判断矩阵的排序方法及相容性研究

发布时间：2018-04-05 18:43

本文选题：互补判断矩阵　切入点：排序方法　出处：《渤海大学》2017年硕士论文

【摘要】：排序方法问题是决策分析中的重要问题,具有广泛的实际应用价值。在现实生活中,公司或企业要进行某项决策或某一项选拔,如何快速而高效的将备选项目进行排序进而择优和决策显得尤为重要。但由于备选项在评价标准等各个方面的相近或相同,很难将其进行衡量排序进而决策,将这些方面以数据来标度并按一定的方式组合起来,形成判断矩阵。其中,互补判断矩阵的排序问题是专家们近几年研究的重点,其相容性问题是研究群组决策的判断信息一致性的关键性问题,它的成果对群组择优问题的精确性和适当性有着重大的影响,于是对相容性题目的钻研拥有至关重要的地位。首先,本文以互补判断矩阵的乘性一致性定义和加性一致性定义为基础,试着拟定一个新的函数,并创建对应的最优化模型,取得了相配的两个排序公式,且从理论上探讨了它们的一些特性,通过仿真实例论证该方法的可行性,简便性。其次,对群组择优问题中以互补判断矩阵的偏好信息为基础的相容性问题,提议了两种新的解析计算方法。基于相对熵和余弦相似度的意义,以提议的两个权衡互补判断矩阵相容性的通用目标为基本,细致的剖析和考虑它的相容性问题和一致性问题,并给出了评定互补判断矩阵的相容性准则和临界值,并经过仿真范例阐述了本文提出的计算方法的适当性和实际性。
[Abstract]:Ranking method is an important problem in decision analysis and has wide practical application value.In real life, it is very important for a company or an enterprise to make a decision or a selection, how to quickly and efficiently sort the candidate items and choose the best and decision.However, because the alternatives are similar or identical in various aspects such as evaluation criteria, it is difficult to measure and sort them and then make decisions. These aspects are scaled by data and combined in a certain way to form a judgment matrix.Among them, the ranking problem of complementary judgment matrix is the focus of experts' research in recent years, and its compatibility is the key problem to study the consistency of judgment information in group decision making.Its results have great influence on the accuracy and appropriateness of group selection, so it is very important to study compatibility problems.Firstly, on the basis of multiplicative consistency definition and additive consistency definition of complementary judgment matrix, we try to draw up a new function and create the corresponding optimization model.Some of their characteristics are discussed theoretically, and the feasibility and simplicity of the method are demonstrated by a simulation example.Secondly, two new analytical methods are proposed for the compatibility problem of group preference problem based on the preference information of complementary judgment matrix.Based on the meaning of relative entropy and cosine similarity, this paper analyzes and considers the compatibility problem and consistency problem of the proposed complementary judgment matrix based on the proposed common objective of balancing the compatibility of the complementary judgment matrix.The compatibility criterion and critical value of the evaluation complementary judgment matrix are given, and the appropriateness and practicability of the calculation method proposed in this paper are illustrated by a simulation example.
【学位授予单位】：渤海大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O225

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