Transactions on Rough Sets XX

329 Pages·2016·4.75 MB·English

by  James F. Peters

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James F. Peters · Andrzej Skowron
Editors-in-Chief
123
Lecture Notes in Computer Science 10020
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James F. Peters Andrzej Skowron (Eds.)
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Transactions on
Rough Sets XX
123
Editors-in-Chief
James F.Peters Andrzej Skowron
University of Manitoba University of Warsaw
Winnipeg, MB Warsaw
Canada Poland
ISSN 0302-9743 ISSN 1611-3349 (electronic)
Lecture Notesin Computer Science
ISSN 1861-2059 ISSN 1861-2067(electronic)
Transactions onRough Sets
ISBN 978-3-662-53610-0 ISBN978-3-662-53611-7 (eBook)
DOI 10.1007/978-3-662-53611-7
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Preface
VolumeXXoftheTransactionsonRoughSets(TRS)isacontinuationofanumberof
researchstreamsthathavegrownoutoftheseminalworkofZdzisławPawlak1during
the first decade of the twenty-first century.
The paper co-authored by Javad Rahimipour Anaraki, Saeed Samet, Wolfgang
Banzhaf,andMahdiEftekhariintroducesanewhybridmeritbasedonaconjunctionof
correlationfeatureselectionandfuzzy-roughfeatureselectionmethods.Thenewmerit
selects fewer redundant features and finds the most relevant features resulting in rea-
sonable classification accuracy. The paper co-authored by Mohammad Azad, Mikhail
Moshkov, and Beata Zielosko presents a study of a greedy algorithm for construction
of approximate decision rules. This algorithm has polynomial time complexity for
binary decision tables with many-valued decisions. The proposed greedy algorithm
constructs relatively short α-decision rules. The paper by Mani presents algebraic
semanticsofproto-transitiveroughsets.Proto-transitivity,accordingtotheauthor,can
be considered as a possible generalization of transitivity that happens often in the
context of applications. The paper by Piero Pagliani presents a uniform approach to
previously introduced covering-based approximation operators from the point of view
ofpointlesstopology.ThemonographauthoredbyMohammadAquilKhanisdevoted
to the study of multiple-source approximation systems, evolving information systems,
and corresponding logics based on rough sets.
The editors would like to express their gratitude to the authors of all submitted
papers. Special thanks are due to the following reviewers: Jan Bazan, Chris Cornelis,
Davide Cuicci, Ivo Düntsch, Soma Dutta, Jouni Järvinen, Richard Jensen, Pradipta
Maji, Sheela Ramanna, Zbigniew Suraj, and Marcin Wolski.
The editors and authors of this volume extend their gratitude to Alfred Hofmann,
ChristineReiss,andtheLNCSstaffatSpringerfortheirsupportinmakingthisvolume
of TRS possible.
The Editors-in-Chief were supported by the Polish National Science Centre
(NCN)grantsDEC-2012/05/B/ST6/06981andDEC-2013/09/B/ST6/01568,thePolish
National Centre for Research and Development (NCBiR) DZP/RID-I-44/8/NCBR/
2016, as well as the Natural Sciences and Engineering Research Council of Canada
(NSERC) discovery grant 185986.
August 2016 James F. Peters
Andrzej Skowron
1 See, e.g., Pawlak, Z., A Treatise on Rough Sets, Transactions on Rough Sets IV, (2006), 1–17.
See, also, Pawlak, Z., Skowron, A.: Rudiments of rough sets, Information Sciences 177 (2007)
3–27; Pawlak, Z., Skowron, A.: Rough sets: Some extensions, Information Sciences 177 (2007)
28–40; Pawlak, Z., Skowron, A.: Rough sets and Boolean reasoning, Information Sciences 177
(2007) 41–73.
LNCS Transactions on Rough Sets
The Transactions on Rough Sets series has as its principal aim the fostering of
professional exchanges between scientists and practitioners who are interested in the
foundationsandapplicationsofroughsets.Topicsincludefoundationsandapplications
of rough sets as well as foundations and applications of hybrid methods combining
roughsetswithotherapproachesimportantforthedevelopmentofintelligentsystems.
Thejournalincludeshigh-qualityresearcharticlesacceptedforpublicationonthebasis
of thorough peer reviews. Dissertations and monographs of up to 250 pages that
include new research results can also be considered as regular papers. Extended and
revisedversionsofselectedpapersfromconferencescanalsobeincludedinregularor
special issues of the journal.
Editors-in-Chief: James F. Peters, Andrzej Skowron
Managing Editor: Sheela Ramanna
Technical Editor: Marcin Szczuka
Editorial Board
Mohua Banerjee Ewa Orłowska
Jan Bazan Sankar K. Pal
Gianpiero Cattaneo Lech Polkowski
Mihir K. Chakraborty Henri Prade
Davide Ciucci Sheela Ramanna
Chris Cornelis Roman Słowiński
Ivo Düntsch Jerzy Stefanowski
Anna Gomolińska Jarosław Stepaniuk
Salvatore Greco Zbigniew Suraj
Jerzy W. Grzymała-Busse Marcin Szczuka
Masahiro Inuiguchi Dominik Ślȩzak
Jouni Järvinen Roman Świniarski
Richard Jensen Shusaku Tsumoto
Bożena Kostek Guoyin Wang
Churn-Jung Liau Marcin Wolski
Pawan Lingras Wei-Zhi Wu
Victor Marek Yiyu Yao
Mikhail Moshkov Ning Zhong
Hung Son Nguyen Wojciech Ziarko
Contents
A New Fuzzy-Rough Hybrid Merit to Feature Selection . . . . . . . . . . . . . . . 1
Javad Rahimipour Anaraki, Saeed Samet, Wolfgang Banzhaf,
and Mahdi Eftekhari
Greedy Algorithm for the Construction of Approximate Decision Rules
for Decision Tables with Many-Valued Decisions. . . . . . . . . . . . . . . . . . . . 24
Mohammad Azad, Mikhail Moshkov, and Beata Zielosko
Algebraic Semantics of Proto-Transitive Rough Sets . . . . . . . . . . . . . . . . . . 51
A. Mani
Covering Rough Sets and Formal Topology – A Uniform Approach
Through Intensional and Extensional Constructors. . . . . . . . . . . . . . . . . . . . 109
Piero Pagliani
Multiple-Source Approximation Systems, Evolving Information Systems
and Corresponding Logics: A Study in Rough Set Theory . . . . . . . . . . . . . . 146
Md. Aquil Khan
Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321
A New Fuzzy-Rough Hybrid Merit
to Feature Selection
B
Javad Rahimipour Anaraki1( ), Saeed Samet2, Wolfgang Banzhaf3,
and Mahdi Eftekhari4
1 Department of Computer Science, Memorial University of Newfoundland,
St. John’s, Nl A1B 3X5, Canada
[email protected]
2 Faculty of Medicine, Memorial University of Newfoundland,
St. John’s, Nl A1B 3V6, Canada
[email protected]
3 Department of Computer Science, Memorial University of Newfoundland,
St. John’s, Nl A1B 3X5, Canada
[email protected]
4 Department of Computer Engineering, Shahid Bahonar University of Kerman,
7616914111 Kerman, Iran
[email protected]
Abstract. Feature selecting is considered as one of the most impor-
tant pre-process methods in machine learning, data mining and bioin-
formatics. By applying pre-process techniques, we can defy the curse of
dimensionality by reducing computational and storage costs, facilitate
data understanding and visualization, and diminish training and test-
ing times, leading to overall performance improvement, especially when
dealing with large datasets. Correlation feature selection method uses a
conventionalmerittoevaluatedifferentfeaturesubsets.Inthispaper,we
propose a new merit by adapting and employing of correlation feature
selection in conjunction with fuzzy-rough feature selection, to improve
theeffectivenessandqualityoftheconventionalmethods.Italsooutper-
formsthenewlyintroducedgradientboostedfeatureselection,byselect-
ingmorerelevantandlessredundantfeatures.Thetwo-stepexperimental
resultsshowtheapplicabilityandefficiencyofourproposedmethodover
some well known and mostly used datasets, as well as newly introduced
ones,especiallyfromtheUCIcollectionwithvarioussizesfromsmallto
large numbers of features and samples.
· ·
Keywords: Feature selection Fuzzy-rough dependency degree
Correlation merit
1 Introduction
Each year the amount of generated data increases dramatically. This expansion
needs to be handled to minimize the time and space complexities as well as the
(cid:2)c Springer-VerlagGmbHGermany2016
J.F.PetersandA.Skowron(Eds.):TRSXX,LNCS10020,pp.1–23,2016.
DOI:10.1007/978-3-662-53611-71
2 J.R. Anaraki et al.
comprehensibilitychallengesinherentinbigdatasets.Machinelearningmethods
tend to sacrifice some accuracy to decrease running time, and to increase the
clarity of the results [1].
Datasets may contain hundreds of thousand of samples with thousands of
features that make further processing on data a tedious job. Reduction can be
done on either features or on samples. However, due to the high cost of sam-
ple gathering and their undoubted utility, such as in bioinformatics and health
systems, data owners usually prefer to keep only the useful and informative fea-
tures and remove the rest, by applying Feature Selection (FS) techniques that
areusuallyconsideredasapreprocessingsteptofurtherprocessing(suchasclas-
sification).Thesemethodsleadtolessclassificationerrorsoratleasttominimal
diminishing of performance [2].
In terms of data usability, each dataset contains three types of features:
1- informative, 2- redundant, and 3- irrelevant. Informative features are those
that contain enough information on the classification outcome. In other words,
they are non-redundant, relevant features. Redundant features contain identi-
cal information compared to other features, whereas irrelevant features have no
information about the outcome. The ideal goal of FS methods is to remove the
last two types of features [1].
FS methods can generally be divided into two main categories [3]. One app-
roach is wrapper based, in which a learning algorithm estimates the accuracy of
the subset of features. This approach is computationally intensive and slow due
to the large number of executions over selected subsets of features, that make
it impractical for large datasets. The second approach is filter based, in which
features are selected based on their quality regardless of the results of learning
algorithm. As a result, it is fast but less accurate. Also, a combinational app-
roach of both methods called embedded has been proposed to accurately handle
big datasets [4]. Inthemethods basedonthis approach, featuresubsetselection
is done while classifier structure is being built.
One of the very first feature selection methods for binary classification
datasets is Relief [5]. This method constructs and updates a weight vector of
a feature, based on the nearest feature vector of the same and different classes
using Euclidean distance. After a predefined number of iterations l, relevant
vector is calculated by dividing the weight vector by l, and the features with
relevancy higher than a specific threshold will be selected. Hall [1] has proposed
ameritbasedontheaverageintra-correlationoffeaturesandinter-correlationof
featuresandtheoutcome.Thosefeatureswithhighercorrelationtotheoutcome
and lower correlation to other features are selected.
Jensen et al. [6] have introduced a novel feature selection method based
on lower approximation of the fuzzy-rough set, in which features and outcome
dependencies are calculated using a merit called Dependency Degree (DD). In
[7], two modifications of the fuzzy-rough feature selection have been introduced
to improve the performance of the conventional method: 1- Encompassing the
selection process in equal situations, where more than one feature result in an
identical fitness value by using correlation merit [1] and 2- Combining the first