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The overall trend of modern science and technology is to synthesize all areas of knowledge into a few major blocks. Another characteristic is that the esthetic standard of scientific workers has been changing constantly. They ask, How can they equip themselves with the newest knowledge? How can they handle new knowledge, the amount of which has been increasing in a geometric series? According to Quastler, systems methodology is essentially the establishment of a structural foundation for four kinds of theories of organization: cybernetics, game theory, decision theory, and information theory. General systems methodology is a theoretical methodology whose purpose is to realize the ideal model of a systems theory described by von Bertalanffy, Quastler, and Zadeh - that is, to establish a general theory applicable to explain phenomena in various specific systems. The present volume is a comprehensive and mathematical approach to general systems theory. Topics explored are na?ve set theory; axiomatic set theory; centralizability and tests of applications; systems of single relations; calculus of generalized numbers; unsolved problems in general systems theory.
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GENERAL SYSTEMS THEORY A MATHEMATICAL APPROACH International Federation for Systems Research International Series on Systems Science and Engineering Series Editor: George J. Klir State University of New York at Binghamton Editorial Board Gerrit Broekstra Erasmus University, Rotterdam, The Netherlands John L. Casti Santa Fe Institute, New Mexico Brian Gaines University of Calgary, Canada Ivan M. Havel Charles University, Prague, Czech Republic Manfred Peschel Academy of Sciences, Berlin, Germany Franz Pichler University of Linz, Austria Volume 8 THE ALTERNATIVE MATHEMATICAL MODEL OF LINGUISTIC SEMANTICS AND PRAGMATICS Vilém Novák Volume 9 CHAOTIC LOGIC: Language, Thought, and Reality from the Perspective of Complex Systems Science Ben Goertzel Volume 10 THE FOUNDATIONS OF FUZZY CONTROL Harold W. Lewis, III Volume 11 FROM COMPLEXITY TO CREATIVITY: Explorations in Evolutionary, Autopoietic, and Cognitive Dynamics Ben Goertzel Volume 12 GENERAL SYSTEMS THEORY: A Mathematical Approach Yi Lin Volume 13 PRINCIPLES OF QUANTITATIVE LIVING SYSTEMS SCIENCE James R. Simms Volume 14 INTELLIGENT ROBOTIC SYSTEMS: Design, Planning, and Control Witold Jacak IFSR was established “to stimulate all activities associated with the scientific study of systems and to coordinate such activities at international level.” The aim of this series is to stimulate publication of high-quality monographs and textbooks on various topics of systems science and engineering. This series complements the Federation’s other publications. A Continuation Order Plan is available for this series. A continuation order will bring delivery of each new volume immediately upon publication. Volumes are billed only upon actual shipment. For further information please contact the publisher. Volumes 1–6 were published by Pergamon Press. GENERAL SYSTEMS THEORY A MATHEMATICAL APPROACH YI LIN Slippery Rock University Slippery Rock, Pennsylvania KLUWER ACADEMIC PUBLISHERS NEW YORK, BOSTON , DORDRECHT, LONDON , MOSCOW eBook ISBN 0-306-46962-6 Print ISBN 0-306-45944-2 ©2002 Kluwer Academic Publishers New York, Boston, Dordrecht, London, Moscow All rights reserved No part of this eBook may be reproduced or transmitted in any form or by any means, electronic, mechanical, recording, or otherwise, without written consent from the Publisher Created in the United States of America Visit Kluwer Online at: and Kluwer's eBookstore at: http://www.kluweronline.com http