Uncertainty-Based Information Elements of Generalized Information Th

Information is precious. It reduces our uncertainty in making decisions. Knowledge about the outcome of an uncertain event gives the possessor an advantage. It changes the course of lives, nations, and history itself. Information is the food of Maxwell's

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Uncertainty -Based Information Elements of Generalized Information Theory Second Corrected Edition

With II Figures and 10 Tables

Springer-Verlag Berlin Heidelberg GmbH

Professor George J. Klir Center for Intelligent Systems and Department of Systems Science and Industrial Engineering Thomas 1. Watson School of Engineering and Applied Science Binghamton University - SUNY Binghamton, NY 13902-600 USA Professor Mark 1. Wierman Center for Research in Fuzzy Mathematics and Computer Science and Mathematics and Computer Science Department Creighton University Omaha, NE 68178-2090 USA

ISBN 978-3-7908-2464-3 Cataloging-in-Publication Data applied for Die Deutsche Bibliothek - CIP-Einheitsaufnahme Uncertainty-based information: elements of generalized information theory: with II figures and 10 tables I George J. Klir; Mark 1. Wierman. (Studies in fuzziness and soft computing; Vol. 15 2nd edition) ISBN 978-3-7908-2464-3 ISBN 978-3-7908-1869-7 (eBook) DOI 10.1007/978-3-7908-1869-7 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. reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provi~ions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag Berlin Heidelberg GmbH. Violations are liable for prosecution under the German Copyright Law. © Springer-Verlag Berlin Heidelberg 1999 Originally published by Physica-Verlag Heidelberg New York in 1999 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. Hardcover Design: Erich Kirchner, Heidelberg SPIN 10741828

88/2202-5 4 3 2 I 0 - Printed on acid-free paper

Uncertainty-Based Infonnation

Studies in Fuzziness and Soft Computing Editor-in-chief Prof. Janusz Kacprzyk Systems Research Institute Polish Academy of Sciences ul. Newelska 6 01-447 Warsaw, Poland E-mail: [email protected] Vol. 3. A. Geyer-Schulz Fuzzy Rule-Based Expert Systems and Genetic Machine Learning, 2nd ed. /996 ISBN 3-7908-0964-0

Vol. 14. E. Hisdal Logical Structures for Representation of Knowledge and Uncertainty, /998 ISBN 3-7908-1056-8

Vol. 4. T. Onisawa and J. Kacprzyk (Eds.) Reliability and Safety Analyses under Fuzziness, /995 ISBN 3-7908-0837-7

Vol. IS. G.1. Klir and M.1. Wierman Uncertainty-Based Information, 2nd ed. /999 ISBN 3-7908-1242-0

Vol. 5. P. Bosc and J. Kacpnyk (Eds.) Fuzziness in Database Management Systems, /995 ISBN 3-7908-0858-X

Vol. 16. D. Driankov and R. Palm (&Is.) Advances in Fuzzy Control, /998 ISBN 3-7908-1090-8

Vol. 6. E.S. Lee and Q. Zhu Fuzzy and Evidence Reasoning, /995 ISBN 3-7908-0880-6 Vol. 7. B.A. Juliano a