基于置信信念函数的群决策过程研究
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摘要
决策问题自身的部分无知性、随机性、难以描述性,决策信息的不确定性、不完备性,决策者的有限理性,使得不确定决策,尤其是不确定群决策成为决策科学研究的一个热点。针对不确定群决策问题,涌现出各种不确定群决策方法,包括模糊多属性群决策方法、基于语言评价信息的群决策方法和基于证据理论的群决策方法等。各种方法注重不确定信息的表达、群体一致性分析、群体意见的集结和方案的统一量纲排序。然而,它们对应的群决策过程缺乏高置信性,主要表现在对专家评价的置信性与偏好无差异性等方面考虑不足。针对这一问题,以证据理论为基础,本文研究如何构建基于置信信念函数的群决策过程,并进行实际应用。具体的研究内容和创新点如下:
(1)信念函数间的一致度分析。本文对Liu Weiru提出的信念函数间的冲突分析进行修正、改进,克服二元冲突测度的内在差异性及基于冲突测度的Dempster规则适应判断的不合理性,提出信念函数间的一致度,基于一致度将信念函数间关系划分为冲突、相容、一致三类,进而运用三类关系进行Dempster规则适用性判断。信念函数间的一致度为源自专家的置信信念函数和群体一致性构建提供了必要基础。
(2)源自专家的置信信念函数构建。本文以Simon的有限理性为理论指导,分析由专家意见定性定量构建信念函数存在的不足;以源自专家的一组给定时间区间上的采样信念函数为基础,提出源自专家的置信信念函数的定性定义;根据定性定义,使用基于一致度的信念函数间关系对采样信念函数组进行一致子集划分,在统计框架下对置信信念函数进行定量定义,并给出获取置信信念函数的一般流程;以某通信公司策略升级为背景,阐述置信信念函数的构建过程及在意向决策中的应用;针对置信信念函数构建方法可能存在的计算复杂度指数增长问题,提出通过计算机实验方法选择合适的框架长度以及对原始问题框架进行层次划分来加以解决。
(3)源自客观观察数据的置信信念函数构建。分析典型工程应用中基于客观观察数据构建信念函数存在的瞬时异常问题;以基于客观观察数据的一组信念函数的最大一致子集为基础,给出置信信念函数的定性定义;针对使用信念函数间关系进行基于客观观察数据的一组信念函数的一致划分存在的不足,构建结构同分布规则,给出规则的5个性质;根据定性定义,给出置信信念函数的量化定义,并分析其合理性;以粗糙集作为理论基础,讨论获取置信信念函数的一般流程。
(4)基于置信信念函数使用扩展TOPSIS(Technique for Order Preference by Similarity to Ideal Solutions)的群决策过程。构建TOPSIS的前向、内部、后向三种扩展模型;提出基于源自专家的置信信念函数使用TOPSIS扩展模型的群决策过程;针对典型算例,分别运用三种扩展TOPSIS模型进行群决策求解,并进行结果对比。所建立的群决策过程适用于客观条件不允许或决策规则不指定群体一致约束的应用场合。
(5)基于置信信念函数面向群体一致的群决策过程。提出以源自专家的置信信念函数为基础,以群体一致性为约束的群决策过程,构建包含属性、方案、全局三个层次上的群体一致性,研究基于选定层次上的群体一致的不确定群体决策问题求解,包括不同专家的决策意见的统一效用正规化,不同方案各属性上各专家的权重确定,方案上评价等级效用集结,以及整个过程的详细叙述。以某汽车制造公司乘用车研究院工程项目管理软件选择问题为背景,描述一个完整的群决策过程。所建立的群决策过程适用于客观条件允许或决策规则指定群体一致约束的应用场合。
上述研究丰富了基于证据理论的不确定群决策方法,发展了一个基于置信信念函数的群决策过程,使得此方法可以应用于更多的实际场合,合理、有效地解决更多的实际问题。
Decision making under uncertainty, especially uncertain group decision making (GDM), has already become a hot point in the domain of decision science owing to the partial ignorance, randomicity, difficult-description of decision problems, the uncertainty and imperfection of decision information, and the unbounded rationality (BR) of decision makers.
Focusing on uncertain GDM problems, many approaches have been emerged, including fuzzy multiattribute GDM approach, linguistic assessment based GDM approach, evidence theory based GDM approach, and etc.. Almost all kings of approaches concentrate on the expressions of uncertain information, the analysis of group consensus, the aggregation of group opinions, and the unified dimensional ranking order of alternatives. However, their corresponding GDM processes take no enough confidence into account, which is shown as lack of consideration for the confidence of group assessments, the non-distinct preference of group assessments, and etc.. For lack of full confidence, based on Dempster-Shafer theory (DST), this dissertation investigates the construction of the GDM process on the basis of confidence belief functions and its real application. The main detailed contents and innovative points include:
(1) The analysis of consistency degree among belief functions. This dissertation improves the conflict analysis among belief functions proposed by Liu Weiru in order to overcome the intrinsic difference between two dimensions of Liu’s conflict measure and the irrationality of Liu’s conflict measure based suggestions on the applicability of Dempster’s rule. A consistency measure between a pair of belief functions is proposed to divide beliefs’pairwise relationships (BPRs) into three categories composed of conflict, compatible, and consistency. Three BPRs are further used to validly recommend the applicability of Dempster’s rule. The consistency measure provides necessary foundations for the constructions of confidence belief functions from experts and group consensus.
(2) The construction of confidence belief functions from experts. Regarding the BR of Simon as theoretical guidance, this dissertation analyzes the drawbacks of qualitatively and quantitatively producing a belief function from an expert, and proposes the qualitative definition of a confidence belief function from the expert based on a set of belief functions sampled from the expert within a given time interval. In terms of the qualitative definition of confidence belief function, a set of belief functions are partitioned into a finite number of consistent subsets with BPRs on the basis of consistency measure, and the confidence belief function is quantitatively defined under a statistical framework. Furthermore, a general procedure for generating a confidence belief function is elaborated. The strategy upgrade of a communication company is examined to demonstrate the construction of a confidence belief function and its application in intention decision. In order to deal with the exponential increasing of computational complexity when constructing confidence belief functions, we discuss how to select an appropriate frame by experimenting on computer and hierarchically partition original problems.
(3) The construction of confidence belief functions from objective observation data. The instantaneous exceptions of constructing belief functions from objective observation data in representative engineering applications are analyzed. On the basis of the maximal consistent subset generated from a set of belief functions constructed from objective observation data, a confidence belief function from objective observation data is qualitatively defined. Because of the drawbacks of consistently partitioning a set of belief functions based on objective observation data using BPRs, a structure-equivalent rule is constructed and its five characteristics are explained. According to the qualitative definition of confidence belief function, the quantitative definition of the confidence belief function is given and its validity is analyzed. Taking Rough Set as theoretical foundations, we discuss a general procedure for generating a confidence belief function from a set of belief functions.
(4) The confidence belief functions based GDM process using extended TOPSISs (Technique for Order Preference by Similarity to Ideal Solutions). Three extended TOPSIS models which are composed of premodel, intermodel, and postmodel, are constructed and used to build a GDM process based on confidence belief functions. A representative example is examined to make solutions using three extended TOPSIS models and compare them. The GDM process is suitable to be used in such applications that is not allowed by objective conditions or is not specified by decision rules.
(5) The confidence belief functions based GDM process oriented to group consensus (GC). A GDM process based on confidence belief functions and constrained by GC is proposed. The GC in three levels including the attribute level, the alternative level, and the global level, is constructed. Solving the uncertain GDM problem based on GC in a specific level is studied. Hereinto, the main research contents include the unification of opinions of different experts using unified utilities, the confirmation of the relative weight of each expert on each attribute for each alternative, the aggregation of group utilities of assessment grades for alternatives, and the detailed interpretation of the whole process. An engineering project management software selection problem in the research institute of passenger car in an automobile manufacturing company is made to describe a whole GDM process. The GDM process is suitable to be used in such applications that is allowed and required by objective conditions or is specified by decision rules.
The above research enriches the DST based uncertain GDM approaches and developes a confidence belief functions based GDM process. This makes the approaches more flexible to be used in practical applications, and further more rational and effective to solve real problems.
(1)信念函数间的一致度分析。本文对Liu Weiru提出的信念函数间的冲突分析进行修正、改进,克服二元冲突测度的内在差异性及基于冲突测度的Dempster规则适应判断的不合理性,提出信念函数间的一致度,基于一致度将信念函数间关系划分为冲突、相容、一致三类,进而运用三类关系进行Dempster规则适用性判断。信念函数间的一致度为源自专家的置信信念函数和群体一致性构建提供了必要基础。
(2)源自专家的置信信念函数构建。本文以Simon的有限理性为理论指导,分析由专家意见定性定量构建信念函数存在的不足;以源自专家的一组给定时间区间上的采样信念函数为基础,提出源自专家的置信信念函数的定性定义;根据定性定义,使用基于一致度的信念函数间关系对采样信念函数组进行一致子集划分,在统计框架下对置信信念函数进行定量定义,并给出获取置信信念函数的一般流程;以某通信公司策略升级为背景,阐述置信信念函数的构建过程及在意向决策中的应用;针对置信信念函数构建方法可能存在的计算复杂度指数增长问题,提出通过计算机实验方法选择合适的框架长度以及对原始问题框架进行层次划分来加以解决。
(3)源自客观观察数据的置信信念函数构建。分析典型工程应用中基于客观观察数据构建信念函数存在的瞬时异常问题;以基于客观观察数据的一组信念函数的最大一致子集为基础,给出置信信念函数的定性定义;针对使用信念函数间关系进行基于客观观察数据的一组信念函数的一致划分存在的不足,构建结构同分布规则,给出规则的5个性质;根据定性定义,给出置信信念函数的量化定义,并分析其合理性;以粗糙集作为理论基础,讨论获取置信信念函数的一般流程。
(4)基于置信信念函数使用扩展TOPSIS(Technique for Order Preference by Similarity to Ideal Solutions)的群决策过程。构建TOPSIS的前向、内部、后向三种扩展模型;提出基于源自专家的置信信念函数使用TOPSIS扩展模型的群决策过程;针对典型算例,分别运用三种扩展TOPSIS模型进行群决策求解,并进行结果对比。所建立的群决策过程适用于客观条件不允许或决策规则不指定群体一致约束的应用场合。
(5)基于置信信念函数面向群体一致的群决策过程。提出以源自专家的置信信念函数为基础,以群体一致性为约束的群决策过程,构建包含属性、方案、全局三个层次上的群体一致性,研究基于选定层次上的群体一致的不确定群体决策问题求解,包括不同专家的决策意见的统一效用正规化,不同方案各属性上各专家的权重确定,方案上评价等级效用集结,以及整个过程的详细叙述。以某汽车制造公司乘用车研究院工程项目管理软件选择问题为背景,描述一个完整的群决策过程。所建立的群决策过程适用于客观条件允许或决策规则指定群体一致约束的应用场合。
上述研究丰富了基于证据理论的不确定群决策方法,发展了一个基于置信信念函数的群决策过程,使得此方法可以应用于更多的实际场合,合理、有效地解决更多的实际问题。
Decision making under uncertainty, especially uncertain group decision making (GDM), has already become a hot point in the domain of decision science owing to the partial ignorance, randomicity, difficult-description of decision problems, the uncertainty and imperfection of decision information, and the unbounded rationality (BR) of decision makers.
Focusing on uncertain GDM problems, many approaches have been emerged, including fuzzy multiattribute GDM approach, linguistic assessment based GDM approach, evidence theory based GDM approach, and etc.. Almost all kings of approaches concentrate on the expressions of uncertain information, the analysis of group consensus, the aggregation of group opinions, and the unified dimensional ranking order of alternatives. However, their corresponding GDM processes take no enough confidence into account, which is shown as lack of consideration for the confidence of group assessments, the non-distinct preference of group assessments, and etc.. For lack of full confidence, based on Dempster-Shafer theory (DST), this dissertation investigates the construction of the GDM process on the basis of confidence belief functions and its real application. The main detailed contents and innovative points include:
(1) The analysis of consistency degree among belief functions. This dissertation improves the conflict analysis among belief functions proposed by Liu Weiru in order to overcome the intrinsic difference between two dimensions of Liu’s conflict measure and the irrationality of Liu’s conflict measure based suggestions on the applicability of Dempster’s rule. A consistency measure between a pair of belief functions is proposed to divide beliefs’pairwise relationships (BPRs) into three categories composed of conflict, compatible, and consistency. Three BPRs are further used to validly recommend the applicability of Dempster’s rule. The consistency measure provides necessary foundations for the constructions of confidence belief functions from experts and group consensus.
(2) The construction of confidence belief functions from experts. Regarding the BR of Simon as theoretical guidance, this dissertation analyzes the drawbacks of qualitatively and quantitatively producing a belief function from an expert, and proposes the qualitative definition of a confidence belief function from the expert based on a set of belief functions sampled from the expert within a given time interval. In terms of the qualitative definition of confidence belief function, a set of belief functions are partitioned into a finite number of consistent subsets with BPRs on the basis of consistency measure, and the confidence belief function is quantitatively defined under a statistical framework. Furthermore, a general procedure for generating a confidence belief function is elaborated. The strategy upgrade of a communication company is examined to demonstrate the construction of a confidence belief function and its application in intention decision. In order to deal with the exponential increasing of computational complexity when constructing confidence belief functions, we discuss how to select an appropriate frame by experimenting on computer and hierarchically partition original problems.
(3) The construction of confidence belief functions from objective observation data. The instantaneous exceptions of constructing belief functions from objective observation data in representative engineering applications are analyzed. On the basis of the maximal consistent subset generated from a set of belief functions constructed from objective observation data, a confidence belief function from objective observation data is qualitatively defined. Because of the drawbacks of consistently partitioning a set of belief functions based on objective observation data using BPRs, a structure-equivalent rule is constructed and its five characteristics are explained. According to the qualitative definition of confidence belief function, the quantitative definition of the confidence belief function is given and its validity is analyzed. Taking Rough Set as theoretical foundations, we discuss a general procedure for generating a confidence belief function from a set of belief functions.
(4) The confidence belief functions based GDM process using extended TOPSISs (Technique for Order Preference by Similarity to Ideal Solutions). Three extended TOPSIS models which are composed of premodel, intermodel, and postmodel, are constructed and used to build a GDM process based on confidence belief functions. A representative example is examined to make solutions using three extended TOPSIS models and compare them. The GDM process is suitable to be used in such applications that is not allowed by objective conditions or is not specified by decision rules.
(5) The confidence belief functions based GDM process oriented to group consensus (GC). A GDM process based on confidence belief functions and constrained by GC is proposed. The GC in three levels including the attribute level, the alternative level, and the global level, is constructed. Solving the uncertain GDM problem based on GC in a specific level is studied. Hereinto, the main research contents include the unification of opinions of different experts using unified utilities, the confirmation of the relative weight of each expert on each attribute for each alternative, the aggregation of group utilities of assessment grades for alternatives, and the detailed interpretation of the whole process. An engineering project management software selection problem in the research institute of passenger car in an automobile manufacturing company is made to describe a whole GDM process. The GDM process is suitable to be used in such applications that is allowed and required by objective conditions or is specified by decision rules.
The above research enriches the DST based uncertain GDM approaches and developes a confidence belief functions based GDM process. This makes the approaches more flexible to be used in practical applications, and further more rational and effective to solve real problems.
引文
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