Incomplete Information Research, Multi-attribute Decision Making Based On Evidence Theory

The multiple attribute decision-making problems generally have both quantitative and qualitative nature. When the factors such as weights and attributes are uncertain, fuzzy or incomplete, the decision making procedure will be rather complicated. This paper studies a kind of multiple attribute decision-making problems under various situation, of which the information about the weights is incomplete and the attribute values are incomplete and uncertain.When the information forms about weights are some kinds of incomplete information forms, first, analyzing the incomplete information of weight coefficients given by decision maker, a group of cardinal weights can be attained. On the basis of describing the uncertain and incomplete attributes as degree of belief, then the alternative's attributes can be integrated by evidential reasoning approach. After comparing the utilities of each alternative under all the cardinal weights, the ranking of the alternatives can be determined.When the information forms of weights are incomplete information forms, by evidential reasoning algorithms, the objective function of each alternative is constructed, so nonlinear programming models of each alternative are developed with the incomplete information of weight coefficients. After using genetic algorithms to solve these nonlinear models, the interval of utility of each alternative is obtained. So the ranking of the whole alternatives can be attained.When there are multiple decision makers, by introduction of group decision-making theory, two kinds of new methods based on the above-mentioned method are proposed. When there is a reference set given by decision maker, a corresponding solution that is an extension of the above-mentioned method is proposed.Examples are given to explain feasibility and availability of all the methods mentioned above. The results of our study prove these methods can afford good decision support to such questions.Finally, taking selecting collaborating partners when establishing Agile Virtual Enterprise for example, we explain how to use the methods in real-life decision making thoroughly.