On Intuitionistic Fuzzy Sets Theory
This book aims to be a comprehensive and accurate survey of state-of-art research on intuitionistic fuzzy sets theory and could be considered a continuation and extension of the author´s previous book on Intuitionistic Fuzzy Sets, published by Sprin
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283
Krassimir T. Atanassov
On Intuitionistic Fuzzy Sets Theory
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Author Prof. Krassimir T. Atanassov, DSc, DSc, PhD Department of Bioinformatics and Mathematical Modelling Institute of Biophysics and Biomedical Engineering Bulgarian Academy of Sciences Acad. G. Bonchev Str., Block 105 Sofia-1113, Bulgaria E-mail: [email protected]
ISSN 1434-9922 e-ISSN 1860-0808 ISBN 978-3-642-29126-5 e-ISBN 978-3-642-29127-2 DOI 10.1007/978-3-642-29127-2 Springer Heidelberg New York Dordrecht London Library of Congress Control Number: 2012935245 c Springer-Verlag Berlin Heidelberg 2012 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. The use of general descriptive names, registered names, trademarks, service marks, 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. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Preface
The bipolar model for evaluation of the events and objects around us has deeply underlined the mankind’s conscience since ancient times. For instance, the Bulgarian thracologists Alexander Fol and Ivan Marazov point out in [231, 367] that ever since the Paleolithic Age, people have been using the opposition pairs good–evil, right–left, up–down, white–black, man–woman, day–night, Sun–Moon, etc. Each of these opposition pairs happens to be a base of a bipolar model. A very good illustration of the idea of “bipolarity” is the following Bulgarian anecdote from the beginning of 1980s:
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