With a stress on interactive decision-making, this work breaks new ground by covering both the random nature of events related to environments, and the fuzziness of human judgements. The text runs from mathematical preliminaries to future research directions.

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.

Presents the latest advances in the new field of multiobjective programming involving fuzziness and randomness Emphasis on human-centered systems under uncertainty in realistic situations Authors are among the leading researchers in the field Includes supplementary material: sn.pub/extras

Autorentext

Masatoshi Sakawa was born in Matsuyama, Japan, on 11 August l947. He received B.E., M.E., and D.E. degrees in applied mathematics and physics at Kyoto University in 1970, 1972, and 1975, respectively. From 1975 he was with Kobe University where, since 1981, he was an Associate Professor in the Department of Systems Engineering. From l987 to 1990 he was a Professor in the Department of Computer Science at Iwate University. At present he is a Professor at Hiroshima University and is working with the Department of Arti cial Complex Systems Engineering in the Graduate School of Engineering. He was an Honorary Visiting Professor at University of Manchester Institute of Science and Technology (UMIST), Computation Department, sponsored by the Japan Society for the Promotion of Science (JSPS) from March to December 1991. He was also a Visiting Professor at the Kyoto Institute of Economic Research, Kyoto University from April l991 to March l992. His research and teaching activities are in the area of systems engineering, especially mathematical optimization, multiobjective decision making, fuzzy mathematical programming and game theory. In addition to over 300 articles in National and International Journals, he is an author and coauthor of 6 books in English and 14 books in Japanese, including the Springer titles Genetic Algorithms and Fuzzy Multiobjective Optimization; Fuzzy Sets and Interactive Multiobjective Optimization; Large-Scale Interactive Fuzzy Multiobjective Programming: Decomposition Approaches; and, with Nishizaki, Fuzzy and Multiobjective Games for Conflict Resolution. Hitoshi Yano is with the Department of Social Sciences, School of Humanities and Social Sciences, Nagoya City University. Ichiro Nishizaki received B.E. and M.E. degrees in systems engineering at Kobe University in 1982 and 1984, respectively, and he received the D.E. degree from Hiroshima University in 1993. From 1984 to 1990, he worked for Nippon SteelCorporation. From 1990 to 1993, he was a Research Associate at the Kyoto Institute of Economic Research, Kyoto University. From 1993 to 1996, he was an Associate Professor in the Faculty of Business Administration and Informatics at Setsunan University. From 1997 to 2001, he was an Associate Professor at Hiroshima University, and was working with the Department of Artificial Complex Systems Engineering in the Graduate School of Engineering. At present, he is a Professor in that department. His research and teaching activities are in the area of systems engineering, especially game theory, multiobjective decision making, and fuzzy mathematical programming. He is an author or coauthor of about eighty papers, one book in English (Springer: "Fuzzy and Multiobjective Games for Conflict Resolution"), and two books in Japanese.

Inhalt
Chapter 1. Introduction and Historical Remarks.- Chapter 2. Fundamentals.- Chapter 3. Fuzzy Multiobjective Stochastic Programming.- Chapter 4. Multiobjective Fuzzy Random Programming.- Chapter 5. Stochastic and Fuzzy Random Two-Level Programming.- Chapter 6. Future Research Directions.