Transactions on Rough Sets V

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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 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 Moshe Y. Vardi Rice University, Houston, TX, USA Gerhard Weikum Max-Planck Institute of Computer Science, Saarbruecken, Germany

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James F. Peters Andrzej Skowron (Eds.)

Transactions on Rough Sets V

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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]

Library of Congress Control Number: 2006933430 CR Subject Classification (1998): F.4.1, F.1, I.2, H.2.8, I.5.1, I.4 LNCS Sublibrary: SL 1 – Theoretical Computer Science and General Issues ISSN ISBN-10 ISBN-13

1861-2059 3-540-39382-X Springer Berlin Heidelberg New York 978-3-540-39382-5 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 is a part of Springer Science+Business Media springer.com © Springer-Verlag Berlin Heidelberg 2006 Printed in Germany Typesetting: Camera-ready by author, data conversion by Scientific Publishing Services, Chennai, India Printed on acid-free paper SPIN: 11847465 06/3142 543210

Preface

Volume V of the Transactions on Rough Sets (TRS) is dedicated to the monumental life and work of Zdzislaw Pawlak1. During the past 35 years, since the introduction of knowledge description systems in the 1970s, the theory and applications of rough sets have grown rapidly. This volume continues the tradition begun with earlier volumes of the TRS series and introduces a number of new advances in the foundations and application of rough sets. These advances have profound implications in a number of research areas such as adaptive learning, approximate reasoning and belief systems, approximation spaces, Boolean reasoning, classification methods, c