Knowledge Representation Techniques A Rough Set Approach

The basis for the material in this book centers around a long term research project with autonomous unmanned aerial vehicle systems. One of the main research topics in the project is knowledge representation and reasoning. The focus of the research has be

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Studies in Fuzziness and Soft Computing, Volume 202 Editor-in-chief Prof. Janusz Kacprzyk Systems Research Institute Polish Academy of Sciences ul. Newelska 6 01-447 Warsaw Poland E-mail: [email protected] Further volumes of this series can be found on our homepage: springer.com Vol. 186. Radim Bˇelohlávek, Vilém Vychodil Fuzzy Equational Logic, 2005 ISBN 3-540-26254-7 Vol. 187. Zhong Li, Wolfgang A. Halang, Guanrong Chen (Eds.) Integration of Fuzzy Logic and Chaos Theory, 2006 ISBN 3-540-26899-5 Vol. 188. James J. Buckley, Leonard J. Jowers Simulating Continuous Fuzzy Systems, 2006 ISBN 3-540-28455-9 Vol. 189. Hans Bandemer Mathematics of Uncertainty, 2006 ISBN 3-540-28457-5 Vol. 190. Ying-ping Chen Extending the Scalability of Linkage Learning Genetic Algorithms, 2006 ISBN 3-540-28459-1 Vol. 191. Martin V. Butz Rule-Based Evolutionary Online Learning Systems, 2006 ISBN 3-540-25379-3 Vol. 192. Jose A. Lozano, Pedro Larrañaga, Iñaki Inza, Endika Bengoetxea (Eds.) Towards a New Evolutionary Computation, 2006 ISBN 3-540-29006-0 Vol. 193. Ingo Glöckner Fuzzy Quantifiers: A Computational Theory, 2006 ISBN 3-540-29634-4

Vol. 194. Dawn E. Holmes, Lakhmi C. Jain (Eds.) Innovations in Machine Learning, 2006 ISBN 3-540-30609-9 Vol. 195. Zongmin Ma Fuzzy Database Modeling of Imprecise and Uncertain Engineering Information, 2006 ISBN 3-540-30675-7 Vol. 196. James J. Buckley Fuzzy Probability and Statistics, 2006 ISBN 3-540-30841-5 Vol. 197. Enrique Herrera-Viedma, Gabriella Pasi, Fabio Crestani (Eds.) Soft Computing in Web Information Retrieval, 2006 ISBN 3-540-31588-8 Vol. 198. Hung T. Nguyen, Berlin Wu Fundamentals of Statistics with Fuzzy Data, 2006 ISBN 3-540-31695-7 Vol. 199. Zhong Li Fuzzy Chaotic Systems, 2006 ISBN 3-540-33220-0 Vol. 200. Kai Michels, Frank Klawonn, Rudolf Kruse, Andreas Nürnberger Fuzzy Control, 2006 ISBN 3-540-31765-1 Vol. 201. Cengiz Kahraman (Ed.) Fuzzy Applications in Industrial Engineering, 2006 ISBN 3-540-33516-1 Vol. 202. Patrick Doherty, Witold Łukaszewicz, Andrzej Skowron, Andrzej Szałas Knowledge Representation Techniques: A Rough Set Approach, 2006 ISBN 3-540-33518-8

Patrick Doherty Witold Łukaszewicz Andrzej Skowron Andrzej Szałas

Knowledge Representation Techniques A Rough Set Approach

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Professor Patrick Doherty

Professor Andrzej Skowron

Department of Computer and Information Science Linköping University, Sweden E-mail: [email protected]

Institute of Mathematics Warsaw University Warsaw, Poland E-mail: [email protected]

Professor Witold Łukaszewicz

Professor Andrzej Szałas

The University of Economics and Computer Science Olsztyn, Poland E-mail: [email protected]

The University of Economics and Computer Science Olsztyn, Poland and Department of Computer and Information Science Linköping University, Sweden E-mail: [email protected]

Library of Congress Control Number: 2006924365

ISSN print edition: 1434-9922 ISSN electronic edition: 1860-0808 ISBN-10 3-540-33518-8 Springer Berlin Heidelberg New York ISBN-13 978-3-540-33518-4 Springer Berlin Heidelberg New York This wor