Structure-Based Attribute Reduction: A Rough Set Approach - Feature Selection for Data and Pattern Recognition - page 108

Chapter 7
Structure-Based Attribute
Reduction: A Rough Set Approach

Yoshifumi Kusunoki and Masahiro Inuiguchi

Abstract We provide an introduction to a rough set approach to attribute
reduction. Analyzed data sets consist of objects which are described by attributes and
partitioned into decision classes. Rough set theory deals with uncertainty decision
classes with respect to attributes by approximating them to precise sets. The aim of
attribute reduction is to remove redundant attributes as well as find important ones
for classification. Several types of attribute reduction have been proposed especially
according to preserving structures of approximated decision classes. We introduce
definitions and theoretical results about structures-based attribute reduction.

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Keywords Rough set model Reduct Boolean function Structure-based reduct

7.1 Introduction

We provide an introduction to attribute reduction or feature selection based on rough
set theory [ 35 , 36 , 39 ]. Rough set theory approaches uncertainty or inconsistency
of membership for sets due to incomplete or granular information. In a rough set
approach for data analysis, data sets are usually given by decision tables which consist
of objects (items) described by attributes. Moreover, each object in decision tables is
classified into decision classes. Because of incompleteness of given attributes, some
objects are indiscernible to each other by the attributes, and that causes uncertainty
of decision classes. Such an uncertain decision class is approximated by two precise
sets, called lower and upper approximations. The difference of the upper and lower
approximations is called a boundary.