Dependent Issues Of Multiple Attribute Decision Making Based On Evidence Theory

Multiple attribute decision making (MADM) is an important part of decision science, and many problems invovled in engineering, economic and managerial areas can be abstracted to MADM problems. Because of the complexity and uncertainty in the real world and the ambiguity in the human thoughts, the classical MADM theory cannot completely meet the demand of people, thus decision making methods under uncertainty was advanced one after another. Due to the advantages in representing and fusing uncertain information of evidence theory, people are increasingly concerned about MADM methods based on evidence theory. However, most of the approaches do not consider the dependent issues in the process of decision making, and it will cause the unreasonable results even fail to decision making if ignoring the issues. So, research on the dependent issues existed in these approaches has greatly theoretical and practical significance. The thesis focuses on various dependent issues. Specific contents are as follows:(1) Evidence dependence. The evaluation of attributes may be partly or totally based on the same facts, data and experiences, thus it can be seen that the evidences are dependent. If Dempster rule is applied directly to dependent evidences, over-estimate will be resulted. For the evidence dependence issue, the existing combination methods as well as their deficiency are analyzed. If the dependent original evidence is known, the combination method for dependent evidence is proposed and exact result will be got; while the dependent orginal evidence is unknown, the average combination method is generalized so as to intergrate multiple dependent evidences. Since experts'opinions are related in general, the way to combine multiple experts opinions based on average fusion rule and to determine the weights of each expert are proposed.(2) Hierarchical dependence. The hierarchical structure always existes in relatively complex multi-attribute decision making problems, that there may be some attributes related to more than one attribute in upper level within hierarchical structure. For this case, synthetical weights of the attributes should be concerned. Since attributes integration of evidential reasoning method is completed by the way of recursion in which the attributes ralationship between different levels is ignored, it can not tell the relative importance among the attributes in the index system and only get approximate results in dealing with such prolems. So it is suggested to represent the attributes' relative importance by synthetical weight, and an approach of how to determine the weights is proposed. In this way, the multi-level problems can be converted to double-level problems and the effect of hierarchical dependent from hierarchical structure could be eliminated.(3) Belief dominance principle. By analyzing belief cumulative distribution, first-degree belief dominance principle is explained and verified, whereafter second-degree and third-degree belief dominance principle as well as almost belief dominance principle are also established guided by stochastic dominance theory. The definition of quantitative belief dominance degree is given and its characteristics are also analyzed. According to the concepts of belief dominance principle and belief dominance degree, different MADM methods are introduced inspired by outranking theory, which provide new perspective into MADM based on evidence theory.(4) Attribute dependence. The dependent issue arised from interaction between attributes in MADM has been gradually concerned by more and more people, but the existing MADM methods based on evidence theory has never taken the problem of attribute dependence into consideration. The author analyzes the behaviour of attribute dependence, and proposes two approaches for attribute dependence which are based on the concept of belief dominance principle and belief dominance degree. By taking the weights of dependent attributes into account, the proposed approaches will better reflect the people's desire of decision making.