基于熵理论的指标体系区分度测算与权重设计
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摘要
评价指标体系已经被广泛应用到当今社会各个领域。但是,目前的研究成果大多集中在应用领域,缺乏对支撑评价指标体系构建的相关理论方法的系统研究。基于此,本文以“熵”的相关理论为研究主线,以指标体系构建过程中的指标筛选和指标赋权两个重要阶段为研究对象,借助于“熵”、“熵权”和“极大熵”的相关思想,对评价指标体系的构建过程理论和评价指标体系的性能评价理论做了一定程度的探讨,研究内容主要包括以下两个方面:
评价指标体系的构建过程理论研究。首先,本文分析了“熵权”应用于指标赋权所引起的争议和不妥,进而结合“熵权”的基本思想,将其合理应用到指标筛选的过程中,并提出了指标“区分度”的概念。通过对指标区分度的测算,实现了在因追求指标体系全面性而造成指标过多时候对指标的合理筛选。针对于区分度,文中还引出了指标“重要性”的概念,并对“区分度”和“重要性”的均衡问题做了部分探讨。其次,本文运用“极大熵”的思想,以双目标规划模型为主要研究工具,构建了全新的基于极大熵准则的指标赋权模型。该模型以客观的目标规划模型为主体,巧妙地将主观因素寓于到目标规划模型的约束条件当中,不仅克服了主、客观赋权方法各自弊病,而且从某种意义上实现了主观赋权和客观赋权的较好融合。
评价指标体系的性能评价理论研究。首先,本文将指标“区分度”的测算扩展到整个评价指标体系中,提出了评价指标体系“整体区分度”的概念,并借助于指标体系的组织架构实现了对该“整体区分度”的有效测算。指标体系的“整体区分度”反映了其对各待评价对象的区分能力的大小,有利于实现对待评价对象的合理排序。其次,本文借助于“极大熵”思想,构建指标体系权重分布情况的测算模型,并对测算结果进行分类分析,实现了对设计出来的指标体系权重分布状态合理性的评价,提高了指标权重设计的可信度。
最后,笔者将文中研究的两大方面的理论成果应用于某高校学科建设项目评价的实例中,并根据研究成果的具体内容将整个案例划分到每一章节当中去,实现了对研究成果的快捷、方便、有效的检验,取得了良好的实际效果。
Evaluation index system has been widely used in every field in our society. However, most of the related researches focus on the application filed, and the systemic research on the related theories and methods which are used to build evaluation index system. Based on these, in this paper, the theories of entropy are chosen to be the main research tool and the two important steps in the constructing process of an evaluation index system, index selection and index weight-setting are the main study objectives. Then, according to the related thoughts of entropy, entropy weight and maximum entropy, we make some studies on the constructing process theories and capability evaluating theories of evaluation index system. The main researches are as follows.
Study on the constructing process theories of evaluation index system. First, after discussing on the agreements and disagreements on entropy weight applying into weight-setting, entropy weight was applied into the process of index selection according to its main thought and the concept for distinguish degree of an index was put forward. By calculating the distinguish degree of an index, it can make the index filtration more reasonable when the indexes are too many as a result of purchasing all sides of the evaluated objectives. And, according to distinguish degree, another concept importance degree is brought in and some studies have been made to discuss the equilibrium between distinguish degree and importance degree. Then, according to the thoughts of maximum entropy, with the help of two-objective program model, a new index weight-setting model was built. This model has lots of advantages. It puts the subjective factors into the restraints of the objective program model, which makes subjective weight-setting thought and objective weight-setting thought combine together well, and overcome all of their shortages.
Study on the capability evaluation theories of evaluation index system. First, the thought of calculation for the distinguish degree is extended to the whole index system. The concept of the whole distinguish degree of the index system was put forward, and with the help of the structure of the index systems, we calculated the value of the whole distinguish degree which reflects the distinguish ability of the index to the evaluated objective and can help to make the proper sequence for all the objectives. Then, according to the thought of maximum entropy, the calculating model which showed the weights distributing state of the index system was built. And we made some analysis on the calculating results which helps to evaluate the reasonability of the weights distributing state of the designed index system and improve the reliability of the index weight-setting.
Finally, we applied the theories and the methods studied in this paper into a real case, which is the subject building evaluation of a university. And, according to the forms of the theories, we divided the whole case into several parts corresponding to each chapter, which helps to prove the theories more quickly, more conveniently and more effectively.
评价指标体系的构建过程理论研究。首先,本文分析了“熵权”应用于指标赋权所引起的争议和不妥,进而结合“熵权”的基本思想,将其合理应用到指标筛选的过程中,并提出了指标“区分度”的概念。通过对指标区分度的测算,实现了在因追求指标体系全面性而造成指标过多时候对指标的合理筛选。针对于区分度,文中还引出了指标“重要性”的概念,并对“区分度”和“重要性”的均衡问题做了部分探讨。其次,本文运用“极大熵”的思想,以双目标规划模型为主要研究工具,构建了全新的基于极大熵准则的指标赋权模型。该模型以客观的目标规划模型为主体,巧妙地将主观因素寓于到目标规划模型的约束条件当中,不仅克服了主、客观赋权方法各自弊病,而且从某种意义上实现了主观赋权和客观赋权的较好融合。
评价指标体系的性能评价理论研究。首先,本文将指标“区分度”的测算扩展到整个评价指标体系中,提出了评价指标体系“整体区分度”的概念,并借助于指标体系的组织架构实现了对该“整体区分度”的有效测算。指标体系的“整体区分度”反映了其对各待评价对象的区分能力的大小,有利于实现对待评价对象的合理排序。其次,本文借助于“极大熵”思想,构建指标体系权重分布情况的测算模型,并对测算结果进行分类分析,实现了对设计出来的指标体系权重分布状态合理性的评价,提高了指标权重设计的可信度。
最后,笔者将文中研究的两大方面的理论成果应用于某高校学科建设项目评价的实例中,并根据研究成果的具体内容将整个案例划分到每一章节当中去,实现了对研究成果的快捷、方便、有效的检验,取得了良好的实际效果。
Evaluation index system has been widely used in every field in our society. However, most of the related researches focus on the application filed, and the systemic research on the related theories and methods which are used to build evaluation index system. Based on these, in this paper, the theories of entropy are chosen to be the main research tool and the two important steps in the constructing process of an evaluation index system, index selection and index weight-setting are the main study objectives. Then, according to the related thoughts of entropy, entropy weight and maximum entropy, we make some studies on the constructing process theories and capability evaluating theories of evaluation index system. The main researches are as follows.
Study on the constructing process theories of evaluation index system. First, after discussing on the agreements and disagreements on entropy weight applying into weight-setting, entropy weight was applied into the process of index selection according to its main thought and the concept for distinguish degree of an index was put forward. By calculating the distinguish degree of an index, it can make the index filtration more reasonable when the indexes are too many as a result of purchasing all sides of the evaluated objectives. And, according to distinguish degree, another concept importance degree is brought in and some studies have been made to discuss the equilibrium between distinguish degree and importance degree. Then, according to the thoughts of maximum entropy, with the help of two-objective program model, a new index weight-setting model was built. This model has lots of advantages. It puts the subjective factors into the restraints of the objective program model, which makes subjective weight-setting thought and objective weight-setting thought combine together well, and overcome all of their shortages.
Study on the capability evaluation theories of evaluation index system. First, the thought of calculation for the distinguish degree is extended to the whole index system. The concept of the whole distinguish degree of the index system was put forward, and with the help of the structure of the index systems, we calculated the value of the whole distinguish degree which reflects the distinguish ability of the index to the evaluated objective and can help to make the proper sequence for all the objectives. Then, according to the thought of maximum entropy, the calculating model which showed the weights distributing state of the index system was built. And we made some analysis on the calculating results which helps to evaluate the reasonability of the weights distributing state of the designed index system and improve the reliability of the index weight-setting.
Finally, we applied the theories and the methods studied in this paper into a real case, which is the subject building evaluation of a university. And, according to the forms of the theories, we divided the whole case into several parts corresponding to each chapter, which helps to prove the theories more quickly, more conveniently and more effectively.
引文
[1]李随成,陈敬东,赵海刚.定性决策指标体系评价研究[J].系统工程理论与实践, 2001: 77～82
[2]张集,张粒子.电力市场中的市场力分层评价指标体系[J].中国电机工程报,2006: 123～128
[3] Li X. Study on Complexity of Social Systems, Systems Engineering, Systems Science and Complexity Research[J]. Research Information Ltd.2002: 146～153
[4]中国学术期刊网. http://dlib.cnki.net/kns50/Navigator.aspx?ID=1
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[8]刘树林.多属性决策的广义双基点排序法[J].系统工程理论与实践, 1998, 18 (2): 23～25.
[9]樊治平.多属性决策的一种新方法[J].系统工程, 1994, 12 (1) : 15～17.
[10]张吉军,刘家才.区间数多指标决策问题的决策方法分析[J].预测, 2002, 21 (1) : 73～75.
[11]张全,樊治平,潘德惠.不确定性多属性决策问题中区间数的一种排序方法[J].系统工程理论与实践, 1999,19 (5) : 129～133.
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[18]汤甦野.熵:一个世纪之谜的解析[M].中国科技大学出版社, 2004年07月
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[20] Shamilov, Aladdin. A development of entropy optimization methods[J]. WSEAS Transactions on Mathematics, May, 2006: 568～575
[21]刘桂雄,阎华.熵概念的发展及在精度理论中的应用[J].华南理工大学学报(自然科学版),1999: 98～103
[22]吴玲,任佩瑜,陈维政,贺红梅.管理系统中的熵理论及利益相关者框架下企业综合绩效的熵值评估法.软科学, 2004,(1):36～39
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[24]高杰.区间估计: AHP指标筛选的一种方法.系统工程理论与实践,2005: 34～43
[25]张君安.优化指标法及自调整松驰系数的数学实质探讨[J].西安工业大学学报,1988: 56～60
[26]李崇明,丁烈.复杂系统评价指标的筛选方法.理论新探, 2004: 8～9
[27]史本山,杨季美.关于评价指标集并合理论和方法的研究.西南交通大学学报,1991: 74～80
[28] Abdou, Samir, Savoy, Jacques. Statistical and comparative evaluation of various indexing and search models. Lecture Notes in Computer Science2006: 362～373
[29]张清河,张云波.不计评价指标权重值时的综合评价[J].华侨大学学报(自然科学版),2002: 112～118
[30]徐泽水,达庆利.多属性决策的组合赋权方法研究.中国管理科学,2002: P84～87
[31]徐泽水.多属性决策的两种方差最大化方法.管理工程学报.2001: 11～14
[32]王宗军.多目标权系数赋值方法及其选择策略[J].系统工程与电子技术, 1993, 15 (6) : 35～41.
[33]刘健.在多目标决策中利用基点计算权重[J].系统工程理论与实践, 2001, 21 (4) : 27～30.
[34]王应明.运用离差最大化方法进行多指标决策与排序[J].系统工程与电子技术, 1998, 20 (7): 24～26.
[35] Ma J, Fan Z P, Huang L H. A subjective and objective integrated approach to determine attribute weights[J ]. European Journal of Operational Research, 1999, 112 (2) : 397～404.
[36]陆明生.多目标决策中的权系数[J].系统工程理论与实践, 1986, 6 (4) : 77～78.
[37]王丽燕.多目标决策的统计赋权[J].统计与决策, 2001: 18～23.
[38]尤天慧,樊治平.不确定性多属性决策中确定熵权的一种误差分析方法[J].系统工程,2003: 101～104
[39]杨玉中,张强,吴立云.基于熵权的TOPSIS供应商选择方法[J].北京理工大学学报,2006: 21～25
[40]张渝,周宗放.商业银行信用风险评价指标的熵权选择方法.电子科技大学学报, 2006: 23～30
[41]朱梅红,李爱华.基于熵权的中国西部各省份科技实力综合评价[J].数学的实践与认识,2006: 120～125
[42]刘智,端木京顺.基于熵权多目标决策的方案评估方法研究.数学的实践与认识, 2005: 114～119
[43]郭东强.利用熵权系数法评价企业信息化建设项目.运筹与管理,2003,(3):76～79
[44]戴文站,陈杰.基于熵权法的教育质量评价方法.系统工程理论与实践,1998,(2):76～79
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[2]张集,张粒子.电力市场中的市场力分层评价指标体系[J].中国电机工程报,2006: 123～128
[3] Li X. Study on Complexity of Social Systems, Systems Engineering, Systems Science and Complexity Research[J]. Research Information Ltd.2002: 146～153
[4]中国学术期刊网. http://dlib.cnki.net/kns50/Navigator.aspx?ID=1
[5]冯尚友.多目标决策理论方法与应用[M].武汉:华中理工大学出版社.1990
[6]吴小萍,张小勇.复杂系统决策的综合评价方法研究.系统工程与电子技术,2004: 1808～1811
[7]刘树林,邱菀华.多属性决策基础理论研究[J].系统工程理论与实践, 1998: 38～43.
[8]刘树林.多属性决策的广义双基点排序法[J].系统工程理论与实践, 1998, 18 (2): 23～25.
[9]樊治平.多属性决策的一种新方法[J].系统工程, 1994, 12 (1) : 15～17.
[10]张吉军,刘家才.区间数多指标决策问题的决策方法分析[J].预测, 2002, 21 (1) : 73～75.
[11]张全,樊治平,潘德惠.不确定性多属性决策问题中区间数的一种排序方法[J].系统工程理论与实践, 1999,19 (5) : 129～133.
[12] Mac. Crimmon K.R. Decision Making Among Multiple-Attribute Alternative: A Survey and Consolidated Approach. RANP memorandum, 1968: 55～63
[13] Geoffrey Gregory. Decision Analysis[M]. Pitman Publishing, London, 1988.
[14] Hwang C L , Yoon K. Multiple attribute decision making: methods and applications [M ]. New York:Springer2 Verlag, 1981.
[15]尚仰震.热力学体系统计熵[M].四川科学技术出版社, 1988年03月
[16]邱菀华.管理决策与应用熵学[M].北京:机械工业出版社, 2001.10
[17]姜璐.熵:系统科学的基本概念[M].沈阳出版社, 1997年12月
[18]汤甦野.熵:一个世纪之谜的解析[M].中国科技大学出版社, 2004年07月
[19]王彬.熵与信息[M].西北工业大学出版社.1994
[20] Shamilov, Aladdin. A development of entropy optimization methods[J]. WSEAS Transactions on Mathematics, May, 2006: 568～575
[21]刘桂雄,阎华.熵概念的发展及在精度理论中的应用[J].华南理工大学学报(自然科学版),1999: 98～103
[22]吴玲,任佩瑜,陈维政,贺红梅.管理系统中的熵理论及利益相关者框架下企业综合绩效的熵值评估法.软科学, 2004,(1):36～39
[23]阎植林.管理决策中的熵理论及应用研究[D].北京:北京航空航天大学, 1996.
[24]高杰.区间估计: AHP指标筛选的一种方法.系统工程理论与实践,2005: 34～43
[25]张君安.优化指标法及自调整松驰系数的数学实质探讨[J].西安工业大学学报,1988: 56～60
[26]李崇明,丁烈.复杂系统评价指标的筛选方法.理论新探, 2004: 8～9
[27]史本山,杨季美.关于评价指标集并合理论和方法的研究.西南交通大学学报,1991: 74～80
[28] Abdou, Samir, Savoy, Jacques. Statistical and comparative evaluation of various indexing and search models. Lecture Notes in Computer Science2006: 362～373
[29]张清河,张云波.不计评价指标权重值时的综合评价[J].华侨大学学报(自然科学版),2002: 112～118
[30]徐泽水,达庆利.多属性决策的组合赋权方法研究.中国管理科学,2002: P84～87
[31]徐泽水.多属性决策的两种方差最大化方法.管理工程学报.2001: 11～14
[32]王宗军.多目标权系数赋值方法及其选择策略[J].系统工程与电子技术, 1993, 15 (6) : 35～41.
[33]刘健.在多目标决策中利用基点计算权重[J].系统工程理论与实践, 2001, 21 (4) : 27～30.
[34]王应明.运用离差最大化方法进行多指标决策与排序[J].系统工程与电子技术, 1998, 20 (7): 24～26.
[35] Ma J, Fan Z P, Huang L H. A subjective and objective integrated approach to determine attribute weights[J ]. European Journal of Operational Research, 1999, 112 (2) : 397～404.
[36]陆明生.多目标决策中的权系数[J].系统工程理论与实践, 1986, 6 (4) : 77～78.
[37]王丽燕.多目标决策的统计赋权[J].统计与决策, 2001: 18～23.
[38]尤天慧,樊治平.不确定性多属性决策中确定熵权的一种误差分析方法[J].系统工程,2003: 101～104
[39]杨玉中,张强,吴立云.基于熵权的TOPSIS供应商选择方法[J].北京理工大学学报,2006: 21～25
[40]张渝,周宗放.商业银行信用风险评价指标的熵权选择方法.电子科技大学学报, 2006: 23～30
[41]朱梅红,李爱华.基于熵权的中国西部各省份科技实力综合评价[J].数学的实践与认识,2006: 120～125
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