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.
General
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