E-Book Overview
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 (1990); Sakawa (1993); Lai and Hwang (1994); Sakawa (2000)), there seems to be no book which concerns both randomness of events related to environments and fuzziness of human judgments simultaneously in multiobjective decision making problems. In this book, the authors are concerned with introducing the latest advances in the field of multiobjective optimization under both fuzziness and randomness on the basis of the authors’ continuing research works. Special stress is placed on interactive decision making aspects of fuzzy stochastic multiobjective programming for human-centered systems under uncertainty in most realistic situations when dealing with both fuzziness and randomness. Organization of each chapter is briefly summarized as follows:
Chapter 2 is devoted to mathematical preliminaries, which will be used throughout the remainder
of the book. Starting with basic notions and methods of multiobjective programming, interactive
fuzzy multiobjective programming as well as fuzzy multiobjective programming is outlined.
In Chapter 3, by considering the imprecision of decision maker’s (DM’s) judgment for stochastic
objective functions and/or constraints in multiobjective problems, fuzzy multiobjective stochastic
programming is developed.
In Chapter 4, through the consideration of not only the randomness of parameters involved in
objective functions and/or constraints but also the experts’ ambiguous understanding of the realized values of the random parameters, multiobjective programming problems with fuzzy random variables are formulated.
In Chapter 5, for resolving conflict of decision making problems in hierarchical managerial or
public organizations where there exist two DMs who have different priorities in making decisions, two-level programming problems are discussed.
Finally, Chapter 6 outlines some future research directions.
E-Book Content
International Series in Operations Research & Management Science
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 ma