Mathematics of Fuzzy Sets and Fuzzy Logic
This book presents a mathematically-based introduction into the fascinating topic of Fuzzy Sets and Fuzzy Logic and might be used as textbook at both undergraduate and graduate levels and also as reference guide for mathematician, scientists or engineers
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295
Barnabas Bede
Mathematics of Fuzzy Sets and Fuzzy Logic
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Author Barnabas Bede Department of Mathematics DigiPen Institute of Technology Redmond, WA USA
ISSN 1434-9922 e-ISSN 1860-0808 ISBN 978-3-642-35220-1 e-ISBN 978-3-642-35221-8 DOI 10.1007/978-3-642-35221-8 Springer Heidelberg New York Dordrecht London Library of Congress Control Number: 2012953384 c Springer-Verlag Berlin Heidelberg 2013 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)
Dedicated to my daughters: Fruzsina and Tekla
Preface
The present manuscript is intended to be a textbook that could serve both undergraduate and graduate students when studying Fuzzy Set Theory and Applications. It is also intended to deepen the research into some existing directions and to investigate some new research directions. The book tries to develop a systematic, Mathematically-based introduction into the theory and applications of fuzzy sets and fuzzy logic. In this way the author tries to cover a gap in the literature. Also, the book can be an introduction into Fuzzy Sets and Systems for researchers who are interested in the topic of fuzzy sets in all areas of Mathematics, Computer Science and Engineering, or simply interested Mathematicians,
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