【作者】 陈增明；

【导师】 梁昌勇； 杨善林；

【作者基本信息】 合肥工业大学 ， 管理科学与工程， 2007， 博士

【摘要】 证据理论是在传统概率论的基础上发展起来的，被视为对概率的一种改变，可以很好描述决策中的不确定性，并且具有综合不同信度函数的合成规则，可以对多个专家的意见进行融合，因此在实际中，常常用做一种群决策方法，称为基于证据理论的群决策方法。在基于证据理论的群决策方法中，个体决策者的偏好用mass函数表示，mass函数可以很好地对“信息的不完全”、“信息的不精确”和“信息的不肯定”进行合理描述；对不确定性问题的处理过程更加符合人们的思维方式。此外DS公式还具有很优良的性质，如“交换性”和“极化性”，所有的这些使得证据理论在群决策领域得到一定程度的应用。但是证据理论存在的一些问题，如计算量问题、悖论问题等，在很大程度上限制了基于证据理论的群决策方法在实际中更为广泛地应用，为了使其在实际决策中得到更为广泛的应用，需要对基于证据理论的群决策方法进行进一步研究。论文的主要研究内容如下：(1)对集结规则的计算复杂度问题进行研究。在基于证据理论的群决策方法中，个体决策者的决策结果是用基本可信度函数表示的，集结规则为DS公式。而用DS公式对基本可信度函数进行合成时会引起焦元“组合爆炸”，导致计算量的巨大增加。现有DS合成近似算法需要人为的对证据的焦元个数进行调整，不仅结果误差比较大，而且很多算法会增大悖论发生的概率。本文将研究不需要人为主观参与的DS合成近似算法，并对算法的有效性进行验证。论文中给出了证据投影分解的概念，并在此基础上给出了证据合成的投影近似算法。此外，给出了基于焦元可信度转移度的证据融合公式和基于焦元可信度转移度的近似融合算法，并对Bayesian近似算法、投影近似算法和基于焦元可信度转移度的近似算法进行了比较分析。(2)对个体决策结果的一致性分析方法进行研究。基于证据理论的群决策方法的集结规则是DS合成公式，这个集结规则的要求是证据间不是完全冲突的，而这种约束是非常弱的，在这种约束下，不一定能保证结果的合理性。实际的群决策要求首先由决策者针对决策问题给出意见，然后要对意见的一致性进行分析，如果满足一致性要求就进入意见的集结与方案的选择过程，否则就需要对决策者的意见进行协调，以往在应用证据理论作为群决策方法时候，忽视了个体决策者意见的一致性分析与调整问题。本文对证据理论群决策方法中的个人意见的一致性问题进行研究，给出了合理度量证据间相似程度的三个条件，并给定一种新的证据相似程度的度量方法，这种新的相似度度量方法满足给定的三个条件。论文在相似度的基础上给出个人意见一致性的检验方法，同时给出在不满足一致性要求下的处理方法与调整措施，以保证群决策结果的合理性。(3)对集结规则悖论及其消除方法展开研究。个体决策者由于受到决策者知识结构、判断水平和个人偏好等众多主观因素的影响，决策者们很可能给出各种不同形式的偏好信息，这些不同的偏好之间可能存在冲突，而DS在融合冲突比较大的mass函数时，可能会产生悖论。为了保证证据理论群决策方法结果的合理性与有效性，本文对悖论的消除方法进行详细研究，归纳了几种常见的悖论形式，寻求通用的悖论消除方法，给出了基于专家权威的悖论消除方法和基于证据相似度的悖论消除方法，这几种悖论消除方法均为通用的悖论消除方法，而且这些消除方法的前提是不改变Ds合成公式。(4)对基于证据理论的群决策方法的应用步骤和系统过程进行研究。论文给出了基于证据理论的群决策方法在实际应用时的具体步骤，建立了基于证据理论的群决策方法的系统过程结构，并绘制了基于证据理论的群决策方法的系统过程结构图，这个系统过程结构图中包含了mass函数构造、一致性分析、一致性调整和悖论消除等方面的研究成果，并进一步通过具体案例对这种群决策方法的应用步骤和系统过程作了相应的分析说明。更多还原

【Abstract】 Evidence theory, also called DS Theory, was presented by Dempster and developed by Shafer. DS theory can describe many uncertainties properly. New explanations and definitions of probability are given in evidence theory, and the combination rule of different evidences is also given in it. So it can be used as a group-decision method.All that mentioned above make the DS Theory be studied as a group decision-making method, and many useful conclusions have been presented, but studies should be continued, and this dissertation mainly studies the following aspects:(1)Study on the computational complexity of DS combination formula. In DS theory, mass function is used to describe the preference of single decision-maker, and the DS combination formula is used to combine different decision-maker’s single decision. One of the major points of criticism the DS combination rule has to face is the computational complexity. The computational complexity of DS formula is NP-Complete. In this dissertation, approximation algorithms will be presented and the efficiency will be proved. This dissertation presents two new approximation algorithms and a new combination formula. One approximation algorithm is called projection approximation algorithm, the other one is called approximation algorithm based on the transferable degree of focal elements. Efficiency of projection algorithm is proved and the similarity and dissimilarity among the Bayesian approximation algorithm, projection approximation algorithm and approximation algorithm based on the transferable degree of focal elements are analyzed.(2)Study on the consistency analysis of single decision-maker’s decision. In most group decision-making methods, consistency analysis should be carried out before the final result is made in order to make the final decision more reasonable and more acceptable. If the decisions given by all decision-makers are satisfied to the condition of the consistency, final decision can be gotten according to the combination rule. The combination rule of evidence theory is DS formula, and this formula can combine any evidences as long as the confliction coefficient is not equal to 1.How to carry out the consistency analysis is studied in this dissertation. This dissertation presents three restriction conditions of a proper definition of similarity between evidence bodies and present a new method to measure the similarity of different evidences. Then a new method to define the consistence of evidences and three methods to adjust the evidences when the consistence is not satisfied are presented.(3) Study on the methods to dispel the absurdities of DS combination rule. The result of each decision-maker is influenced by the decision-maker’s knowledge, preference, and judgment ability. Each decision made by the single decision-maker may conflict to others. When the evidences contradict to others, some absurdities might be generated if the DS formula is used to combine the evidences. In order to settle this problem, this dissertation presents several methods to dispel the absurdities. These methods are universal methods to dispel the absurdities. And the presuppositions of all these methods are not to change the DS formula in combining the evidences.(4)Study on the steps of using the group-decision method based on the DS theory in actual decision problems. Detailed steps of using the group-decision method based on the DS theory and the systematical construction are presented. The systematical construction includes all have been studied above. Samples of using the group-decision method based on DS theory in uncertainty decision problems are used to illustrate the steps and the systematical construction in the end.更多还原