不确定性多属性决策方法的若干问题研究

发布时间：2018-02-25 15:13

本文关键词： 多属性决策区间数可能度满意一致性近似一致性　出处：《广西大学》2017年硕士论文　论文类型：学位论文

【摘要】：多属性决策作为现代决策领域的重要分支,就是通过一定的方式对一组(有限个)备选方案进行排序并选择.在层次分析法中,决策者(专家)对备选方案进行两两比较,给出判断矩阵.由于问题的复杂性,决策者往往很难用一个准确的数值表示其判断,因此判断矩阵的元素采用区间数、三角模糊数等来进行刻画就更为合理.从而形成了以模糊数排序、模糊数判断矩阵的一致性分析等重要研究内容的模糊多属性决策方法.本文针对不确定性多属性决策方法的若干问题进行了研究,主要取得了以下几个方面的成果:(1)区间数排序方法研究.证明了现有的基于可能度公式的两种区间数排序方法是等价的.基于区间数本身的不确定性,给出态度函数,利用积分的思想得到一个一般的区间数排序的可能度公式,发现已有的公式是该公式的特殊情形.给出了区间数互补判断矩阵的弱传递性一般定义.(2)发展了高校科研项目评估方法.针对同一专家给出不同偏好信息的情形,运用转换公式将互反判断矩阵与混合判断矩阵都转化为模糊互补判断矩阵,再利用最小方差法导出其排序向量.采用集结算子对专家给出的判断信息进行集结,建立了多属性群体决策分析模型.对于判断信息为三角模糊数的情形,基于Saaty经典层次分析法中的特征向量法,给出三角模糊数互反判断矩阵的满意一致性定义,提出一种基于三角模糊数互反判断矩阵的方案排序新方法.(3)给出了虚拟企业伙伴选择问题的一种新方法.考虑决策者在对方案进行两两比较时具有随机性,提出区间数互反判断矩阵的近似一致性概念,利用区间数互反判断矩阵的互反性及近似一致性概念,给出了构造出满足近似一致的区间数互反判断矩阵的方法.
[Abstract]:As an important branch of modern decision making field, multi-attribute decision making is to sort and select a group of (limited) alternatives in a certain way. In the Analytic hierarchy process (AHP), decision makers (experts) compare the alternatives by two or two. Because of the complexity of the problem, it is difficult for the decision maker to express his judgment with an accurate value, so the element of the judgment matrix is interval number. It is more reasonable to characterize triangular fuzzy numbers, so that the order of fuzzy numbers is formed. The fuzzy multi-attribute decision making method, which is used to analyze the consistency of fuzzy number judgment matrix, is studied in this paper. In this paper, we have obtained the following results: 1) the method of interval number ranking is studied. It is proved that the two kinds of interval number sorting methods based on possibility degree formula are equivalent. Based on the uncertainty of interval number itself, the attitude function is given. By using the idea of integral, we obtain a general formula for the possibility of ordering interval numbers. It is found that the existing formula is the special case of the formula. The general definition of weak transitivity of interval number complementary judgment matrix is given. The evaluation method of scientific research projects in colleges and universities is developed. Different preference information is given for the same expert. The reciprocal judgment matrix and the mixed judgment matrix are transformed into fuzzy complementary judgment matrix by using the transformation formula, and then the ranking vector is derived by using the method of minimum variance. The aggregation operator is used to aggregate the judgment information given by the experts. In this paper, a multi-attribute group decision analysis model is established. In the case that the judgment information is a triangular fuzzy number, the satisfactory consistency definition of the triangular fuzzy number reciprocal judgment matrix is given based on the eigenvector method in the classical analytic hierarchy process (Saaty). A new scheme ranking method based on triangular fuzzy number reciprocal judgment matrix is proposed. A new method for partner selection in virtual enterprises is presented. The concept of approximate consistency of interval number reciprocal judgment matrix is put forward, and the method of constructing interval number reciprocal judgement matrix which satisfies the approximate consistency is given by using the concepts of interval number reciprocal judgement matrix and approximate consistency.
【学位授予单位】：广西大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O225

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