segments
are presented.
In the table condition attributes describing client profile are:
In – incoming calls, Out – outgoing calls within the same
operator, Change – outgoing calls to other mobile operator,
the decision attribute describing the consequence is Churn
and N is the number of similar cases.
Decision tables and decision rules
If we distinguish in an information system two disjoint
classes of attributes, called condition and decision at-
tributes, respectively, then the system will be called a de-
cision table and will be denoted by S = (U;C;D), where C
and D are disjoint sets of condition and decision attributes,
respectively.
Summary
In this paper the basic concepts of rough set theory and its
application to drawing conclusions from data are discussed.
For the sake of illustration an example of churn modeling
in telecommunications is presented.