区间数不确定多属性决策方法研究
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摘要
本文主要研究区间数不确定多属性决策问题,主要成果如下:
研究了区间数互反判断矩阵的一致性。给出了区间数互反判断矩阵的完全一致性、强一致性、一致性和满意一致性定义,讨论了这些定义和现有文献中相关定义的关系,并且给出了强一致性、一致性以及满意一致性的判别方法,为检验区间数互反判断矩阵是否合理提供了解决途径,并通过算例验证了判别方法的有效性、适用性。
研究了区间数互补判断矩阵的一致性及排序方法。从加型和积型两个角度就区间数互补判断矩阵的一致性问题进行了深入探讨,分别提出了加型(积型)完全一致性、加型(积型)强一致性、加型(积型)一致性和加型(积型)满意一致性定义,并给出了强一致性、一致性和满意一致性判别方法。其中,给出的区间数互补判断矩阵加型满意一致性概念及判别方法是建立在互补判断矩阵的满意一致性指标(CGCI)的基础上,避免了满意度(隶属度)函数参数的设置问题。此外,在一致性理论的基础上详细研究了区间数互补判断矩阵排序方法,分别基于加型(满意)一致性、积型完全一致、一致性和满意一致性的性质,给出了求解排序向量的优化模型。
研究了区间数判断矩阵偏好信息的群集结问题。针对区间数互补判断矩阵偏好信息的群组集结问题,给出了群组判断不一致的协调方法和群组偏好信息的集结方法。针对两种不同类型的区间数判断矩阵偏好信息的集结问题,构造了基于群组满意度最大的相对熵最优化偏好集结模型和基于互反判断矩阵一致性指标(CR)和互补判断矩阵一致性指标(CGCI)的集结模型。
研究了区间数多属性决策方法。针对无偏好信息的区间数多属性决策问题,提出了通过区间数的中值和长度信息求解属性熵权的一种新客观权重确定方法;针对有部分权重信息的区间数多属性决策问题提出了逼近理想关联度的决策分析方法和优劣势(SIR)排序方法;针对属性偏好信息以区间数互补判断矩阵形式给出、方案偏好信息以区间数互反判断矩阵给出的区间数多属性决策问题,提出了属性和方案偏好信息一致性程度的概念,给出了基于一致性程度最大的排序方法;提出了三角模糊数互反判断矩阵的概念,给出了求解三角模糊数互反判断矩阵权重向量的特征根方法,并给出了属性偏好以三角模糊数互反判断矩阵形式给出的区间数多属性决策问题的决策方法。
This dissertation mainly deals with multiple attribute decision making problems under interval uncertainty as follows.
The consistent theories of interval number reciprocal judgment matrix are discussed. The concepts such as perfect consistency, strong consistency, consistency and satisfactory consistency are introduced. Moreover, the relationships between these definitions and the existing ones in some papers are studied. It is also demonstrated that the consistent concept given is sound. The methods for testing strong consistency, consistency, and satisfactory are also proposed, which are illustrated valid and practical by numerical examples.
The consistency theories and priority methods of interval number complementary matrix are researched. This paper proposes the additive and multiplicative consistency for interval complementary judgment matrix and correlative definitions as well, such as the complete consistency, the strong consistency, the consistency and the satisfied consistency. At the same time, simple algorithms for testing the strong consistency, the consistency and the satisfied consistency are given. The definition and testing method of the additive satisfied consistency are based on the satisfactory consistency index (CGCI) of the complementary comparison matrix, so it is avoided to presume the thresholds for the tolerance parameter of fuzzy membership function that expresses the decision maker’s satisfaction. On the basis of consistency theories, programming models for priorities of interval number complementary judgment matrix are set up, which are examined to show the applications by numerical examples.
The group aggregation approach of interval number judgment matrix is studied. The coordinating techniques and aggregation method for the group preference information of interval number complementary judgment matrices are presented. Two models aggregating interval number reciprocal judgment matrix and interval number complementary judgment matrix are given. One is a relative entropy optimal model maximizing the group’s overall satisfaction. The other is a programming model based on the satisfactory consistency index CR of reciprocal judgment matrix and the satisfactory consistency index CGCI of complementary judgment matrix.
The interval multiple attribute decision making problems are studied. A method is proposed to determine entropy weights based on the midpoint and width of interval numbers under the situations where the decision maker has no preference information on attribute and alternative. Two interval multiple attribute decision making methods with only partial attribute weighting information are present. They are interval multiple attribute decision making method based on ideal incidence degree and superiority and inferiority ranking (SIR) method. As for the decision-making problems with the attribute preference information in the form of interval complementary judgment matrix and alternative preference information in the form of interval reciprocal judgment matrix, the concept of consistency degree for the preference information between attributes and alternatives is set forth. And, a quadratic programming model based on maximal consistency degree of preference information is established. Based on the eigenvector method to derive the priority weights from triangular fuzzy numbers reciprocal judgment matrix, an interval multiple attribute decision making method with attribute weighting information which takes the form of triangular fuzzy numbers reciprocal judgment matrix. Every method is illustrated the validity and practicality by example.
研究了区间数互反判断矩阵的一致性。给出了区间数互反判断矩阵的完全一致性、强一致性、一致性和满意一致性定义,讨论了这些定义和现有文献中相关定义的关系,并且给出了强一致性、一致性以及满意一致性的判别方法,为检验区间数互反判断矩阵是否合理提供了解决途径,并通过算例验证了判别方法的有效性、适用性。
研究了区间数互补判断矩阵的一致性及排序方法。从加型和积型两个角度就区间数互补判断矩阵的一致性问题进行了深入探讨,分别提出了加型(积型)完全一致性、加型(积型)强一致性、加型(积型)一致性和加型(积型)满意一致性定义,并给出了强一致性、一致性和满意一致性判别方法。其中,给出的区间数互补判断矩阵加型满意一致性概念及判别方法是建立在互补判断矩阵的满意一致性指标(CGCI)的基础上,避免了满意度(隶属度)函数参数的设置问题。此外,在一致性理论的基础上详细研究了区间数互补判断矩阵排序方法,分别基于加型(满意)一致性、积型完全一致、一致性和满意一致性的性质,给出了求解排序向量的优化模型。
研究了区间数判断矩阵偏好信息的群集结问题。针对区间数互补判断矩阵偏好信息的群组集结问题,给出了群组判断不一致的协调方法和群组偏好信息的集结方法。针对两种不同类型的区间数判断矩阵偏好信息的集结问题,构造了基于群组满意度最大的相对熵最优化偏好集结模型和基于互反判断矩阵一致性指标(CR)和互补判断矩阵一致性指标(CGCI)的集结模型。
研究了区间数多属性决策方法。针对无偏好信息的区间数多属性决策问题,提出了通过区间数的中值和长度信息求解属性熵权的一种新客观权重确定方法;针对有部分权重信息的区间数多属性决策问题提出了逼近理想关联度的决策分析方法和优劣势(SIR)排序方法;针对属性偏好信息以区间数互补判断矩阵形式给出、方案偏好信息以区间数互反判断矩阵给出的区间数多属性决策问题,提出了属性和方案偏好信息一致性程度的概念,给出了基于一致性程度最大的排序方法;提出了三角模糊数互反判断矩阵的概念,给出了求解三角模糊数互反判断矩阵权重向量的特征根方法,并给出了属性偏好以三角模糊数互反判断矩阵形式给出的区间数多属性决策问题的决策方法。
This dissertation mainly deals with multiple attribute decision making problems under interval uncertainty as follows.
The consistent theories of interval number reciprocal judgment matrix are discussed. The concepts such as perfect consistency, strong consistency, consistency and satisfactory consistency are introduced. Moreover, the relationships between these definitions and the existing ones in some papers are studied. It is also demonstrated that the consistent concept given is sound. The methods for testing strong consistency, consistency, and satisfactory are also proposed, which are illustrated valid and practical by numerical examples.
The consistency theories and priority methods of interval number complementary matrix are researched. This paper proposes the additive and multiplicative consistency for interval complementary judgment matrix and correlative definitions as well, such as the complete consistency, the strong consistency, the consistency and the satisfied consistency. At the same time, simple algorithms for testing the strong consistency, the consistency and the satisfied consistency are given. The definition and testing method of the additive satisfied consistency are based on the satisfactory consistency index (CGCI) of the complementary comparison matrix, so it is avoided to presume the thresholds for the tolerance parameter of fuzzy membership function that expresses the decision maker’s satisfaction. On the basis of consistency theories, programming models for priorities of interval number complementary judgment matrix are set up, which are examined to show the applications by numerical examples.
The group aggregation approach of interval number judgment matrix is studied. The coordinating techniques and aggregation method for the group preference information of interval number complementary judgment matrices are presented. Two models aggregating interval number reciprocal judgment matrix and interval number complementary judgment matrix are given. One is a relative entropy optimal model maximizing the group’s overall satisfaction. The other is a programming model based on the satisfactory consistency index CR of reciprocal judgment matrix and the satisfactory consistency index CGCI of complementary judgment matrix.
The interval multiple attribute decision making problems are studied. A method is proposed to determine entropy weights based on the midpoint and width of interval numbers under the situations where the decision maker has no preference information on attribute and alternative. Two interval multiple attribute decision making methods with only partial attribute weighting information are present. They are interval multiple attribute decision making method based on ideal incidence degree and superiority and inferiority ranking (SIR) method. As for the decision-making problems with the attribute preference information in the form of interval complementary judgment matrix and alternative preference information in the form of interval reciprocal judgment matrix, the concept of consistency degree for the preference information between attributes and alternatives is set forth. And, a quadratic programming model based on maximal consistency degree of preference information is established. Based on the eigenvector method to derive the priority weights from triangular fuzzy numbers reciprocal judgment matrix, an interval multiple attribute decision making method with attribute weighting information which takes the form of triangular fuzzy numbers reciprocal judgment matrix. Every method is illustrated the validity and practicality by example.
引文
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