【作者】 肖文；

【导师】 王耀德；

【作者基本信息】 江西财经大学 ， 管理科学与工程， 2011， 博士

【摘要】 多属性决策是决策科学的一个重要组成部分,工程、经济和管理领域中诸多问题均可以抽象为多属性决策问题,由于客观事物的复杂性、不确定性以及人类思维的模糊性,经典的多属性决策理论与方法不能完全满足人们的需求,一些不确定多属性决策方法相继提出。由于证据理论在表示及融合不确定信息方面的优势,基于证据理论的多属性决策方法日益受到人们的关注。然而,这些方法大多未考虑决策中存在的关联问题,忽略这些关联问题可能导致决策结果不合理,甚至决策失误,因此,对多属性决策的证据理论方法中存在的关联问题进行研究具有重要的理论意义与实际意义。论文针对基于证据理论的多属性决策中常见的若干关联问题展开研究,具体研究内容如下：(1)证据关联问题。在多属性决策中,由于对属性的评价可能基于部分或完全相同的事实、数据、经验等,这样形成的证据是相关的,若直接用Dempster规则合成会产生过估计的合成结果。针对证据关联问题,首先分析了已有的相关证据合成方法,指出了一些不足之处。对于相关源证据己知的情况,提出一种相关证据的合成规则,在已知相关源证据的情况下能够得到准确的合成结果；对于相关源证据未知时,提出多证据的平均融合规则,以同时融合多个相关证据。考虑多专家意见的综合,由于专家意见存在关联,提出了基于平均融合规则的证据合成方法综合多专家的意见,并给出了一种确定专家权值的方法。(2)层次关联问题。较复杂的多属性决策问题的指标往往具有递阶层次结构,在递阶层次结构中可能存在某属性与上层多个属性相关,这种情况下需要考虑属性的综合权值。在基于证据推理的多属性决策方法中,对多层次的属性集结是分层递归完成的,这一过程并未考虑属性的层次关联问题,不能准确反映基本属性在指标体系中的相对重要性,在解决递阶层次结构问题时仅能获得近似结果,因此建议采取综合权值表示属性的相对重要性,并给出确定综合属性权值的方法,将其应用于层次关联的多属性决策问题,将多层次结构转化为两个层次的决策问题,从而消除层次关联的影响。(3)信任优势准则。基于信任累积分布的分析,解释和验证了一阶信任优势准则,在随机优势理论的指导下建立了二阶、三阶信任优势及近似信任优势准则。在信任优势准则的基础上,给出了定量的信任优势度定义,分析了信任优势度的性质。根据信任优势与信任优势度概念,结合级别优先序理论,分别提出了不同的多属性决策方法,为基于证据理论的多属性决策提供了新的研究思路。(4)属性关联问题。多属性决策中属性相互作用的关联问题已逐渐受到人们的关注,但已有的基于证据理论的多属性决策方法均未考虑属性关联问题。针对属性关联问题,分析了属性关联的表现,基于信任优势和信任优势度的概念,提出了属性关联的信任优势决策方法,两种方法均考虑了属性关联时权值的处理,能够更好地满足人们实际决策的需求。更多还原

【Abstract】 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.更多还原