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 remainderof the book. Starting with basic notions and methods of multiobjective programming, interactivefuzzy 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 stochasticobjective functions and/or constraints in multiobjective problems, fuzzy multiobjective stochasticprogramming is developed.In Chapter 4, through the consideration of not only the randomness of parameters involved inobjective 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 orpublic 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

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.