Transactions on Rough Sets IX

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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Transactions on

Rough Sets IX James F. Peters · Andrzej Skowron Editors-in-Chief

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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, UK Takeo Kanade Carnegie Mellon University, Pittsburgh, PA, USA Josef Kittler University of Surrey, Guildford, UK Jon M. Kleinberg Cornell University, Ithaca, NY, USA Alfred Kobsa University of California, Irvine, CA, 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 University of Dortmund, Germany Madhu Sudan Massachusetts Institute of Technology, MA, USA Demetri Terzopoulos University of California, Los Angeles, CA, USA Doug Tygar University of California, Berkeley, CA, USA Gerhard Weikum Max-Planck Institute of Computer Science, Saarbruecken, Germany

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James F. Peters Andrzej Skowron Henryk Rybi´nski (Eds.)

Transactions on Rough Sets IX

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Volume Editors James F. Peters University of Manitoba Department of Electrical and Computer Engineering Winnipeg, Manitoba, R3T 5V6, Canada E-mail: [email protected] Andrzej Skowron Warsaw University Institute of Mathematics Banacha 2, 02-097, Warsaw, Poland E-mail: [email protected] Henryk Rybi´nski Warsaw University of Technology Institute of Computer Science Nowowiejska 15/19, 00-665 Warsaw, Poland E-mail: [email protected]

Library of Congress Control Number: 2008942076 CR Subject Classification (1998): F.4.3, I.5, H.2.8, I.2, G.2 LNCS Sublibrary: SL 1 – Theoretical Computer Science and General Issues ISSN ISSN ISBN-10 ISBN-13

0302-9743 (Lecture Notes in Computer Science) 1861-2059 (Transaction on Rough Sets) 3-540-89875-1 Springer Berlin Heidelberg New York 978-3-540-89875-7 Springer Berlin Heidelberg New York

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 its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. springer.com © Springer-Verlag Berlin Heidelberg 2008 Printed in Germany Typesetting: Camera-ready by author, data conversion by Scientific Publishing Services, Chennai, India Printed on acid-free paper SPIN: 12586622 06/3180 543210

Preface

Volume IX of the Transactions on Rough Sets (TRS) provides evidence of the continuing growth of a number of research streams that were either directly or indirectly begun by the seminal work on rough sets by Zd