Research On Stochastic Multi-attribute Decision Making Methods Based On Dominance Degree Analysis

Stochastic multi-attribute decision making (SMADM) is an important research branch of uncertain multi-attribute decision making, and it's also a kind of common problem in economic and management activities. Stochastic multi-attribute decision making is ranking a certain number of alternatives based on the attribute values which are random variables on multiple attributes. Because of the complexity and indeterminacy of the problems in the real practice of decision making, it is normal that the attribute values of alternatives are random variables, such as in project investment decision, project evaluation and production decision and so on. Despite stochastic multi-attribute decision making problems have wide practical backgrounds, but the theory of stochastic multi-attribute decision making, especially the practical methods is rarely seen. Therefore, the theoretical value of systemic research on theories and methods for stochastic multi-attribute decision making is great. In practical application, those methods are applied to economic activities or administration departments in enterprises and they assist relevant managers in decision making in order to reduce the risk and improve the quality of decision making. Thereby, they have important theory significance and appliance value.On the basis of a comprehensive review of the research status and development of stochastic multi-attribute decision making theories and methods, this thesis made thorough research to stochastic multi-attribute decision making problems whose attribute values of the alternatives are random variables with known probability distributions based on the theory of stochastic dominance. The purpose and significance of the research are as follows:in the theory and method research aspect, proposes a method for stochastic multi-attribute decision making based on stochastic dominance degree and a method for stochastic multi-attribute decision making with multiple formats of information based on mixed-data dominance degree, intend to enrich or improve the research of stochastic multi-attribute decision making; in the practical research aspect, chose some decision problems of investment decision making as the numerical examples to illustrate the feasibility and validity of the proposed methods. And it has great guidance and reference significance to project investment decision, project evaluation and risk assessment and so on.This thesis mainly finishes the following works:(1) Firstly, the concepts of stochastic dominance degree and mixed-data dominance degree on pairwise comparisons of alternatives are defined. Since the stochastic multi-attribute decision making method based on stochastic dominance rules can only determine the dominance relation of part of the alternatives, but cannot determine the degree of the stochastic dominance relations, this thesis proposed the concepts of stochastic dominance degree and mixed-data dominance degree. The concepts proposed by this thesis laid the foundation for the research on stochastic multi-attribute decision making method based on dominance degree analysis.(2) Secondly, with regard to stochastic multi-attribute decision making problems where the attribute values of the alternatives are random variables, a stochastic multi-attribute decision making method based on stochastic dominance degree is proposed. Concretely, the definition of stochastic dominance relation on pairwise comparisons of alternatives is given through comparisons of cumulative distribution functions. And on the basis of the stochastic dominance relation, the concept of stochastic dominance degree for pairwise comparisons of alternatives is presented. Then, the stochastic dominance degree matrix is built by calculating the stochastic dominance degree on pairwise comparisons of alternatives with regard to each attribute. Furthermore, PROMETHEEâ…¡method is used to obtain the ranking result of alternatives. This method made up for the limitations which are information missing and can't describe the preferences of the existing stochastic multi-attribute decision making methods based on stochastic dominance rules.(3) Thirdly, with regard to stochastic multi-attribute decision making problems with multiple formats information, a method with multiple formats information based on mixed-data dominance degree is proposed. Concretely, the description of the stochastic multi-attribute decision making problems with four formats of information such as stochastic variables, crisp numbers, interval numbers and fuzzy numbers are given, and the four formats of information on attribute values are transformed into the formats of stochastic variables with cumulative distribution functions. Then, the definition of mixed-data dominance relation and mixed-data dominance degree on pairwise comparisons of alternatives are given based on the theory of stochastic dominance. The mixed-data dominance degree matrix is built by calculating the mixed-data dominance degree on pairwise comparisons of alternatives with regard to each attribute. Furthermore, PROMETHEE II method is used to obtain the ranking result of alternatives.(4) Fourthly, some numerical examples in the investment projects selection have been indicated and verified the feasibility, effectiveness and scientific of the proposed methods. It provided a useful reference for potential applications of the proposed methods in economic management, engineering systems and other relevant fields.This thesis analyzed the methods of stochastic multi-attribute decision making methods based on dominance degree analysis systematically, not only enriched the research of stochastic multi-attribute decision making, but also provided the thought and guidance for the decision making problems in the real practices.