Intuitionistic Fuzzy Aggregation and Clustering
This book offers a systematic introduction to the clustering algorithms for intuitionistic fuzzy values, the latest research results in intuitionistic fuzzy aggregation techniques, the extended results in interval-valued intuitionistic fuzzy environments,
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For further volumes: http://www.springer.com/series/2941
279
Zeshui Xu
Intuitionistic Fuzzy Aggregation and Clustering
123
Zeshui Xu College of Sciences PLA University of Science and Technology Nanjing People’s Republic of China
ISSN 1434-9922 ISBN 978-3-642-28405-2 DOI 10.1007/978-3-642-28406-9
ISSN 1860-0808 (electronic) ISBN 978-3-642-28406-9 (eBook)
Springer Heidelberg New York Dordrecht London Library of Congress Control Number: 2012953466 Ó 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 concept of intuitionistic fuzzy set (IFS) was originally introduced by Atanassov (1983) to extend the concept of the traditional fuzzy set. Each element in an IFS is expressed by an ordered pair which is called an intuitionistic fuzzy value (IFV) (or intuitionistic fuzzy number (IFN)), and each IFV is characterized by a membership degree, a nonmembership degree, and a hesitancy degree. The sum of the membership degree, the nonmembership degree, and the hesitancy degree of each IFV is equal to one. IFVs can describe the fuzzy characters of things comprehensively, and thus are a powerful and effective tool in expressing uncertain or fuzzy information in actual applications. Recently, a lot of research work has been
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