Research On Theoretics And Methods For Solving Stochastic Multiple Attribute Decision Making Problems

Among types of uncertainty surrounding real life problems, randomness play a pivotal role. Randomness is one type of uncertainty that describes occurrence of affairs, and random variables are used to describe the stochastic phenomena. Accordingly, stochastic multiple attribute decision making (SMADM) has been proposed to make decision under uncertainty environment, and it is an important research branch of uncertain multiple attribute decision making, and it has wide practical backgrounds in economic management and engineering systems. Stochastic multiple attribute decision making is that 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 portfolio selection, decision and evaluation in project investment and production alternatives decision and so on. Despite stochastic multiple attribute decision making problems is a kind of common problem in economic and management activities, and has aroused some scholars’curiosity, but the theories and methods of stochastic multiple attribute decision making are rarely seen. Therefore, the value of systemic research on theories and methods for stochastic multiple attribute decision making is great. Those theories and methods which are applied to economic activities, administration departments in enterprises or engineering systems will assist relevant managers in decision making in order to reduce the risk and improve the quality of decision making. Thereby, researching on theories and methods for solving the stochastic multiple attribute decision making problems have important applied value in practical application.On the bases of some relevant research results, this paper systematically studied the theoretical methods and several problems of stochastic multiple attribute decision making, which the purpose and significance of the research includes are as follows:in the theory and method research aspect, proposes several methods for stochastic multiple attribute decision making based on theoretical studying, which includes:proposing a method for stochastic multiple attribute decision making based on stochastic (almost) dominance rules, proposing a method for stochastic multiple attribute decision making based on dominance probabilities, proposing a method for multiple attribute decision making with normal random variables and proposing an approach to stochastic multiple attribute decision making with multiple formats of information; in the practical research aspect, choose several decision problems as the numerical examples to illustrate the feasibility and validity of these proposed methods and validate the great guidance and reference significance to portfolio selection, decision and evaluation in project investment and risk assessment and so on.This main work of the dissertation is in several aspects as following:(1) Proposing a method for stochastic multiple attribute decision making based on both stochastic dominance rules and almost stochastic dominance rules. With regard to the existing stochastic multiple attribute decision making methods which can not establish the dominance relations on pairwise comparisons of alternatives using the first stochastic dominance rule, second stochastic dominance rule and third stochastic dominance rule, proposing a new method for solving the problem based on both stochastic dominance rules and almost stochastic dominance rules. the description of stochastic dominance rules and almost stochastic dominance rules is given, and the related theoretical analysis of stochastic dominance is also given. Enriching and perfecting the research on stochastic multiple attribute decision making method.(2) The definition of dominance degree on pairwise comparisons of alternatives is described. Whereas the existing stochastic multiple attribute decision making methods which can only determine the dominance relation of the alternatives, but cannot determine the degree on them, the concept of dominance degree is given, and a new method for stochastic multiple attribute decision making based on dominance probabilities is proposed. 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 dominance degree for pairwise comparisons of alternatives is presented. Then, the dominance degree matrix is built by calculating the dominance degree on pairwise comparisons of alternatives with regard to each attribute. Furthermore, PROMETHEEⅡmethod is used to obtain the ranking result of alternatives. This method make up the existing stochastic multiple attribute decision making methods for the limitations which cannot determine the degree on pairwise comparisons of alternatives and become the foundation for the research on stochastic multiple attribute decision making method based on dominance degree analysis.(3) Proposing two methods for solving the multiple attribute decision making problems with normal random variables. On the one hand, Firstly, the comprehensive utility value of each alternative is obtained by disposing the decision matrix with normal random variables using probability and statistics knowledge, and by the analysis the comprehensive utility value of each alternative is still normal random variable. Secondly, the interval of the comprehensive utility value of each alternative is determined according to 3σrule, and the dominance possibility degree matrix for pairwise comparison of alternatives is built through comparisons of the intervals. Thirdly, based on the dominance possibility degree matrix, PROMETHEEⅡmethod is used to obtain the ranking of alternatives. On the other hand, Firstly, the stochastic dominance relations between pairwise comparisons of alternatives are obtained by the analysis of the expectation and variance values with normal random variables, and the relative theorems are given. Then, the dominance relation matrix with regard to each attribute is built according to the stochastic dominance relations on pairwise comparisons of alternatives. Furthermore, ELECTREⅢmethod is used to obtain the ranking result of alternatives.(4) Proposing to solve the multiple attribute decision-making (MADM) problems with multiple formats of information. In this paper, Firstly, the description of the MADM problem with three formats of information such as stochastic variables, crisp numbers and interval numbers are given. Then, the three formats of information on attribute values are transformed into the formats of stochastic variables with cumulative distribution functions, and stochastic dominance relations between pairwise comparisons of alternatives are judged using the stochastic dominance rules. Furthermore, ELECTREⅢmethod is used to obtain the ranking result of alternatives. (5) Some numerical examples are used to illustrate the feasibility and validity of proposed methods in economic management, engineering systems and other relevant fields, and provide that not only they are a useful reference for potential applications on decision making problems surrounding real life, but also they are the guidance for the decision making problems in the real practices.Finally, the dissertation makes a summary, and shows the future study.