Some Theories And Methods In Group Decision-Making And Multiobjective Decision-Making

Group decision-making and multiobjective decision-making are important research fields of operational research and decision science. Their theories and methods are widely used in the areas of modern economic planning, production administration, financial investment, item evaluation, engineering design, transportation, environmental protection, military, etc. In this thesis, we study the theories and methods of group decision-making, multiobjective programming and related nonlinear programming and achieve the following results in three aspects: (1) Two methods with stochastic preference in group decision-making are given and stability theory of group multiobjective programming is established; (2) Some new results of stability and connectedness for multiobjective programming are obtained and relations between two properly efficient solutions of multiobjective programming are established; (3) Two constraint nonlinear programming models are presented and the related theories are established. The obtained results are of great significance to the development of the theories of group decision-making, multiobjective programming and nonlinear programming and will have brilliant prospects in practical application.This thesis is divided into eight chapters. Chapter 1 summarizes the development of group decision-making, group multiobjective decision-making, multiobjective programming and nonlinear programming and related research trends associated with this thesis.In Chapter 2 two group decision-making methods with stochastic preference are given. One is stochastic Borda-number method. It introduces the concepts of stochastic Borda-number at an alternative and stochastic Borda-number mapping on a set of alternatives. After checking the stochastic Borda-number mapping and the corresponding stochastic preference axioms, it gives a group sequencing method for all alternatives. The other is stochastic preference-number method. With the help of the subjective probability of individual preference, it introduces the concept of stochastic Borda-number mapping. After discussing the some fundamental properties of this mapping, it gives a group order method for all alternatives. They are two important methods in stochastic group decision-making.In Chapter 3 a study has been made of the stability of a class of the joint cone weakly efficient solution sets for group multiobjective programming problem. The stability results of the joint cone weakly efficient solution sets in the sense of upper semi-continuance with respect to variable perturbation and objective order perturbationhave been obtained respectively. In addition, this chapter also proves the joint cone weakly efficient solution sets are stable in the sense of continuance with respect to variable perturbation and order perturbation respectively on the contents of Baire category when the perturbation variables form Baire space.Chapter 4 establishes the stability theory of cone efficient solution sets and cone weakly efficient solution sets for multiobjective programming under constraint cone perturbations in topological vector spaces. The chapter first studies the closedness, semicontinuity and cone semicontinuity of cone efficient point sets and cone weakly efficient point sets of the perturbed objective sets when both the objective maps and constraint maps are continuous and the constraint cone is semicontinuous. On this basis, the closedness and semicontinuity of cone efficient solution sets and cone weakly efficient solution sets for multiobjective programming problem under constraint cone perturbations are obtained. To the stability of multiobjective programming problem, almost complete conclusions have been obtained in the areas of variable perturbation and objective order perturbation since 1980s. However, none of the previous discussions is concerned with constraint cone perturbation at home and abroad. This chapter opens up the study of this new area.Chapter 5 consists of two parts. The first part studies the connectedness of the cone-efficient solution set f...