Advances in Fuzzy Implication Functions
Fuzzy implication functions are one of the main operations in fuzzy logic. They generalize the classical implication, which takes values in the set {0,1}, to fuzzy logic, where the truth values belong to the unit interval [0,1]. These functions are not on
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Michał Baczy´nski, Gleb Beliakov, Humberto Bustince Sola, and Ana Pradera (Eds.)
Advances in Fuzzy Implication Functions
ABC
Editors Michał Baczy´nski Institute of Mathematics University of Silesia Katowice Poland Gleb Beliakov School of Information Technology Deakin University Burwood Australia
Humberto Bustince Sola Departamento de Automática y Computación Universidad Pública de Navarra Pamplona Spain Ana Pradera Departamento de Ciencias de la Computación Universidad Rey Juan Carlos Madrid Spain
ISSN 1434-9922 e-ISSN 1860-0808 ISBN 978-3-642-35676-6 e-ISBN 978-3-642-35677-3 DOI 10.1007/978-3-642-35677-3 Springer Heidelberg New York Dordrecht London Library of Congress Control Number: 2012954617 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)
Preface
This volume collects research papers on fuzzy implication functions, which are fundamental for fuzzy logic systems, fuzzy control, decision theory, expert systems etc. They play also a key role in fuzzy mathematical morphology and in solving fuzzy relation equations. Based on the evaluations of our referees, we have accepted 8 manuscripts. These papers aim to present today’s state-of-the-art in this area.
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