Fuzzy Stochastic Optimization Theory, Models and Applications
Covering in detail both theoretical and practical perspectives, this book is a self-contained and systematic depiction of current fuzzy stochastic optimization that deploys the fuzzy random variable as a core mathematical tool to model the integrated fuzz
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Shuming Wang • Junzo Watada
Fuzzy Stochastic Optimization Theory, Models and Applications
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Shuming Wang Waseda University Hibikino, Wakamatsu-ku Kitakyushu-City 2-7 Fukuoka, Japan
Junzo Watada Waseda University Hibikino, Wakamatsu-ku Kitakyushu-City 2-7 Fukuoka, Japan
ISBN 978-1-4419-9559-9 ISBN 978-1-4419-9560-5 (eBook) DOI 10.1007/978-1-4419-9560-5 Springer New York Heidelberg Dordrecht London Library of Congress Control Number: 2012934832 © Springer Science+Business Media New York 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)
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Preface
Randomness and fuzziness (or vagueness) are two major sources of uncertainty in the real world. In practical applications in areas of industrial engineering, management, and economics, chances are pretty good that decision makers are being confronted with information that are simultaneously probabilistically uncertain and fuzzily imprecise, and an optimization (decision making) has to be performed under such a twofold uncertain environment of a co-occurrence of randomness and fuzziness. Fuzzy random variable originally presented by H. Kwakernaak is a tailor-made mathematical tool to describe the twofold or hybrid uncertainty. It owns a twofold distribution structure being able to carry a joint in
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