Theory and Practice of Uncertain Programming
Real-life decisions are usually made in the state of uncertainty such as randomness and fuzziness. How do we model optimization problems in uncertain environments? How do we solve these models? In order to answer these questions, this book provides a self
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Studies in Fuzziness and Soft Computing, Volume 239 Editor-in-Chief Prof. Janusz Kacprzyk Systems Research Institute Polish Academy of Sciences ul. Newelska 6 01-447 Warsaw Poland E-mail: [email protected] Further volumes of this series can be found on our homepage: springer.com Vol. 224. Rafael Bello, Rafael Falcón, Witold Pedrycz, Janusz Kacprzyk (Eds.) Contributions to Fuzzy and Rough Sets Theories and Their Applications, 2008 ISBN 978-3-540-76972-9 Vol. 225. Terry D. Clark, Jennifer M. Larson, John N. Mordeson, Joshua D. Potter, Mark J. Wierman Applying Fuzzy Mathematics to Formal Models in Comparative Politics, 2008 ISBN 978-3-540-77460-0 Vol. 226. Bhanu Prasad (Ed.) Soft Computing Applications in Industry, 2008 ISBN 978-3-540-77464-8 Vol. 227. Eugene Roventa, Tiberiu Spircu Management of Knowledge Imperfection in Building Intelligent Systems, 2008 ISBN 978-3-540-77462-4
Vol. 232. Eduardo Massad, Neli Regina Siqueira Ortega, Laécio Carvalho de Barros, Claudio José Struchiner Fuzzy Logic in Action: Applications in Epidemiology and Beyond, 2008 ISBN 978-3-540-69092-4 Vol. 233. Cengiz Kahraman (Ed.) Fuzzy Engineering Economics with Applications, 2008 ISBN 978-3-540-70809-4 Vol. 234. Eyal Kolman, Michael Margaliot Knowledge-Based Neurocomputing: A Fuzzy Logic Approach, 2009 ISBN 978-3-540-88076-9 Vol. 235. Kofi Kissi Dompere Fuzzy Rationality, 2009 ISBN 978-3-540-88082-0
Vol. 228. Adam Kasperski Discrete Optimization with Interval Data, 2008 ISBN 978-3-540-78483-8
Vol. 236. Kofi Kissi Dompere Epistemic Foundations of Fuzziness, 2009 ISBN 978-3-540-88084-4
Vol. 229. Sadaaki Miyamoto, Hidetomo Ichihashi, Katsuhiro Honda Algorithms for Fuzzy Clustering, 2008 ISBN 978-3-540-78736-5
Vol. 237. Kofi Kissi Dompere Fuzziness and Approximate Reasoning, 2009 ISBN 978-3-540-88086-8
Vol. 230. Bhanu Prasad (Ed.) Soft Computing Applications in Business, 2008 ISBN 978-3-540-79004-4
Vol. 238. Atanu Sengupta, Tapan Kumar Pal Fuzzy Preference Ordering of Interval Numbers in Decision Problems, 2009 ISBN 978-3-540-89914-3
Vol. 231. Michal Baczynski, Balasubramaniam Jayaram Fuzzy Implications, 2008 ISBN 978-3-540-69080-1
Vol. 239. Baoding Liu Theory and Practice of Uncertain Programming, 2009 ISBN 978-3-540-89483-4
Baoding Liu
Theory and Practice of Uncertain Programming
2nd Edition
ABC
Author Baoding Liu Uncertainty Theory Laboratory Department of Mathematical Sciences Tsinghua University Beijing 100084 China E-Mail: [email protected]
ISBN 978-3-540-89483-4
e-ISBN 978-3-540-89484-1
DOI 10.1007/978-3-540-89484-1 Studies in Fuzziness and Soft Computing
ISSN 1434-9922
Library of Congress Control Number: 2008941016 The first edition appeared as volume 102 of Studies in Fuzziness and Soft Computing ISBN 3-7908-1490-3 Physica-Verlag Heidelberg, 2002. c 2009 Springer-Verlag Berlin Heidelberg This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproducti
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