基于群决策理论的智能信息处理方法及其应用
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摘要
随着现代决策科学的发展,决策理论在许多领域得到了广泛的应用,如工程建设和设计、系统工程、经济与管理、军事等方面；在决策分析中,由于人类思维判断的模糊性、不确定性以及客观事物的复杂性和不确定性,决策者在对事物进行两两比较或评价时往往不能给出确定的数值,这时用模糊数、语言短语或区间数等偏好信息表示会更加合理,目前有关以偏好信息形成判断矩阵的群决策方法已引起广泛关注,并取得了许多研究成果；但由各个专家给出的偏好信息要得到群体偏好信息,各个专家给出的判断矩阵就应具有较好的一致性,所以对判断矩阵本身一致性的研究具有重要意义。在给出方案综合评价时,合理、科学的确定方案各属性的权重也是非常重要的。电能质量作为一个多指标的综合体,只从某一项指标评判其质量是否合格不能满足用户对电能的要求；随着科技和电力市场的发展,电能作为配电方和用电方之间的交易商品,它的质量如何显得越来越重要,因此如何判断和衡量电能质量的好坏成为了研究的重要内容。
本文在国内外学者研究的基础上,基于矩阵的理论,对如何判定判断矩阵是否具有满意一致性进行研究,若具有满意一致性可以直接给出方案的排序；若判断矩阵不具有满意一致性,找出判断不合逻辑的元素并给出修正原则进行修正,得到具有满意一致性的判断矩阵；在判断矩阵具有一致性的基础上,研究如何确定对方案有偏好信息且偏好信息为判断矩阵的属性权重确定方法,这将为在电能质量综合评价过程中确定各指标主客观权重提供一定的理论基础。本文主要取得了如下几个方面的研究成果：
第一部分,分别给出了一种语言判断矩阵与偏好次序、效用值、互反判断矩阵和互补判断矩阵之间的相互转换方法,并从理论上证明了转换方法的合理性；给出了一种不同粒度语言判断矩阵之间的相互转化方法,这给决策者根据自己的知识背景和决策爱好给出不同偏好信息提供了理论基础；并给出了三种语言判断矩阵和互补判断矩阵的完全一致性判定方法。
第二部分,给出用判断矩阵的0-1型排列偏好关系矩阵是否是标准0-1型排列矩阵来判定判断矩阵是否具有满意一致性,并证明了这个条件是充要条件。这种方法不需要大量计算,只需要对判断矩阵做简单变换和调整,也适用于存在等价方案的情况；对于具有严格偏好关系的判断矩阵还给出了利用其偏好关系矩阵的不变因子或初等因子判定其是否具有满意一致性,并给出了证明过程。
第三部分,给出了一种判断矩阵不具有满意一致性时的一致性修正方法；利用二阶矩阵表示判断不合逻辑的三元素即循环圈矩阵,若判断矩阵不具有一致性,利用其0-1型排列偏好关系矩阵的二级子式是否是循环圈矩阵,找出所有三个元素组成的不合逻辑判断；还可以利用二级子式找出四个元素组成的不合逻辑判断,并根据行偏好值大小的修正原则进行修正,得到具有满意一致性的判断矩阵。
第四部分,针对决策者对方案有无偏好信息分别给出了属性权重确定方法。对于决策者对方案没有偏好信息的,给出了基于标准差最大化、属性值差值最大化及与正理想方案距离最小化、与负理想方案距离最大化的属性权重确定方法；对于决策者对方案有偏好信息的,利用方案综合属性值之比与对应的偏好信息之比相接近,分别给出了对方案有偏好信息且偏好信息为互反判断矩阵、互补判断矩阵和效用值的属性权重确定方法；另外还给出了基于语言评价矩阵和语言判断矩阵的决策者权重确定方法。
第五部分,将利用判断矩阵可得到各属性的主观权重确定方法和根据属性值得到属性客观权重确定方法运用到电能质量的综合评价中。根据专家或电能用户给出的两两电能指标比较的判断矩阵得出各指标的先后重要程度,按各指标占总重要程度的比重得出其主观权重；根据实际检测到的各电能指标在各个等级出现的时间段,利用属性客观权重确定方法得出各指标客观权重。
With the development of modern decision science, decision theory has been widely applied in many fields. Such as engineering design and construction, system engineering, economics and management, military, and etc. Due to the fuzziness, uncertainty of human judgment and the complexity, uncertainty of the objective things, decision makers can not give the exact numerical to the comparison of alternatives, and using the preference information of fuzzy number, interval number and language phrase will be more reasonable. To date, the group decision making of judgment matrices has obtained a lot of achievements. According to the different preference information to get the group preference information, each the judgment matrix should keep good consistency. So the research on the consistency of the judgment matrix is very important. It is also important to scientifically determine the attribute weight in the process of the comprehensive evaluation of alternatives.
Based on the state-of-the-art in this field and the theory of matrix, we study whether the judgment matrix has satisfying consistency. If the judgment matrix has satisfying consistency, the ranking of alternatives can be directly given. If the judgment matrix does not have satisfying consistency, we find all the judgment elements which are illegitimate and efficiently adjust circle. Based on satisfying consistency, we study how to determine attribute weight with preference information for judgment matrix, which will provid a theoretical foundation for determining the subjective and objective weight in comprehensive evaluation of power quality.
The specific contents are as follows:
In section one, the mutual transformation relations of linguistic judgment matrix and other four forms of preference information, including preference ordering, utility value, reciprocal judgment matrix and complementary judgment matrix, and the mutual transformation, are researched. A mutual transformation method of linguistic judgment matrices which have different granularity is given too. This provides a theoretical foundation for decision makers according to their background and decision making preference. The judgment methods of complete consistency of linguistic judgment matrix, reciprocal judgment matrix and complementary judgment matrix are given.
In section two, we judge whether a judgment matrix has satisfying consistency according to whether its0-1permutation preference relation matrix is standard0-1permutation matrix. And we further prove this condition is necessary and sufficient. The advantage of the proposed method is only simple transformation and adjustment is involved. This method also applies to the judgment matrix of existing alternatives which are equivalent. We also give another method to determine a judgment matrix whether has satisfying consistency according to the invariant factor or primary factor of its preference relation matrix.
In section three, we give an approach for regulating consistency according to two order matrices. If the judgment matrix is inconsistent, a definition of cyclic matrix is presented. We can get all the teams of the judgment elements that are illegitimate form the cyclic matrix and thereby efficiently adjust circle according to the row preference value. We can also find four elements which are illegitimate according to the two order matrix. Then the ranking of alternatives and the judgment matrix with satisfying consistency can be obtained.
In section four, we give methods of determine attribute weight with preference information or without. If decision makers do not give preference information, based on the standard deviation maximization, attribute value maximization, positive ideal solution minimization, negative ideal solution maximization, and methods of determine weight are given. If decision makers give preference information, methods of determine weight are presented according to the ratio of comprehensive attribute value and the corresponding preference information of reciprocal judgment matrix, complementary judgment matrix and utility value. In addition, the weights of decision makers are given based on linguistic evaluation matrix and linguistic judgment matrix.
In section five, the methods of determining the subjective weight based on judgment matrix and determining the objective weight based on the attribute value are applied to the comprehensive evaluation of power quality. Though the important degree obtained form the judgment matrix which are provided by experts or electric users, the subjective weights can be obtained according to the proportion of total degree of importance. According to the actual detected data at time of the various levels of the power index, the objective weights are obtained by using methods of determining the objective attribute weight.
本文在国内外学者研究的基础上,基于矩阵的理论,对如何判定判断矩阵是否具有满意一致性进行研究,若具有满意一致性可以直接给出方案的排序；若判断矩阵不具有满意一致性,找出判断不合逻辑的元素并给出修正原则进行修正,得到具有满意一致性的判断矩阵；在判断矩阵具有一致性的基础上,研究如何确定对方案有偏好信息且偏好信息为判断矩阵的属性权重确定方法,这将为在电能质量综合评价过程中确定各指标主客观权重提供一定的理论基础。本文主要取得了如下几个方面的研究成果：
第一部分,分别给出了一种语言判断矩阵与偏好次序、效用值、互反判断矩阵和互补判断矩阵之间的相互转换方法,并从理论上证明了转换方法的合理性；给出了一种不同粒度语言判断矩阵之间的相互转化方法,这给决策者根据自己的知识背景和决策爱好给出不同偏好信息提供了理论基础；并给出了三种语言判断矩阵和互补判断矩阵的完全一致性判定方法。
第二部分,给出用判断矩阵的0-1型排列偏好关系矩阵是否是标准0-1型排列矩阵来判定判断矩阵是否具有满意一致性,并证明了这个条件是充要条件。这种方法不需要大量计算,只需要对判断矩阵做简单变换和调整,也适用于存在等价方案的情况；对于具有严格偏好关系的判断矩阵还给出了利用其偏好关系矩阵的不变因子或初等因子判定其是否具有满意一致性,并给出了证明过程。
第三部分,给出了一种判断矩阵不具有满意一致性时的一致性修正方法；利用二阶矩阵表示判断不合逻辑的三元素即循环圈矩阵,若判断矩阵不具有一致性,利用其0-1型排列偏好关系矩阵的二级子式是否是循环圈矩阵,找出所有三个元素组成的不合逻辑判断；还可以利用二级子式找出四个元素组成的不合逻辑判断,并根据行偏好值大小的修正原则进行修正,得到具有满意一致性的判断矩阵。
第四部分,针对决策者对方案有无偏好信息分别给出了属性权重确定方法。对于决策者对方案没有偏好信息的,给出了基于标准差最大化、属性值差值最大化及与正理想方案距离最小化、与负理想方案距离最大化的属性权重确定方法；对于决策者对方案有偏好信息的,利用方案综合属性值之比与对应的偏好信息之比相接近,分别给出了对方案有偏好信息且偏好信息为互反判断矩阵、互补判断矩阵和效用值的属性权重确定方法；另外还给出了基于语言评价矩阵和语言判断矩阵的决策者权重确定方法。
第五部分,将利用判断矩阵可得到各属性的主观权重确定方法和根据属性值得到属性客观权重确定方法运用到电能质量的综合评价中。根据专家或电能用户给出的两两电能指标比较的判断矩阵得出各指标的先后重要程度,按各指标占总重要程度的比重得出其主观权重；根据实际检测到的各电能指标在各个等级出现的时间段,利用属性客观权重确定方法得出各指标客观权重。
With the development of modern decision science, decision theory has been widely applied in many fields. Such as engineering design and construction, system engineering, economics and management, military, and etc. Due to the fuzziness, uncertainty of human judgment and the complexity, uncertainty of the objective things, decision makers can not give the exact numerical to the comparison of alternatives, and using the preference information of fuzzy number, interval number and language phrase will be more reasonable. To date, the group decision making of judgment matrices has obtained a lot of achievements. According to the different preference information to get the group preference information, each the judgment matrix should keep good consistency. So the research on the consistency of the judgment matrix is very important. It is also important to scientifically determine the attribute weight in the process of the comprehensive evaluation of alternatives.
Based on the state-of-the-art in this field and the theory of matrix, we study whether the judgment matrix has satisfying consistency. If the judgment matrix has satisfying consistency, the ranking of alternatives can be directly given. If the judgment matrix does not have satisfying consistency, we find all the judgment elements which are illegitimate and efficiently adjust circle. Based on satisfying consistency, we study how to determine attribute weight with preference information for judgment matrix, which will provid a theoretical foundation for determining the subjective and objective weight in comprehensive evaluation of power quality.
The specific contents are as follows:
In section one, the mutual transformation relations of linguistic judgment matrix and other four forms of preference information, including preference ordering, utility value, reciprocal judgment matrix and complementary judgment matrix, and the mutual transformation, are researched. A mutual transformation method of linguistic judgment matrices which have different granularity is given too. This provides a theoretical foundation for decision makers according to their background and decision making preference. The judgment methods of complete consistency of linguistic judgment matrix, reciprocal judgment matrix and complementary judgment matrix are given.
In section two, we judge whether a judgment matrix has satisfying consistency according to whether its0-1permutation preference relation matrix is standard0-1permutation matrix. And we further prove this condition is necessary and sufficient. The advantage of the proposed method is only simple transformation and adjustment is involved. This method also applies to the judgment matrix of existing alternatives which are equivalent. We also give another method to determine a judgment matrix whether has satisfying consistency according to the invariant factor or primary factor of its preference relation matrix.
In section three, we give an approach for regulating consistency according to two order matrices. If the judgment matrix is inconsistent, a definition of cyclic matrix is presented. We can get all the teams of the judgment elements that are illegitimate form the cyclic matrix and thereby efficiently adjust circle according to the row preference value. We can also find four elements which are illegitimate according to the two order matrix. Then the ranking of alternatives and the judgment matrix with satisfying consistency can be obtained.
In section four, we give methods of determine attribute weight with preference information or without. If decision makers do not give preference information, based on the standard deviation maximization, attribute value maximization, positive ideal solution minimization, negative ideal solution maximization, and methods of determine weight are given. If decision makers give preference information, methods of determine weight are presented according to the ratio of comprehensive attribute value and the corresponding preference information of reciprocal judgment matrix, complementary judgment matrix and utility value. In addition, the weights of decision makers are given based on linguistic evaluation matrix and linguistic judgment matrix.
In section five, the methods of determining the subjective weight based on judgment matrix and determining the objective weight based on the attribute value are applied to the comprehensive evaluation of power quality. Though the important degree obtained form the judgment matrix which are provided by experts or electric users, the subjective weights can be obtained according to the proportion of total degree of importance. According to the actual detected data at time of the various levels of the power index, the objective weights are obtained by using methods of determining the objective attribute weight.
引文
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