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Everyday people need to make decisions, and the decision makers usually face multiple,
conflicting objectives and uncertain environments. The research about uncertain
multi-objective decision making problems has been profolic. It mainly provides
decision makers with the help to find optimal solutions for many objectives under
uncertain environments, and has been a permanent focus for many years.
To trace the origins of the multi-objective decision making with certain parameters,
we have to go back over the eighteenth century. B. Franklin introduced how to
coordinate multiple objectives in 1772. A. A. Cournot proposed the multi-objective
decision making model from the standpoint of the economics in 1836. V. Pareto
firstly presented the optimal solution to the multi-objective decision making model
from the standpoint of the mathematics in 1896 and then K. J. Arrow et al. proposed
the concept of efficient points. Traditional multi-objective decision making is only
aimed at problems with certain parameters, but as we know, it is usual that many
decision making problems have uncertain factors. As people know more and more
about the uncertain event, the research about random multi-objective decision making,
fuzzy multi-objective decision making, rough multi-objective decision making
and two-fold uncertain multi-objective decision making problems were gradually
developed.
In the last 25 years, fuzzy set theory has been applied to many disciplines such as
operations research, management science, control theory, artificial intelligent/expert
systems, human behavior, etc. Growth of the applications of fuzzy set theory have
been accumulating. In 1978, H. Kwakernaak combined randomness with fuzziness
and initialized the concept of the fuzzy random variable, then introduced its basic
definition and properties. This viewpoint which combined two different uncertain
variables to describe complicated events received approval from many scholars and
move forward a further step to uncertain events. Then many papers and books about
the two-fold uncertain theory presented more and more, and therefore promoted
the development of two-fold uncertain theory. This monograph presents systematically
state-of-art of fuzzy-like multiple objective mathematical programming in
both techniques and applications. |