Transactions on Rough Sets XV

The LNCS journal Transactions on Rough Sets is devoted to the entire spectrum of rough sets related issues, from logical and mathematical foundations, through all aspects of rough set theory and its applications, such as data mining, knowledge discovery,

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Editorial Board David Hutchison Lancaster University, 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, Switzerland John C. Mitchell Stanford University, CA, USA Moni Naor Weizmann Institute of Science, Rehovot, Israel Oscar Nierstrasz University of Bern, Switzerland C. Pandu Rangan Indian Institute of Technology, Madras, India Bernhard Steffen TU Dortmund University, Germany Madhu Sudan Microsoft Research, Cambridge, MA, USA Demetri Terzopoulos University of California, Los Angeles, CA, USA Doug Tygar University of California, Berkeley, CA, USA Moshe Y. Vardi Rice University, Houston, TX, USA Gerhard Weikum Max Planck Institute for Informatics, Saarbruecken, Germany

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James F. Peters Andrzej Skowron (Eds.)

Transactions on Rough Sets XV

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Volume Editors James F. Peters University of Manitoba, Winnipeg, MB, Canada E-mail: [email protected] Andrzej Skowron University of Warsaw, Poland E-mail: [email protected]

ISSN 0302-9743 (LNCS) e-ISSN 1611-3349 (LNCS) e-ISSN 1861-2067 (TRS) ISSN 1861-2059 (TRS) ISBN 978-3-642-31902-0 e-ISBN 978-3-642-31903-7 DOI 10.1007/978-3-642-31903-7 Springer Heidelberg Dordrecht London New York CR Subject Classification (1998): I.5.1-3, I.2.4, I.2.6, I.2, F.4.1, G.1.2, I.4, H.3

© Springer-Verlag Berlin Heidelberg 2012 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in ist current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, 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. Typesetting: Camera-ready by author, data conversion by Scientific Publishing Services, Chennai, India Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)

Preface

Volume XV of the Transactions on Rough Sets (TRSXV) offers a number research streams that have grown out of the seminal work by Zdzislaw Pawlak1 during the first decade of the twenty-first century. These research streams include work on a promising rough set approach in machine learning by A. Janusz, the introduction of multi-valued near set theory by M.E. Abd El-Monsef, H.M. Abu-Donia and E.A. Marei, the advent of a complete system that supports a rough-near set approach to digital image analysis by C.J. Henry, and an exhaustive study of the mathematics of vagueness