不确定型判断矩阵的一致性研究
发布时间：2018-09-05 15:53
【摘要】：在决策分析问题中,精确给出方案间重要程度的判断数值往往比较困难,决策者通常只能给出判断值的大致范围,如以区间数、区间粗糙数等形式给出.用大致范围给出重要程度间的判断值,更能反映客观事物间的模糊不确定性,也更符合人类的思维习惯.本文针对判断矩阵值为区间数和区间粗糙数的层次分析法,从以下几个方面进行研究:1、提出一种区间粗糙数间大小比较的新方法.现有文献对区间数大小比较的研究已获得丰硕的成果,但对区间粗糙数大小比较的研究相对欠缺,新的比较的方法充分吸收众多区间数间大小比较方法中的互补性、传递性等优点,为后续研究区间粗糙数判断矩阵的排序方法打基础.2、引入指数型区间数标度和指数型区间粗糙数标度.合理的标度是构建判断矩阵的基础,也是影响最终排序的决定性因素.新的标度不但充分克服了 1-9标度与人们心理感觉判断差距较大、评价结果与事实相反、一致性检验与思维一致性不协调等缺点,还融入指数标度的传递性、平均相对误差小于其他标度等优点.为判断矩阵的构建及判断矩阵一致性研究打下坚实的基础.3、重新定义了区间数判断矩阵及区间粗糙数判断矩阵的一致性.单一准则下,由所给定标度构建的判断矩阵的一致性,直接影响该准则下的排序向量,也间接决定了最终的排序向量,所以判断矩阵一致性的判断方法极为关键.新的一致性定义从直接与间接判断区间重叠部分比例的角度,抓住“具有一致性的判断矩阵在间接比较中,区间的占比较大”这一思想给出.新定义不但克服现有文献中对区间数判断矩阵及区间粗糙数判断矩阵一致性定义过于严格或过于宽松的缺点,还参照Saaty给出的一致性条件的方法,通过大量计算机的仿真实验给出判断矩阵具有一致性时应具有的数值条件.
[Abstract]:In the decision analysis problem, it is difficult to accurately give the judgment value of the importance degree between the schemes. The decision maker usually can only give the approximate range of the judgment value, such as interval number, interval rough number and so on. It can reflect the fuzzy uncertainty between the objective things and accord with the human thinking habits by giving the judgment value of the important degree in the general range. In this paper, a new method of comparing the size of interval rough numbers is proposed by using the Analytic hierarchy process (AHP), in which the judgment matrix values are interval numbers and interval rough numbers. The research on the comparison of interval numbers in the existing literature has been fruitful, but the study on the size comparison of interval rough numbers is relatively lacking. The new comparison method fully absorbs the complementarities of many interval number size comparison methods. Based on the transitivity, the paper introduces the exponential interval number scale and the exponential interval rough number scale for the further study of the ranking method of interval rough number judgment matrix. Reasonable scale is the basis of constructing judgment matrix and the decisive factor that affects the final ranking. The new scale not only overcomes the gap between 1-9 scale and people's psychological feeling judgment, but also integrates the transitivity of index scale. The average relative error is smaller than other scales. The consistency of interval number judgment matrix and interval rough number judgment matrix is redefined. Under the single criterion, the consistency of the judgment matrix constructed by the given scale directly affects the sorting vector under the criterion, and indirectly determines the final sorting vector, so the judgment method of the consistency of the judgment matrix is very important. The new definition of consistency, from the angle of directly and indirectly judging the proportion of overlapped parts of the interval, grasps the idea that the judgment matrix with consistency has a large proportion of the interval in the indirect comparison. The new definition not only overcomes the shortcomings of the consistency definition of interval number judgment matrix and interval rough number judgment matrix, but also refers to the method of consistency condition given by Saaty. Through a lot of computer simulation experiments, the numerical conditions for consistency of judgment matrix are given.
【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】：O151.21
本文编号：2224746
[Abstract]:In the decision analysis problem, it is difficult to accurately give the judgment value of the importance degree between the schemes. The decision maker usually can only give the approximate range of the judgment value, such as interval number, interval rough number and so on. It can reflect the fuzzy uncertainty between the objective things and accord with the human thinking habits by giving the judgment value of the important degree in the general range. In this paper, a new method of comparing the size of interval rough numbers is proposed by using the Analytic hierarchy process (AHP), in which the judgment matrix values are interval numbers and interval rough numbers. The research on the comparison of interval numbers in the existing literature has been fruitful, but the study on the size comparison of interval rough numbers is relatively lacking. The new comparison method fully absorbs the complementarities of many interval number size comparison methods. Based on the transitivity, the paper introduces the exponential interval number scale and the exponential interval rough number scale for the further study of the ranking method of interval rough number judgment matrix. Reasonable scale is the basis of constructing judgment matrix and the decisive factor that affects the final ranking. The new scale not only overcomes the gap between 1-9 scale and people's psychological feeling judgment, but also integrates the transitivity of index scale. The average relative error is smaller than other scales. The consistency of interval number judgment matrix and interval rough number judgment matrix is redefined. Under the single criterion, the consistency of the judgment matrix constructed by the given scale directly affects the sorting vector under the criterion, and indirectly determines the final sorting vector, so the judgment method of the consistency of the judgment matrix is very important. The new definition of consistency, from the angle of directly and indirectly judging the proportion of overlapped parts of the interval, grasps the idea that the judgment matrix with consistency has a large proportion of the interval in the indirect comparison. The new definition not only overcomes the shortcomings of the consistency definition of interval number judgment matrix and interval rough number judgment matrix, but also refers to the method of consistency condition given by Saaty. Through a lot of computer simulation experiments, the numerical conditions for consistency of judgment matrix are given.
【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】：O151.21
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