Research On Risk Multi-attribute Decision Making: Theory, Methods And Applications

Multi-attribute decision making (MADM) is an important composing part of modern decision science. It deals with decision problems with finite set of alternatives under several conflictive criteria. So far, many mature approaches for solving MADM problems have been developed. Almost all of these approaches require exact values of the alternatives on each attribute. Due to the complexity of things and the limitation of cognition of human beings, however, uncertainty such as randomness and fuzziness is usually involved in MADM problems. In this situation, it is difficult even impossible to obtain the exact values of alternatives on attributes. In recent years, more and more attentions are paid to the MADM problems under uncertainty.On the basis of a full review of the state of the art on stochastic multi-criteria decision making, the present dissertation is to probe into the risk multi-attribute decision problems (RMA), namely the MADM problems whose performances of the alternatives are random variables with known probability distribution from the theoretical and practical viewpoint. The main contents and contributions are outlines in the following paragraph.Firstly, several basic theoretical problems of RMA are studied in the dissertation. After the formalization of the RMA problems, methods for normalizing the original stochastic decision matrix are proposed. For discrete RMA problems, the concepts of C-type solution and S-type solution are defined, and the inclusion relations between different sets of solution in the same type and between different sets of solution in different types are concluded. For continuous RMA problems, the decision analysis based on Dα-dominance relation is illustrated. These notions of solution and analytical method have important meaning to the filtration and classification of the alternatives.Secondly, a series of decision methods for solving RMA are proposed from different point of view.Methods for solving RMA problems with known weights of the attributes are studied in this dissertation. The following three methods are presented: the single-objective method, the method based on TOPSIS and the method based on stochastic dominance and probability dominance. The single-objective method has the merit of simplicity. The method based on TOPSIS is the extended method of the classical TOPSIS method in deterministic MADM. In the last method, stochastic dominance and probability dominance are combined to describe the local preference between alternatives on each attribute. Compared with the method based only on stochastic dominance, the ranking result of the new method is more elaborate.Methods for solving RMA problems with incomplete information on weights of the attributes are studied in the dissertation. For the RMA problems with completely unknown weights, the method based on maximizing deviations is proposed to assign objective weights of the attributes. The objective weights and the subjective weights are synthesized to rank alternatives in this method. The characteristic of this method is that the objective weights and the synthetical weights are expressed explicitly. For the RMA problems with weights expressed by a set of linear inequalities, a superiority and inferiority ranking method is proposed. In the method, the weights can be easily obtained by solving a linear programming or a convex quadratic programming.The method based on rough sets theory for solving RMA problems is proposed in the dissertation. In this method, the global preference of the decision-maker (DM) is approximated by the graded probabilistic dominance relation. The deduced rules are applied to rank the alternatives. This method present a new way to solving RMA problems with a few attributes and many alternatives or with experiential decision data.At last, the application of RMA to the choice of river diversion schemes during initial stage construction for hydroelectric project is studied. A risk double attribute decision making model is established for the problem of optimization of the river diversion schemes. And the decision model is solved by the method based on stochastic dominance and probability dominance. Compared with other existed decision model for the problem, the proposed model can reflect the characteristic of randomness of the problem, and the decision method can embody DM's preferences and risk attitude.