层次分析法的若干问题研究及应用
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摘要
随着社会的发展,决策问题越来越复杂,不但需要快速做出决策,而且需要分析决策问题中多种不确定因素所带来的决策困难。多属性决策作为决策分析的重要组成部分,在实际生活中广泛存在。层次分析法(Analytic hierarchy process, AHP)是经典的多属性决策方法,在很多领域得到了应用。然而,AHP仍有许多理论问题没有得到解决,现有方法尚存在很多不足之处,需要提出新方法加以解决。对此,本文在理论方法上进行了分析和研究,集中在以下四个方面:
(1) 判断矩阵一致性研究
判断矩阵的一致性问题是AHP的核心问题。对判断矩阵一致性检验来说,仅仅通过检验一致性比例来判定其是否具有一致性是不够的,而是需要同时检验基本一致性和次序一致性。在次序一致性方面,提出把1～9标度的判断矩阵转化成0～1矩阵,利用图论理论得到检验判断矩阵是否具有次序一致性的算法,并对不具有次序一致性的判断矩阵提出两条修改原则。
在基本一致性研究方面,指出现有改进方法的主要缺点是没有考虑保留决策者的原始判断信息。对此,以最大程度保留决策者原始判断信息为出发点,提出两个新的改进模型。
此外,依据判断矩阵一致性的研究成果,提出一种将灵敏度分析和一致性分析相结合的研究方法,进而给出既能保持决策者原始偏好,又满足一致性要求的综合决策区域。
(2) 不确定AHP理论研究
区间数AHP方法在解决复杂决策问题时得到了广泛应用。针对区间数判断矩阵的特点,基于随机确定性判断矩阵的概念,给出区间数判断矩阵局部一致性和一致性程度的定义,进而提出一种新的权重求解模型。本文还针对另一类区间数判断矩阵——区间数互补判断矩阵提出了一种新的权重求解方法,进一步完善了区间数判断矩阵权重求解的理论框架。
决策者在进行复杂问题决策时,经常得到不完全判断矩阵。本文定义了不完全判断矩阵局部一致性和局部满意一致性,并建立了判别其是否具
With the development of society, the decision problems are becoming more and more complicated. One side, the decision makers need to make decisions rapidly. The other side, they need to analyze the decision-making difficulty owing to the uncertainty of the decision-making problems. As one important constitutive part of the decision-making problem, the multi attribute decision-making problem exists widely in our life. The analytic hierarchy process (AHP) is widely used in many fields as a classical multi attribute decision-making approach. However, many theories problem haven't solved and some approaches have many shortcomings. Therefore, new approaches should be put forward. The following four sides about the AHP theories and approaches are concerned.(1) Comparison matrix consistency research. Comparison matrix consistency is the core problem in the AHP. To the consistency test of the comparison matrix, it is not enough to check its consistency ratio to test whether the comparison matrix is consistent or not. Otherwise, it should check both the basic consistency and the rank consistency of the comparison matrix. Firstly, the 1~9 scale comparison matrix is transferred into the 0~1 comparison matrix. And then, the test algorithm is put forward based on the chart theory. Secondly, two modification rules are developed to modify the rank inconsistent matrix.The existing modification approaches to modify the inconsistent comparison matrix have not considered keeping the original decision-making information. To solve this problem, two new modification models based on keeping the most information that the original comparison matrix contains are put forward.In addition, the sensitivity and consistency integration analysis approach is put forward based on the consistency analysis result of the comparison matrix.Then, the integration decision-making region which can preserve the original preference and can satisfy the consistency requirement is obtained via the suggested approach.
(2) AHP theory research under the uncertainty decision-making condition.The interval numbers AHP is widely used when solving the complicated decision-making problems. However, the consistency and weights analysis are not perfectly.The notions of the local consistency and the consistency extent are introduced to measure the consistency of the interval numbers comparison matrix based on the idea of the stochastic crisp comparison matrix. Then a new model is developed to estimate the weights. Furthermore, the weights of the interval numbers complementary comparison matrix are studied. The aim of this paper is to perfect the weights theory frame of the AHP under the uncertainty decision-making condition.When solving the complicated decision-making problems, the decision maker can often obtain the incomplete pairwise comparison matrix (IPCM). The consistency and weights analysis of the incomplete pairwise comparison matrix are studied in this paper. According to the definition of stochastic crisp comparison matrix, the local consistency and local satisfactory consistency for the incomplete pairwise comparison matrix are defined. Then, a mathematical notion model is developed to test whether the IPCM is consistent or not. In addition, to solve the problem of Harker's weights method that it cannot estimate the uncertainty that the incomplete pairwise comparison matrix contains, a new weight model solved by particle swarm optimization is put forward to estimate the weight upper range and low range.The decision makers may not express their preferences correctly via the original approaches or its extensions in AHP under some uncertainty decision-making environments. In addition, information losing is inevitable when integrating multiple experts' preferences under the group. decision-making environments. To solve these problems, the comparison matrix which entries are subject to the discrete distribution is studied and the unascertained number is introduced for a pairwise comparison matrix. Moreover, the consistency concept of the unascertained numbers comparison matrix is analyzed, and two consistency indexes, the local consistency and the consistency extent are developed. According to the property of the unascertained numbers comparison matrix, two weight approaches are put forward, one is based on the rule of unascertained numbers, and the other is via the Monte Carlo simulation.(3) Combination weights based on the AHP. When solving the multi attribute decision-making problems, most approaches are involved in the attribute weights calculation. It can be divided into the subjective weights and the objective weights approaches. To make the decision-making results more
(1) 判断矩阵一致性研究
判断矩阵的一致性问题是AHP的核心问题。对判断矩阵一致性检验来说,仅仅通过检验一致性比例来判定其是否具有一致性是不够的,而是需要同时检验基本一致性和次序一致性。在次序一致性方面,提出把1～9标度的判断矩阵转化成0～1矩阵,利用图论理论得到检验判断矩阵是否具有次序一致性的算法,并对不具有次序一致性的判断矩阵提出两条修改原则。
在基本一致性研究方面,指出现有改进方法的主要缺点是没有考虑保留决策者的原始判断信息。对此,以最大程度保留决策者原始判断信息为出发点,提出两个新的改进模型。
此外,依据判断矩阵一致性的研究成果,提出一种将灵敏度分析和一致性分析相结合的研究方法,进而给出既能保持决策者原始偏好,又满足一致性要求的综合决策区域。
(2) 不确定AHP理论研究
区间数AHP方法在解决复杂决策问题时得到了广泛应用。针对区间数判断矩阵的特点,基于随机确定性判断矩阵的概念,给出区间数判断矩阵局部一致性和一致性程度的定义,进而提出一种新的权重求解模型。本文还针对另一类区间数判断矩阵——区间数互补判断矩阵提出了一种新的权重求解方法,进一步完善了区间数判断矩阵权重求解的理论框架。
决策者在进行复杂问题决策时,经常得到不完全判断矩阵。本文定义了不完全判断矩阵局部一致性和局部满意一致性,并建立了判别其是否具
With the development of society, the decision problems are becoming more and more complicated. One side, the decision makers need to make decisions rapidly. The other side, they need to analyze the decision-making difficulty owing to the uncertainty of the decision-making problems. As one important constitutive part of the decision-making problem, the multi attribute decision-making problem exists widely in our life. The analytic hierarchy process (AHP) is widely used in many fields as a classical multi attribute decision-making approach. However, many theories problem haven't solved and some approaches have many shortcomings. Therefore, new approaches should be put forward. The following four sides about the AHP theories and approaches are concerned.(1) Comparison matrix consistency research. Comparison matrix consistency is the core problem in the AHP. To the consistency test of the comparison matrix, it is not enough to check its consistency ratio to test whether the comparison matrix is consistent or not. Otherwise, it should check both the basic consistency and the rank consistency of the comparison matrix. Firstly, the 1~9 scale comparison matrix is transferred into the 0~1 comparison matrix. And then, the test algorithm is put forward based on the chart theory. Secondly, two modification rules are developed to modify the rank inconsistent matrix.The existing modification approaches to modify the inconsistent comparison matrix have not considered keeping the original decision-making information. To solve this problem, two new modification models based on keeping the most information that the original comparison matrix contains are put forward.In addition, the sensitivity and consistency integration analysis approach is put forward based on the consistency analysis result of the comparison matrix.Then, the integration decision-making region which can preserve the original preference and can satisfy the consistency requirement is obtained via the suggested approach.
(2) AHP theory research under the uncertainty decision-making condition.The interval numbers AHP is widely used when solving the complicated decision-making problems. However, the consistency and weights analysis are not perfectly.The notions of the local consistency and the consistency extent are introduced to measure the consistency of the interval numbers comparison matrix based on the idea of the stochastic crisp comparison matrix. Then a new model is developed to estimate the weights. Furthermore, the weights of the interval numbers complementary comparison matrix are studied. The aim of this paper is to perfect the weights theory frame of the AHP under the uncertainty decision-making condition.When solving the complicated decision-making problems, the decision maker can often obtain the incomplete pairwise comparison matrix (IPCM). The consistency and weights analysis of the incomplete pairwise comparison matrix are studied in this paper. According to the definition of stochastic crisp comparison matrix, the local consistency and local satisfactory consistency for the incomplete pairwise comparison matrix are defined. Then, a mathematical notion model is developed to test whether the IPCM is consistent or not. In addition, to solve the problem of Harker's weights method that it cannot estimate the uncertainty that the incomplete pairwise comparison matrix contains, a new weight model solved by particle swarm optimization is put forward to estimate the weight upper range and low range.The decision makers may not express their preferences correctly via the original approaches or its extensions in AHP under some uncertainty decision-making environments. In addition, information losing is inevitable when integrating multiple experts' preferences under the group. decision-making environments. To solve these problems, the comparison matrix which entries are subject to the discrete distribution is studied and the unascertained number is introduced for a pairwise comparison matrix. Moreover, the consistency concept of the unascertained numbers comparison matrix is analyzed, and two consistency indexes, the local consistency and the consistency extent are developed. According to the property of the unascertained numbers comparison matrix, two weight approaches are put forward, one is based on the rule of unascertained numbers, and the other is via the Monte Carlo simulation.(3) Combination weights based on the AHP. When solving the multi attribute decision-making problems, most approaches are involved in the attribute weights calculation. It can be divided into the subjective weights and the objective weights approaches. To make the decision-making results more
引文
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