Fuzzy Stochastic Multiobjective Programming
Although studies on multiobjective mathematical programming under uncertainty have been accumulated and several books on multiobjective mathematical programming under uncertainty have been published (e.g., Stancu-Minasian (1984); Slowinski and Teghem (199
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Volume 159
Series Editor: Frederick S. Hillier Stanford University, CA, USA Special Editorial Consultant: Camille C. Price Stephen F. Austin, State University, TX, USA
For further volumes: http://www.springer.com/series/6161
Masatoshi Sakawa • Ichiro Nishizaki Hideki Katagiri
Fuzzy Stochastic Multiobjective Programming
1C
Prof. Dr. Masatoshi Sakawa Hiroshima University Graduate School of Engineering Department of System Cybernetics Kagamiyama 1-4-1 739-8527 Higashi-Hiroshima Japan [email protected]
Dr. Hideki Katagiri Hiroshima University Graduate School of Engineering Department of System Cybernetics Kagamiyama 1-4-1 739-8527 Higashi-Hiroshima Japan [email protected]
Prof. Dr. Ichiro Nishizaki Hiroshima University Graduate School of Engineering Department of System Cybernetics Kagamiyama 1-4-1 739-8527 Higashi-Hiroshima Japan [email protected]
ISSN 0884-8289 ISBN 978-1-4419-8401-2 e-ISBN 978-1-4419-8402-9 DOI 10.1007/978-1-4419-8402-9 Springer New York Dordrecht Heidelberg London Library of Congress Control Number: 2011921329 © Springer Science+Business Media, LLC 2011 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
To Our Parents and Families
Preface
The increasing complexity of modern-day society has brought new problems having multiple objectives including economic, environmental, social and technical ones. Hence, it seems that the consideration of many objectives in the actual decision making process requires multiobjective approaches rather than that of a single objective. One of the major systems-analytic multiobjective approaches to decision making under constraints is multiobjective programming as a generalization of traditional single objective programming. For such multiobjective programming problems, it is significant to realize that multiple objectives are often noncommensurable and conflict with each other. With this observation, in multiobjective programming problems, the notion of Pareto optimality or efficiency has been introduced instead of the optimality concept for single-objective problems. However, decisions with Pareto optimality or efficiency are not uniquely determined; the final decision must be selected by a decision maker (DM), which well represents the subjective judgments, from the se
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