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Fuzzy-Like Multiple Objective Decision Making (Studies in Fuzziness and Soft Computing)

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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.
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