LNCS 10020 Journal Subline Transactions on Rough Sets XX James F Peters · Andrzej Skowron Editors-in-Chief 123 Lecture Notes in Computer Science Commenced Publication in 1973 Founding and Former Series Editors: Gerhard Goos, Juris Hartmanis, and Jan van Leeuwen Editorial Board David Hutchison Lancaster University, Lancaster, UK Takeo Kanade Carnegie Mellon University, Pittsburgh, PA, USA Josef Kittler University of Surrey, Guildford, UK Jon M Kleinberg Cornell University, Ithaca, NY, USA Friedemann Mattern ETH Zurich, Zurich, Switzerland John C Mitchell Stanford University, Stanford, CA, USA Moni Naor Weizmann Institute of Science, Rehovot, Israel C Pandu Rangan Indian Institute of Technology, Madras, India Bernhard Steffen TU Dortmund University, Dortmund, Germany Demetri Terzopoulos University of California, Los Angeles, CA, USA Doug Tygar University of California, Berkeley, CA, USA Gerhard Weikum Max Planck Institute for Informatics, Saarbrücken, Germany 10020 More information about this series at http://www.springer.com/series/7151 James F Peters Andrzej Skowron (Eds.) • Transactions on Rough Sets XX 123 Editors-in-Chief James F Peters University of Manitoba Winnipeg, MB Canada Andrzej Skowron University of Warsaw Warsaw Poland ISSN 0302-9743 ISSN 1611-3349 (electronic) Lecture Notes in Computer Science ISSN 1861-2059 ISSN 1861-2067 (electronic) Transactions on Rough Sets ISBN 978-3-662-53610-0 ISBN 978-3-662-53611-7 (eBook) DOI 10.1007/978-3-662-53611-7 Library of Congress Control Number: 2016954935 © Springer-Verlag GmbH Germany 2016 This work is subject to copyright All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed The use of general descriptive names, registered names, trademarks, service marks, etc in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer-Verlag GmbH Germany The registered company address is: Heidelberger Platz 3, 14197 Berlin, Germany Preface Volume XX of the Transactions on Rough Sets (TRS) is a continuation of a number of research streams that have grown out of the seminal work of Zdzisław Pawlak1 during the first decade of the twenty-first century The paper co-authored by Javad Rahimipour Anaraki, Saeed Samet, Wolfgang Banzhaf, and Mahdi Eftekhari introduces a new hybrid merit based on a conjunction of correlation feature selection and fuzzy-rough feature selection methods The new merit selects fewer redundant features and finds the most relevant features resulting in reasonable 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 semantics of proto-transitive rough sets Proto-transitivity, according to the author, 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 of pointless topology The monograph authored by Mohammad Aquil Khan is devoted 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, Christine Reiss, and the LNCS staff at Springer for their support in making this volume of TRS possible The Editors-in-Chief were supported by the Polish National Science Centre (NCN) grants DEC-2012/05/B/ST6/06981 and DEC-2013/09/B/ST6/01568, the Polish 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 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 foundations and applications of rough sets Topics include foundations and applications of rough sets as well as foundations and applications of hybrid methods combining rough sets with other approaches important for the development of intelligent systems The journal includes high-quality research articles accepted for publication on the basis 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 revised versions of selected papers from conferences can also be included in regular or 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 Jan Bazan Gianpiero Cattaneo Mihir K Chakraborty Davide Ciucci Chris Cornelis Ivo Düntsch Anna Gomolińska Salvatore Greco Jerzy W Grzymała-Busse Masahiro Inuiguchi Jouni Järvinen Richard Jensen Bożena Kostek Churn-Jung Liau Pawan Lingras Victor Marek Mikhail Moshkov Hung Son Nguyen Ewa Orłowska Sankar K Pal Lech Polkowski Henri Prade Sheela Ramanna Roman Słowiński Jerzy Stefanowski Jarosław Stepaniuk Zbigniew Suraj Marcin Szczuka Dominik Ślȩzak Roman Świniarski Shusaku Tsumoto Guoyin Wang Marcin Wolski Wei-Zhi Wu Yiyu Yao Ning Zhong Wojciech Ziarko Contents A New Fuzzy-Rough Hybrid Merit to Feature Selection 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 Mohammad Azad, Mikhail Moshkov, and Beata Zielosko Algebraic Semantics of Proto-Transitive Rough Sets A Mani 24 51 Covering Rough Sets and Formal Topology – A Uniform Approach Through Intensional and Extensional Constructors Piero Pagliani 109 Multiple-Source Approximation Systems, Evolving Information Systems and Corresponding Logics: A Study in Rough Set Theory Md Aquil Khan 146 Author Index 321 A New Fuzzy-Rough Hybrid Merit to Feature Selection Javad Rahimipour Anaraki1(B) , Saeed Samet2 , Wolfgang Banzhaf3 , and Mahdi Eftekhari4 Department of Computer Science, Memorial University of Newfoundland, St John’s, Nl A1B 3X5, Canada jra066@mun.ca Faculty of Medicine, Memorial University of Newfoundland, St John’s, Nl A1B 3V6, Canada saeed.samet@med.mun.ca Department of Computer Science, Memorial University of Newfoundland, St John’s, Nl A1B 3X5, Canada banzhaf@mun.ca Department of Computer Engineering, Shahid Bahonar University of Kerman, 7616914111 Kerman, Iran m.eftekhari@uk.ac.ir Abstract Feature selecting is considered as one of the most important pre-process methods in machine learning, data mining and bioinformatics 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 testing times, leading to overall performance improvement, especially when dealing with large datasets Correlation feature selection method uses a conventional merit to evaluate different feature subsets In this paper, we propose a new merit by adapting and employing of correlation feature selection in conjunction with fuzzy-rough feature selection, to improve the effectiveness and quality of the conventional methods It also outperforms the newly introduced gradient boosted feature selection, by selecting more relevant and less redundant features The two-step experimental results show the applicability and efficiency of our proposed method over some well known and mostly used datasets, as well as newly introduced ones, especially from the UCI collection with various sizes from small to large numbers of features and samples Keywords: Feature selection Correlation merit · Fuzzy-rough dependency degree · 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 c Springer-Verlag GmbH Germany 2016 J.F Peters and A Skowron (Eds.): TRS XX, LNCS 10020, pp 1–23, 2016 DOI: 10.1007/978-3-662-53611-7 J.R Anaraki et al comprehensibility challenges inherent in big datasets Machine learning methods 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 sample gathering and their undoubted utility, such as in bioinformatics and health systems, data owners usually prefer to keep only the useful and informative features and remove the rest, by applying Feature Selection (FS) techniques that are usually considered as a preprocessing step to further processing (such as classification) These methods lead to less classification errors or at least to minimal 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 identical 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 approach 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 approach of both methods called embedded has been proposed to accurately handle big datasets [4] In the methods based on this approach, feature subset selection 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 a merit based on the average intra-correlation of features and inter-correlation of features and the outcome Those features with higher correlation to the outcome 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 Multiple-Source Approximation Systems, Evolving Information Systems 317 45 Khan, M.A., Banerjee, M.: Formal reasoning with rough sets in multiple-source approximation systems Int J Approx Reason 49(2), 466–477 (2008) 46 Khan, M.A., Banerjee, M.: Multiple-source approximation systems: membership functions and indiscernibility In: Wang, G., Li, T., Grzymala-Busse, J.W., Miao, D., Skowron, A., Yao, Y (eds.) 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RSFDGrC 1999 LNCS (LNAI), vol 1711, pp 285–293 Springer, Heidelberg (1999) 111 Ziarko, W.: Variable precision rough set model J Comput Syst Sci 46, 39–59 (1993) Author Index Anaraki, Javad Rahimipour Azad, Mohammad 24 Banzhaf, Wolfgang 1 Mani, A 51 Moshkov, Mikhail Pagliani, Piero 109 Eftekhari, Mahdi Samet, Saeed Khan, Md Aquil 146 Zielosko, Beata 24 24 ... Andrzej Skowron 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... 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. .. 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 foundations