Some Theories And Methods In Group Decision-Making And Multicriteria Decision-Making, And Atmospheric Propagation Study

This thesis describes research works in three parts: some results in the theory and method of group decision-making and incomplete information group decision-making, new conclusions regarding the connectedness and stability of efficient solution sets and weakly efficient solution sets for multictiteria decision-making problem, and some applications of optimization methods in atmospheric propagation.Group decision-making and multicriteria decision-making are important branches of operational research and decision-making science and have broad application. Group decision-making studies ways of aggregating individual preference to form group preference, and by which to ordering all alternatives of group decision-making problem. The research of its theories and methods involves modern logic theroy, ordinal theory, probability and statistics theory, and various methods in optimization theory. The application of group decision-making theory extends to social choice, welfare economics, political bargain, physical game and military decision-making. Multicriteria decision-making investigates optimization problem with multi-attribute or multi-numerical-objective. Its theory involves non-linear functional analysis, convex analysis, non-smooth analysis, set-value mapping etc. And it has found wide application in modern production administration, financial investment, transportation, environmental protection, and military decision-making etc. Group multicriteria decision-making extends theories and methods of group decision-making and Multicriteria decision-making and is a new cross field of two, and investigates the decision-making processes of multicriteria optimization problem with group preference structure.This thesis presents the following five aspects of results:(1) Some new conditions of rationality for cardinal group decision-making preference mapping are introduced and that group penalty-mark-mapping and grouppreference-ratio-mapping are proved to satisfy these conditions; (2) The Borda-number stochastic preference method for solving group decision-making problems and the Utopian preference method for solving group multiobjective optimization problems are given; (3)The methods of aggregating the incomplete information of attribute weights, alternative utilities and weights of decision-makers for group multicriteria decision-making problem with incomplete information are studied, and a new interactive preference-strength method for solving group multicriteria decision-making problems with incomplete information is established; (4)New results with regard to the connectedness of efficient solution sets and stability of cone-weakly-efficient solution sets for multiobjective programming problems are obtained; (5)Some applications of optimization methods in atmospheric refraction and atmospheric inversion are studied and discussed.This thesis consists of five chapters.In Chapter 1, the development of group decision-making and Multicriteria decision-making are summarized and the related research works are introduced. Then the atmospheric refraction and atmospheric inversion problems are presented.In Chapter 2, the rational condition checking and ordering method for group decision-making is studied. In the first two sections the six conditions of rationality for cardinal group decision-making preference mapping as anonymity, neutrality, positive responsiveness, nonnegative responsiveness, strong Pareto rule, and local non-dictatorship are defined and the group penalty-mark-mapping and group preference-ratio-mapping are verified to satisfy all these conditions. In the third section a new stochastic preference method to solve group decision-making problem is established. After introducing the concepts of stochastic Borda-number for an alternative and stochastic Borda-number mapping on a set of alternatives for group decision-making problem, various fundamental properties of Borda-number mapping are discussed and the corresponding stochastic preference axiom system is established, and a group ordering method for all alternatives is constructed.In Charter 3, The methods to congregate the incomplete information of attribute weights, alternative utilities and decision-maker weights for group multicriteriadecision-making problem with incomplete information are studied. In the first section, a method to congregate the incomplete and inconsistent information of attribute weights is given. In the second section,the hierarchical clustering method is used to classify the decision-makers. In the third section a new interactive preference-strength method for solving group multicriteria decision-making problem with incomplete information is established in the sense of weak ordering.In Chapter 4, some results on the connectedness of efficient solution sets for multiobjective optimization problems and the stability of cone-weak-efficient solution sets are obtained, and the Utopian preference method for solving group multiobjective optimization problems are established. In the first section, the connectedness of efficient solution sets and upper-semicontinuity of point-to-set map are studied. When studying the connectedness of efficient solution sets of multiobjective programming problems, many papers represent efficient point sets as the image sets of the closed point-to-set map of some connected sets.Using a counterexample,this section shows that a closed point-to-set map on a connected set is not necessary connected. And with the help of the upper-semicontinuity of point-to-set map, a new result about the connectedness of efficient point sets of the sets is derived. In the second section some new results on stability of cone-weak-efficient point sets are obtained. In the third section the Utopian preference method for solving group multiobjective decision-making problem are established. The concept of the Utopian preference mapping from the individual Utopian preferences to the group Utopian preferences, based on the Utopian points of the corresponding multiobjective optimization models proposed by decision makers are introduced. Through the study of various fundamental properties of the Utopian preference mapping, a method for solving group multiobjective optimization problems with multiple multiobjective optimization models is constructed.In Chapter 5, two applications of optimization methods in atmospheric refraction and atmospheric inversion problems are discussed. In the first section incorporated with two representative radiosonde stations data, the mapping functions from the Standard Atmosphere with that from radiosonde data ray-tracking technique are...