两维语义证据推理方法及其在科学基金评估中的应用研究
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摘要
随着科学技术和经济社会的发展,人们正面临着愈来愈复杂的决策问题。利用专家的知识和经验解决复杂决策问题成为常用的方法之一。面对复杂决策问题,证据理论提供了一种基于证据与决策者知识和经验的决策方法。但是,经典证据理论要求在一维框架上建模,未反映决策者由实证据和知识、经验给出决策结论的相关过程与特征信息,而这个信息对决策意见合成的质量有着重要的影响。类似地,经典语言型决策通常使用一维语言表示决策信息,也未能反映决策者提供的决策信息的质量。因此,研究如何在原有语言信息的基础上,增加一维反映专家决策知识和行为特征的信息,并对原有决策信息进行修正,对拓展证据理论、更加精确有效地利用专家信息、提高复杂语言型决策质量具有重要理论意义与应用价值。
基于此,本文以两维语义信息为主线,以多维框架证据推理为主要工具,根据两维语义信息形式的不同,分别提出基本的两维语义证据推理方法、不同粒度两维语义证据推理方法和基于两维语义判断矩阵的决策方法,并以科学基金立项评估为应用背景,构建基于两维语义的科学基金立项评估方法。具体研究内容和创新性成果如下：
1.区间证据推理方法研究。通过分析基本证据推理算子、区间证据推理算子和模糊证据推理算子的特点及适用范围,针对现有区间证据推理算子存在不满足交换律、计算复杂等问题,提出一种基于C-OWA的区间证据推理方法。该方法通过引入C-OWA算子,构建区间信度转化为点信度的区间信度点化算子,通过区间信度点化算子判断区间信度是否有效、决策者风险态度等,再利用基本证据推理(ER)算子将点化后的区间信度进行融合。
2.两维语义证据推理方法研究。通过对经典语言型决策进行系统的梳理,针对其未能反映决策信息质量等问题,提出两维语义证据推理方法。在经典语言型决策的基础上,增加一维反映决策主体与决策过程特征信息的语言集,提出两维语义信息的概念,分析两维语义信息与多维识别框架信息的关系,探索两维语义的语义表示规则,给出基于证据推理的两维语义信息集结方法；根据两维语义信息的内涵,探讨基于两维语义的专家组合赋权法,构建基于两维语义的群决策方法。
3.不同粒度两维语义证据推理方法研究。分析多维识别框架等相关概念,根据多个识别框架的逻辑关系,将多个识别框架分为平行框架、递进框架和混合框架,根据识别框架的元素特征,将识别框架分为精确语言型框架、模糊语言型框架和其他识别框架,分析各类识别框架的特点：研究识别框架等价、识别框架以概率等价等内涵,分别给出不同精确语言框架和不同模糊语言框架下信息一致性转化方法,探讨两种一致性转化方法的性质；根据两维语义信息的模糊性,将两维语义信息分为两维精确语义和两维模糊语义信息,分析不同粒度两维语义信息与不同识别框架信息之间的关系,分别给出不同粒度两维精确语义和两维模糊语义的一致性转化方法。由基本证据推理算子或基于C-OWA的区间证据推理算子对多个不同粒度两维语义信息进行集结,从而构建了两种不同粒度下两维语义证据推理方法。
4.两维语义判断矩阵研究。对现有语言型判断矩阵进行了拓展,在原有语言判断信息的基础上增加了一维反映判断信息可靠性和不确定性的语言信息,从而形成了两维语义判断矩阵。分析了两维语义判断矩阵的内涵,根据两维语义的语义表示,将两维语义判断矩阵表示为信度判断矩阵,研究了信度判断的内涵、性质、一致性的界定以及多个信度判断矩阵的集结方法,通过将信度判断矩阵转化为加权几何均值矩阵,构造了信度判断矩阵的排序向量的求解方法。根据两维语义判断矩阵和信度判断矩阵的关系,分析了两维语义判断矩阵的一致性概念,构建多个两维语义判断矩阵集结和排序方法。
5.基于两维语义的科学基金立项评估方法研究。以科学基金立项评估为应用背景,通过前期在国家自然科学基金委员会调研获取的同行评议意见,在不改变现行同行专家评议信息的基础上,研究基于两维语义证据推理的科学基金立项评估方法。以项目的最终审定结果(是否立项)为评判依据,对国家自然科学基金立项评估进行实证研究,并将本文方法和现行方法进行了对比分析。
With the devolvement of science&technology as well as the development of economic society, the decision-making problems in daily life are increasingly complex. In view of the status quo, it has become a common way of solving complex decision-making problem that utilizing experts'knowledge and experience. As one of the major decision-making methods, the evidence theory provides a way of thinking based on experts'knowledge and experience. However, the classical evidence theory is required to be modeled on one-dimensional frame of discernment, which cannot capture the characteristics of decision-making process by using evidence, knowledge and experience of experts, and these characteristics would be of significant influence in the quality of decision-making opinions synthesis. Similarly, the classical linguistic decisions express decision-making information often by one-dimensional linguistic label, which fails to make clear the quality of the information provided by experts. Therefore, how to add one dimension of information to amend the original linguistic information has become of theoretical and practical significance for the development of evidence theory, especially in using expert information more accurately and effectively and improving the quality of the complex linguistic decision-making.
Based on the above, two-dimensional linguistic information is taken as the main line, and the multi-dimensional framework of evidential reasoning as the main tool in this paper. According to the different forms of two-dimensional linguistic information, the basic two-dimensional linguistic information evidential reasoning method, multi-granularity two-dimension linguistic information evidential reasoning method, and Judgment matrix based on two-dimension linguistic information are proposed respectively. For the purpose of test and verification, this paper make use of the method in the context of the evaluation of peer review performance in National Natural Science Foundation of China (NSFC) and builds Science Foundation project evaluation methods based on two-dimension linguistic information. The main content and research results are as follows:
1. A new interval evidential reasoning methods. First of all, this paper compares the pros and cons and application scope of different operators of ER, including the original ER algorithm, fuzzy ER algorithm and interval ER algorithm. In order to solve current problems of interval ER algorithm, such as dissatisfaction of commutative law and computational complexity, we propose a new interval ER operator based on C-OWA. In the method, a point belief operator is constructed to transfer the interval belief to a point belief. Moreover, the validity of the interval belief and the risk attitude of decision maker can be estimated by the proposed operator. And then, the interval belief can be aggregated by the basic evidential reasoning (ER) operator.
2. ER method based on two-dimension linguistic information. On the basis of the systematic literature review of classic linguistic decision-making methods, we propose ER method based on two-dimension linguistic information in order to solve the problem which fails to make clear the quality of the information provided by decision-makers. To elaborate the method, based on the concept of two-dimension linguistic information, this paper firstly analyzes the relationship between two-dimension linguistic information and the information under multi-dimensional discernment frame. After that, the representational rules of two-dimension linguistic information are defined, and the aggregation method of it based on ER is given in this paper. In the aggregation method, we probe in the expert weighting approach and structure a group decision method based on two-dimension linguistic information.
3. ER method based on multi-granularity two-dimension linguistic information. Firstly, we analyze the concept of multi-dimensional discernment framework; divide the relationship between different discernment frame into parallel pattern, progressive pattern, and mix pattern based on its logic. Then, we elaborate the concepts of discernment frames' simple equivalent relationship, probability equivalence, etc. Secondly, with regard to the characteristics of elements in discernment frame, the frameworks are categorized into exact linguistic frameworks, fuzzy linguistic frameworks and etc. in order to illustrate the features of these frameworks. Under each category, we put forward a method of consistent transformation between different discernment frames and discuss the properties of the method. Thirdly, two-dimension linguistic information is divided into fuzzy and accurate categories according to its fuzziness. We analyze the relationship between linguistic information of multi-granularity and of different discernment frameworks, and then give the consistent transformation approach among two-dimension fuzzy linguistic information of different granularity as well as accurate information of different granularity respectively. Finally, the various two-dimension linguistic information of disparate granularity are aggregated by ER algorithm or interval ER algorithm based on C-OWA operator.
4. Judgment matrix based on two-dimension linguistic information. With the purpose of displaying the reliability or uncertainty of information, the linguistic judgment matrix is developed into the two-dimension linguistic judgment matrix by adding one linguistic dimension to represent the uncertainty. According to the connotation of the new matrix, we find that the two-dimension linguistic judgment matrix can be expressed as belief comparison matrix. Based on the analysis of the concept, property, as well as the definition of consistent transformation, the aggregation approach of multiple belief comparison matrices has been concluded. And then the approach of solving the priority vector of belief comparison matrix is provided through transforming belief comparison matrix into weighted geometric average matrix. Finally, on the basis of the relationship between linguistic judgment matrix and belief comparison matrix, the definition of consistent transformation, the aggregation approaches, as well as the priority method are all analogized to the two-dimension linguistic judgment matrix.
5. Study on evaluation method of peer review in NSFC based on two-dimension linguistic information. In the context of NSFC peer review, this paper apply the methods mentioned above in the performance evaluation of NSFC peer review by making use of the two-dimension linguistic judgment:information of experts'judgment to each application as well as their familiarity with its research subject from NSFC. Then, according to the actual result of peer review (grant or not), empirical study is conducted, and the advantages of our methods are revealed by the comparison with current methods in NSFC.
基于此,本文以两维语义信息为主线,以多维框架证据推理为主要工具,根据两维语义信息形式的不同,分别提出基本的两维语义证据推理方法、不同粒度两维语义证据推理方法和基于两维语义判断矩阵的决策方法,并以科学基金立项评估为应用背景,构建基于两维语义的科学基金立项评估方法。具体研究内容和创新性成果如下：
1.区间证据推理方法研究。通过分析基本证据推理算子、区间证据推理算子和模糊证据推理算子的特点及适用范围,针对现有区间证据推理算子存在不满足交换律、计算复杂等问题,提出一种基于C-OWA的区间证据推理方法。该方法通过引入C-OWA算子,构建区间信度转化为点信度的区间信度点化算子,通过区间信度点化算子判断区间信度是否有效、决策者风险态度等,再利用基本证据推理(ER)算子将点化后的区间信度进行融合。
2.两维语义证据推理方法研究。通过对经典语言型决策进行系统的梳理,针对其未能反映决策信息质量等问题,提出两维语义证据推理方法。在经典语言型决策的基础上,增加一维反映决策主体与决策过程特征信息的语言集,提出两维语义信息的概念,分析两维语义信息与多维识别框架信息的关系,探索两维语义的语义表示规则,给出基于证据推理的两维语义信息集结方法；根据两维语义信息的内涵,探讨基于两维语义的专家组合赋权法,构建基于两维语义的群决策方法。
3.不同粒度两维语义证据推理方法研究。分析多维识别框架等相关概念,根据多个识别框架的逻辑关系,将多个识别框架分为平行框架、递进框架和混合框架,根据识别框架的元素特征,将识别框架分为精确语言型框架、模糊语言型框架和其他识别框架,分析各类识别框架的特点：研究识别框架等价、识别框架以概率等价等内涵,分别给出不同精确语言框架和不同模糊语言框架下信息一致性转化方法,探讨两种一致性转化方法的性质；根据两维语义信息的模糊性,将两维语义信息分为两维精确语义和两维模糊语义信息,分析不同粒度两维语义信息与不同识别框架信息之间的关系,分别给出不同粒度两维精确语义和两维模糊语义的一致性转化方法。由基本证据推理算子或基于C-OWA的区间证据推理算子对多个不同粒度两维语义信息进行集结,从而构建了两种不同粒度下两维语义证据推理方法。
4.两维语义判断矩阵研究。对现有语言型判断矩阵进行了拓展,在原有语言判断信息的基础上增加了一维反映判断信息可靠性和不确定性的语言信息,从而形成了两维语义判断矩阵。分析了两维语义判断矩阵的内涵,根据两维语义的语义表示,将两维语义判断矩阵表示为信度判断矩阵,研究了信度判断的内涵、性质、一致性的界定以及多个信度判断矩阵的集结方法,通过将信度判断矩阵转化为加权几何均值矩阵,构造了信度判断矩阵的排序向量的求解方法。根据两维语义判断矩阵和信度判断矩阵的关系,分析了两维语义判断矩阵的一致性概念,构建多个两维语义判断矩阵集结和排序方法。
5.基于两维语义的科学基金立项评估方法研究。以科学基金立项评估为应用背景,通过前期在国家自然科学基金委员会调研获取的同行评议意见,在不改变现行同行专家评议信息的基础上,研究基于两维语义证据推理的科学基金立项评估方法。以项目的最终审定结果(是否立项)为评判依据,对国家自然科学基金立项评估进行实证研究,并将本文方法和现行方法进行了对比分析。
With the devolvement of science&technology as well as the development of economic society, the decision-making problems in daily life are increasingly complex. In view of the status quo, it has become a common way of solving complex decision-making problem that utilizing experts'knowledge and experience. As one of the major decision-making methods, the evidence theory provides a way of thinking based on experts'knowledge and experience. However, the classical evidence theory is required to be modeled on one-dimensional frame of discernment, which cannot capture the characteristics of decision-making process by using evidence, knowledge and experience of experts, and these characteristics would be of significant influence in the quality of decision-making opinions synthesis. Similarly, the classical linguistic decisions express decision-making information often by one-dimensional linguistic label, which fails to make clear the quality of the information provided by experts. Therefore, how to add one dimension of information to amend the original linguistic information has become of theoretical and practical significance for the development of evidence theory, especially in using expert information more accurately and effectively and improving the quality of the complex linguistic decision-making.
Based on the above, two-dimensional linguistic information is taken as the main line, and the multi-dimensional framework of evidential reasoning as the main tool in this paper. According to the different forms of two-dimensional linguistic information, the basic two-dimensional linguistic information evidential reasoning method, multi-granularity two-dimension linguistic information evidential reasoning method, and Judgment matrix based on two-dimension linguistic information are proposed respectively. For the purpose of test and verification, this paper make use of the method in the context of the evaluation of peer review performance in National Natural Science Foundation of China (NSFC) and builds Science Foundation project evaluation methods based on two-dimension linguistic information. The main content and research results are as follows:
1. A new interval evidential reasoning methods. First of all, this paper compares the pros and cons and application scope of different operators of ER, including the original ER algorithm, fuzzy ER algorithm and interval ER algorithm. In order to solve current problems of interval ER algorithm, such as dissatisfaction of commutative law and computational complexity, we propose a new interval ER operator based on C-OWA. In the method, a point belief operator is constructed to transfer the interval belief to a point belief. Moreover, the validity of the interval belief and the risk attitude of decision maker can be estimated by the proposed operator. And then, the interval belief can be aggregated by the basic evidential reasoning (ER) operator.
2. ER method based on two-dimension linguistic information. On the basis of the systematic literature review of classic linguistic decision-making methods, we propose ER method based on two-dimension linguistic information in order to solve the problem which fails to make clear the quality of the information provided by decision-makers. To elaborate the method, based on the concept of two-dimension linguistic information, this paper firstly analyzes the relationship between two-dimension linguistic information and the information under multi-dimensional discernment frame. After that, the representational rules of two-dimension linguistic information are defined, and the aggregation method of it based on ER is given in this paper. In the aggregation method, we probe in the expert weighting approach and structure a group decision method based on two-dimension linguistic information.
3. ER method based on multi-granularity two-dimension linguistic information. Firstly, we analyze the concept of multi-dimensional discernment framework; divide the relationship between different discernment frame into parallel pattern, progressive pattern, and mix pattern based on its logic. Then, we elaborate the concepts of discernment frames' simple equivalent relationship, probability equivalence, etc. Secondly, with regard to the characteristics of elements in discernment frame, the frameworks are categorized into exact linguistic frameworks, fuzzy linguistic frameworks and etc. in order to illustrate the features of these frameworks. Under each category, we put forward a method of consistent transformation between different discernment frames and discuss the properties of the method. Thirdly, two-dimension linguistic information is divided into fuzzy and accurate categories according to its fuzziness. We analyze the relationship between linguistic information of multi-granularity and of different discernment frameworks, and then give the consistent transformation approach among two-dimension fuzzy linguistic information of different granularity as well as accurate information of different granularity respectively. Finally, the various two-dimension linguistic information of disparate granularity are aggregated by ER algorithm or interval ER algorithm based on C-OWA operator.
4. Judgment matrix based on two-dimension linguistic information. With the purpose of displaying the reliability or uncertainty of information, the linguistic judgment matrix is developed into the two-dimension linguistic judgment matrix by adding one linguistic dimension to represent the uncertainty. According to the connotation of the new matrix, we find that the two-dimension linguistic judgment matrix can be expressed as belief comparison matrix. Based on the analysis of the concept, property, as well as the definition of consistent transformation, the aggregation approach of multiple belief comparison matrices has been concluded. And then the approach of solving the priority vector of belief comparison matrix is provided through transforming belief comparison matrix into weighted geometric average matrix. Finally, on the basis of the relationship between linguistic judgment matrix and belief comparison matrix, the definition of consistent transformation, the aggregation approaches, as well as the priority method are all analogized to the two-dimension linguistic judgment matrix.
5. Study on evaluation method of peer review in NSFC based on two-dimension linguistic information. In the context of NSFC peer review, this paper apply the methods mentioned above in the performance evaluation of NSFC peer review by making use of the two-dimension linguistic judgment:information of experts'judgment to each application as well as their familiarity with its research subject from NSFC. Then, according to the actual result of peer review (grant or not), empirical study is conducted, and the advantages of our methods are revealed by the comparison with current methods in NSFC.
引文
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