混合型多属性群决策方法研究
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摘要
在社会、经济与军事等许多领域中都存在大量的多属性群决策问题,这些问题中常常同时包含定量属性和定性属性,由于不同属性往往具有不同的性质,因此用多种类型的数据(如精确实数、区间数、模糊数、语言值等)来表示对这些属性的评价更为合适,并且为了避免因单个决策者的失误而导致错误决策,造成不良后果,提高决策水平和效率,决策过程中需要多个决策者(专家)参与,这样就产生了混合型多属性群决策问题。多属性群决策主要研究决策群体如何在集结决策者个体判断的基础上,构造群体判断,根据问题的属性对备选方案进行群体偏好的选优、排序、分类或分级。而混合型多属性群决策问题需要同时处理定量属性和定性属性,其属性值包括多种数据类型,使得决策问题更为复杂。对混合型多属性群决策问题的研究具有重要的理论意义和实际应用背景。本文针对属性值为精确数、区间数、模糊数和语言值的混合多属性群决策中的相关问题进行研”究,给出具体的解决方法,主要研究成果如下：
(1)研究了混合型多属性群决策中的群体一致性问题,针对专家的评价信息完全和评价信息不完全两种情况分别提出了群体一致性分析方法。在评价信息完全时,提出一个基于属性层面的差异度——一致度的群体一致性方法。在该方法中,计算过程不需进行数据类型转换,避免了因数据类型转换而造成的信息损失和信息扭曲；当群体未达成一致时,专家可以有针对性地修改相应的评价信息,从而使群体尽快达成一致,同时避免了专家评价信息的过度修改。当评价信息不完全时,根据不完全信息处理的两种思路分别给出了两种相应的群体一致性分析方法,一种是根据一定的约束条件建立线性规划模型,对缺失值进行填充,将评价信息不完全的评价矩阵转换成评价信息完全的评价矩阵后进行群体一致性分析；另一种是不进行缺失信息的填充直接在评价信息不完全的评价矩阵上进行群体一致性的分析。最后将这三种分析方法进行了比较,从中可以看出,在评价信息不完全的情况下,不改变初始的评价信息直接对不完全评价矩阵进行群体一致性分析更符合实际情况。另外,还针对不完全信息下评价矩阵的完全度、方案的完全度和属性的完全度进行了探讨。
(2)研究了混合型多属性群决策中的排序问题,根据评价信息的完全性和属性之间的补偿性分四种情况即评价信息完全且属性之间可以完全相互补偿、评价信息完全且属性之间不可以完全相互补偿、评价信息不完全且属性之间可以完全相互补偿和评价信息不完全且属性之间不可以完全相互补偿相应的提出基于优势度和优势关系的群排序方法,并将这些方法与现有的一些方法进行了比较。这些方法通过比较方案的优势度对备选方案进行排序,这样即避免了现有的一部分关于混合型决策问题的研究中进行不同类型的偏好信息一致化时造成的信息损失和信息扭曲,又避免了现有的用扩展的TOPSIS方法解决混合型多属性群决策问题时需找出正负理想方案的过程和进行复杂的计算,而直接在候选方案之间进行优势度的计算其结果也更为精确。为了计算方案之间的优势度,分别针对各数据类型定义了数据之间优势度的计算方法。
(3)关于群决策中的分级问题现有的研究并不多。本文研究了混合型多属性群决策中的分级问题,根据不同的情况分别提出了不同的分级方法。当相邻类间的类边界值已知时,根据属性之间是否可以相互补偿分别建立了基于优势度和优势关系的分级方法；当类边界值未知但已知各类别的代表方案时,将基于距离的聚类方法扩展到群决策的分级问题中,建立了相应的基于距离的混合型多属性群决策分级方法；当专家给出各自关于各方案的分级意见时,提出了基于概率的分级方法。这些方法为混合型多属性群决策中的分级问题的解决提供了新的途径。
(4)通过相应的一些实例如供应商选择、供应商分级等实例验证了所提方法的实用性和有效性,并研究了所提出的方法在企业合作创新伙伴选择中的应用。
本文的研究成果丰富了混合型多属性群决策的研究,为混合型多属性群决策中群体一致性的分析、某些条件下的群排序问题和分级问题的解决提供了新的有效的方法。
There are a lot of multi-attribute group decision making in many domains such as society、economy and military. These problems often contain quantitative attributes and qualitative attributes, these values of attribute are precise number, interval number, fuzzy number and linguistic values, etc., and in order to avoid wrong decisions due to the mistakes of individual decision-makers lead to adverse consequences to improve decision-making level and efficiency of decision-making processes, there require multiple decision-makers involved in the decision-making process, which form hybrid multi-attribute group decision-making (HMAGDM)problems. Main researches of the multiple attribute group decision-making focused on how to aggregate individual judgment to form group judgment, to select the relative satisfactory alternatives, to rank alternatives, to classify or sort alternatives according to the attribute value of alternatives. Because of quantitative attributes and qualitative attributes are handled in HMAGDM, these values of attribute are various types of data, which improve the complexity of problems. The study for HMAGDM problem has important theoretical significance and practical application background. In this thesis, some problems of HMAGDM in which its attribute values are precise numbers, interval numbers, fuzzy numbers and linguistic values are investigated, some specific solutions are proposed. The main contributions of this thesis are summarized as follows:
(l)The problem of consensus among group opinions in hybrid multi-attribute group decision making is studied. Several consensus analysis methods for two cases which decision makers'assessment information is complete and decision makers'assessment information is incomplete are separately proposed. Aimed at the case of complete assessment information, this paper proposes a consensus analysis method which based on the degree of difference-the degree of consensus in the attribute level, so, in the process of calculating, data type does not need any conversion, which, in turn, secures no information losses. When the group is not in consensus, experts targeted revising the assessment information of relevant attribute making the group agree each other as soon as possible. At the same time, excessive modification of assessment information can be avoided. Then, aimed at the case of incomplete assessment information, two new consensus analysis methods are proposed according to two ways of processing incomplete information. In fist method, a linear programming model is build up according to a certain constraint conditions for filling missing value, through the calculation of the model to get missing value, so, incomplete assessment matrix is converted complete assessment matrix, then consensus analysis is done in this complete assessment matrix. In the second method, missing value not to be filled, consensus analysis is directly done in the incomplete assessment matrix. Finally the three methods of consensus analysis are compared. The compared result shows that in the case of incomplete assessment information, consensus analysis is directly done on the incomplete assessment matrix without change to initial assessment information and that is more consistent with the actual situation. In addition, aimed at the case of incomplete assessment information, the completely degree of assessment matrix, alternative's complete degree and attribute's completely degree were discussed.
(2)Ranking problem in hybrid multi-attribute group decision making is researched. Four ranking methods based on dominance degree and dominance relation are proposed according to four cases of the completeness of the assessment information and the compensatory among attributes namely complete assessment information and complete mutual compensation among attributes, complete assessment information and incomplete mutual compensation among attributes, incomplete assessment information and complete mutual compensation among attributes and incomplete assessment information and incomplete mutual compensation among attributes,and these methods were compared with some existing methods.These methods rank alternatives by comparing the dominance degree of alternative.These methods avoid information loss and information distortion be caused by uniform the preference information in the most of the existing ranking methods of hybrid decision making problems. Furthermore, these methods omitted the process to find positive ideal solution (PIS) and negative ideal solution (NIS) with the expanded TOPSIS method to solve hybrid group decision making problems,and that directly calculated the dominance degree between alternatives,the results are also more accurately. In order to calculate the dominance degree between alternatives, methods of calculation for dominance degree between data on the each data type are respectively proposed.
(3) This paper proposed several different sorting methods to solve sorting problem in hybrid multi-attribute group decision making. When the limit profiles of between adjacent classes are known, a sorting method based on the dominance degree and dominance relation is proposed. when the limit profiles between adjacent classes are unknown but reference alternatives which represent each class are known, the clustering method based on the distance is expanded to the sorting of group decision making problems, a sorting method based on distance is established. When experts given their rating opinion about each alternative, a sorting method based on the probability is proposed. These methods provide new ways to solve sorting problems of hybrid multi-attribute group decision making.
(4)Some examples such as supplier selection, suppliers sorting, etc are given to illustrate the feasibility and validity of these proposed methods, and, application of the proposed ranking method in enterprise cooperation innovation partner selection is studied.
The above mentioned contributions has further enriched the study of hybrid multi-attribute group decision-making, and provide new methods for consensus analysis in HMAGDM,ranking under certain conditions in HMAGDM and sorting in HMAGDM.
(1)研究了混合型多属性群决策中的群体一致性问题,针对专家的评价信息完全和评价信息不完全两种情况分别提出了群体一致性分析方法。在评价信息完全时,提出一个基于属性层面的差异度——一致度的群体一致性方法。在该方法中,计算过程不需进行数据类型转换,避免了因数据类型转换而造成的信息损失和信息扭曲；当群体未达成一致时,专家可以有针对性地修改相应的评价信息,从而使群体尽快达成一致,同时避免了专家评价信息的过度修改。当评价信息不完全时,根据不完全信息处理的两种思路分别给出了两种相应的群体一致性分析方法,一种是根据一定的约束条件建立线性规划模型,对缺失值进行填充,将评价信息不完全的评价矩阵转换成评价信息完全的评价矩阵后进行群体一致性分析；另一种是不进行缺失信息的填充直接在评价信息不完全的评价矩阵上进行群体一致性的分析。最后将这三种分析方法进行了比较,从中可以看出,在评价信息不完全的情况下,不改变初始的评价信息直接对不完全评价矩阵进行群体一致性分析更符合实际情况。另外,还针对不完全信息下评价矩阵的完全度、方案的完全度和属性的完全度进行了探讨。
(2)研究了混合型多属性群决策中的排序问题,根据评价信息的完全性和属性之间的补偿性分四种情况即评价信息完全且属性之间可以完全相互补偿、评价信息完全且属性之间不可以完全相互补偿、评价信息不完全且属性之间可以完全相互补偿和评价信息不完全且属性之间不可以完全相互补偿相应的提出基于优势度和优势关系的群排序方法,并将这些方法与现有的一些方法进行了比较。这些方法通过比较方案的优势度对备选方案进行排序,这样即避免了现有的一部分关于混合型决策问题的研究中进行不同类型的偏好信息一致化时造成的信息损失和信息扭曲,又避免了现有的用扩展的TOPSIS方法解决混合型多属性群决策问题时需找出正负理想方案的过程和进行复杂的计算,而直接在候选方案之间进行优势度的计算其结果也更为精确。为了计算方案之间的优势度,分别针对各数据类型定义了数据之间优势度的计算方法。
(3)关于群决策中的分级问题现有的研究并不多。本文研究了混合型多属性群决策中的分级问题,根据不同的情况分别提出了不同的分级方法。当相邻类间的类边界值已知时,根据属性之间是否可以相互补偿分别建立了基于优势度和优势关系的分级方法；当类边界值未知但已知各类别的代表方案时,将基于距离的聚类方法扩展到群决策的分级问题中,建立了相应的基于距离的混合型多属性群决策分级方法；当专家给出各自关于各方案的分级意见时,提出了基于概率的分级方法。这些方法为混合型多属性群决策中的分级问题的解决提供了新的途径。
(4)通过相应的一些实例如供应商选择、供应商分级等实例验证了所提方法的实用性和有效性,并研究了所提出的方法在企业合作创新伙伴选择中的应用。
本文的研究成果丰富了混合型多属性群决策的研究,为混合型多属性群决策中群体一致性的分析、某些条件下的群排序问题和分级问题的解决提供了新的有效的方法。
There are a lot of multi-attribute group decision making in many domains such as society、economy and military. These problems often contain quantitative attributes and qualitative attributes, these values of attribute are precise number, interval number, fuzzy number and linguistic values, etc., and in order to avoid wrong decisions due to the mistakes of individual decision-makers lead to adverse consequences to improve decision-making level and efficiency of decision-making processes, there require multiple decision-makers involved in the decision-making process, which form hybrid multi-attribute group decision-making (HMAGDM)problems. Main researches of the multiple attribute group decision-making focused on how to aggregate individual judgment to form group judgment, to select the relative satisfactory alternatives, to rank alternatives, to classify or sort alternatives according to the attribute value of alternatives. Because of quantitative attributes and qualitative attributes are handled in HMAGDM, these values of attribute are various types of data, which improve the complexity of problems. The study for HMAGDM problem has important theoretical significance and practical application background. In this thesis, some problems of HMAGDM in which its attribute values are precise numbers, interval numbers, fuzzy numbers and linguistic values are investigated, some specific solutions are proposed. The main contributions of this thesis are summarized as follows:
(l)The problem of consensus among group opinions in hybrid multi-attribute group decision making is studied. Several consensus analysis methods for two cases which decision makers'assessment information is complete and decision makers'assessment information is incomplete are separately proposed. Aimed at the case of complete assessment information, this paper proposes a consensus analysis method which based on the degree of difference-the degree of consensus in the attribute level, so, in the process of calculating, data type does not need any conversion, which, in turn, secures no information losses. When the group is not in consensus, experts targeted revising the assessment information of relevant attribute making the group agree each other as soon as possible. At the same time, excessive modification of assessment information can be avoided. Then, aimed at the case of incomplete assessment information, two new consensus analysis methods are proposed according to two ways of processing incomplete information. In fist method, a linear programming model is build up according to a certain constraint conditions for filling missing value, through the calculation of the model to get missing value, so, incomplete assessment matrix is converted complete assessment matrix, then consensus analysis is done in this complete assessment matrix. In the second method, missing value not to be filled, consensus analysis is directly done in the incomplete assessment matrix. Finally the three methods of consensus analysis are compared. The compared result shows that in the case of incomplete assessment information, consensus analysis is directly done on the incomplete assessment matrix without change to initial assessment information and that is more consistent with the actual situation. In addition, aimed at the case of incomplete assessment information, the completely degree of assessment matrix, alternative's complete degree and attribute's completely degree were discussed.
(2)Ranking problem in hybrid multi-attribute group decision making is researched. Four ranking methods based on dominance degree and dominance relation are proposed according to four cases of the completeness of the assessment information and the compensatory among attributes namely complete assessment information and complete mutual compensation among attributes, complete assessment information and incomplete mutual compensation among attributes, incomplete assessment information and complete mutual compensation among attributes and incomplete assessment information and incomplete mutual compensation among attributes,and these methods were compared with some existing methods.These methods rank alternatives by comparing the dominance degree of alternative.These methods avoid information loss and information distortion be caused by uniform the preference information in the most of the existing ranking methods of hybrid decision making problems. Furthermore, these methods omitted the process to find positive ideal solution (PIS) and negative ideal solution (NIS) with the expanded TOPSIS method to solve hybrid group decision making problems,and that directly calculated the dominance degree between alternatives,the results are also more accurately. In order to calculate the dominance degree between alternatives, methods of calculation for dominance degree between data on the each data type are respectively proposed.
(3) This paper proposed several different sorting methods to solve sorting problem in hybrid multi-attribute group decision making. When the limit profiles of between adjacent classes are known, a sorting method based on the dominance degree and dominance relation is proposed. when the limit profiles between adjacent classes are unknown but reference alternatives which represent each class are known, the clustering method based on the distance is expanded to the sorting of group decision making problems, a sorting method based on distance is established. When experts given their rating opinion about each alternative, a sorting method based on the probability is proposed. These methods provide new ways to solve sorting problems of hybrid multi-attribute group decision making.
(4)Some examples such as supplier selection, suppliers sorting, etc are given to illustrate the feasibility and validity of these proposed methods, and, application of the proposed ranking method in enterprise cooperation innovation partner selection is studied.
The above mentioned contributions has further enriched the study of hybrid multi-attribute group decision-making, and provide new methods for consensus analysis in HMAGDM,ranking under certain conditions in HMAGDM and sorting in HMAGDM.
引文
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