Incomplete Information Group The Language Decision-making Method

In the social and economic activities, it is common that people will encounter a great deal of group decision-making problems with linguistic information. There are many methods proposed to deal with the linguistic information of the group decision-making factors. The method of transforming the linguistic information into two tuple is adopted in this paper, which can prevent the linguistic information from being twisted and lost. Because of the complexity and vagueness of the problems to be decided, it is normal that some information of the decision-making factors, such as the weights and the preference values given by the decision-makers, may be incomplete, and on such group decision-making problems with linguistic information, few literatures are focused, so it is significant and meaningful to do some researches on the theory and methods of the linguistic group decision-making problems, which having incomplete information about the decision making factors. This paper have researched a few types of such problems, and the corresponding models have been created and then worked out on the basis of the latest optimization theories and the popular optimizing algorithms. And the details are as follows:(1) A linear programming model is created and worked out directed by programming in the environment of Matlab7.0 for such a group decision-making problems with linguistic information, in which the preference information are obtained according to comparing any two alternatives by the decision-makers, and may take the form of standard linguistic evaluation grade, or may be between two continuous standard linguistic evaluation grade, or may be not given, and the weights of the decision-makers are numeric and certain.(2) As concerning such decision making problems as mentioned above, when the weights of the decision-makers are uncertain and numeric, then a nonlinear programming model is created and worked out with the improved Particle Swarm Optimization Algorithm.(3) As for the group multi-criteria linguistic assignment problem with incomplete certain information, in which the decision-makers' weightsand the evaluation criteria's weights are numeric and uncertain, andrthe assessment information may be between two continuous linguistic assessment grades or not be given by the decision makers, according to the function A and A"1 of two tuple, a nonlinear mixed integral programming model is constructed and worked out with the improved Particle Swarm Optimization Algorithm and Hungary Algorithm.(4) As concerning such decision-making problems as mentioned above, when the decision-makers' weights and the evaluation criteria's weights are linguistic and uncertain, a nonlinear integral programming model is constructed and worked out with the proposed Particle Swarm Optimization Algorithm combined with the ideal of -the Genetic Algorithm and Hungary Algorithm.(5) As for the group multi-criteria linguistic ordered clustering problems with incomplete certain information, in which the decision-makers' weights and the evaluation criteria's weights are numeric and uncertain, and the assessment information may be between two continuous linguistic assessment grades or not be given by the decision makers, the improved Particle Swarm Optimization Algorithm is adopted to solve such problems according to the way the K-means does.