Study On Multi-objective Decision-makingmodel And Algorithm Based On Uncertaininformation Description

The multiple objective decision-making problem based on uncertain information description is becoming a research topic of modern decision science.It has universal theoretical and practical background in the areas of data processing,item evaluation,systems engineering and so on.The related models and algorithms about its problem are studied in this thesis,and the main research works are as follows:Firstly,the multiple objective decision-making problems,in which the preference information provided by the decision maker takes the form of triangular fuzzy number complementary and reciprocal judgment matrix are studied.The decision-making method based on objective programming and linear programming is proposed respectively.With regard to the former,an objective programming model based on the judgment theorem of triangular fuzzy number additive consistent complementary judgment matrix by using the least deviation is established and the ranking vector of the triangular fuzzy number complementary judgment matrix is obtained by solving the model.The objectives are ranked by the expected value of the ranked vector.With regard to the latter,a linear programming model based on the least deviation is established by using the judgment theorem of triangular fuzzy number consistent reciprocal judgment matrix and the ranking vector of triangular fuzzy number reciprocal judgment matrix is obtained by solving the model.The objectives are ranked by using the ranking formula of number complementary judgment matrix which is established according to the possibility degree compared the ranking vector.Secondly,the multiple objective decision-making problem that the attribute weights are known partly or unknown is investigated.With regard to the fuzzy multiple objective decision-making problem that the attribute weights are known partly and the decision maker has avail preference information on alternatives,the optimization model based on the minimum sum of deviation squares between the subjective and objective decisionmaking preference information on alternatives is established.The attribute weights are obtained by solving the model and thus the overall values of every alternative are gained by using the linear weighting method.The fuzzy positive and negative ideal solution of alternatives are introduced.The objectives are ranked by using the relative membershipbetween the overall values of every alternative and the fuzzy positive and negative ideal solution with fuzzy sets theory.The relative membership degree approach based on quadratic programming model is proposed.With regard to the multiple objective decisionmaking problem that the decision maker has avail preference information on alternatives and the attribute weights are unknown,the model of the minimum sum of deviation squares between the subjective and objective decision-making information on alternatives is established.The condition on the existence of solution and the calculated formula of the attribute weights are given by using Lagrange multiplier method to solve the model.Thus the overall values of the alternatives are gained by using the additive weighting method.Based on these values,the ranking priorities on alternatives are processed.The nonlinear programming decision-making approach is developed.Thirdly,the group decision-making problems with different forms of fuzzy preference information are investigated and a new method is proposed.The core of the method is the preference information on alternatives are uniformed into fuzzy complementary judgment matrices.We make use of fuzzy ordered weighted averaging(FOWA)operator for aggregating tools both the uniformed decision-making information and the dominance degree of each objective.Finally,the practical examples are illustrated to show the effectiveness and feasibility of the developed models respectively.