基于可拓数学理论的多属性决策方法研究
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摘要
可拓数学是以矛盾问题为研究对象、以矛盾问题的智能化处理为主要研究内容、以可拓方法论为主要研究方法的一门新兴学科。本文在可拓数学理论、多属性决策理论与方法的基础上,主要对以下几个方面的问题进行了研究。
在可拓关联函数方面,引入了一种非线性K次抛物型的关联函数,这种非线性关联函数,既能反映各属性间的非线性关系,又能反映各属性值在不同区间内变化对被评事物的影响程度。
在区间数多属性决策中,对一类需要进行点与区间数距离计算的多属性决策,应用可拓数学距的概念拓展了经典数学中点与区间的距离的概念,从而决策也更加科学。
在决策模型求解方面,根据可拓逆向思维方法对期望-方差决策的求解属性权重模型进行改进,提高了属性权重计算的精确度,决策更加合理。
在可拓层次分析法中,为了把可拓判断矩阵中的每个元素定量化,一般取可拓区间数的中值作为定量化的数字。但是有时候属性的权重的实际值可能在可拓区间数中值的左侧或者右侧,由于中值的选取可能使得属性权重的确定偏离实际。为了克服上述缺陷,对可拓判断矩阵定量化进行改进,使得属性权重的确定在实际应用中更加有效。
Extension mathematics is a new study which takes contradiction problems as research object, take the intelligent processing of contradiction problems as the main research contents and take the extension methodology as main research method. Based on the extension mathematics theory and multi-attribute decision-making theory, this paper mainly studied the following problem.
In the study of extension correlation function, this paper introduce a new correlation function, non-linear parabolic of Kth order. This non-linear correlation function can reflect not only the non-linear relationship between the attributes, but also the influence that the values of each attributes in different intervals exert on the things which are evaluated.
In the interval multi-attribute decision-making, for the kind of multi-attribute decision-making which need to calculate the distance between dot and interval, the distance in extension mathematics is introduced to expand the classical mathematical concept of distance between dot and interval, which make decision-making more scientific.
In the aspect of solving the model of decision-making, through improving the solving attribute weights in expectation-variance decision-making model using extension reverse thinking, make calculating more accurate and decision-making more rational.
In extension analytic hierarchy process (EAHP), in order to quantify every elements of the extension judgment matrix, generally take the median of extension interval as a quantitative number. But sometimes the actual value of attribute weights maybe on the left or right of median of extension interval, because the select of median may make the attribute weights deviate the actual value. To overcome these shortcomings, the quantification of the extension judgment matrix is improved. And this can make the selection of the attribute weights more effective in practical applications.
在可拓关联函数方面,引入了一种非线性K次抛物型的关联函数,这种非线性关联函数,既能反映各属性间的非线性关系,又能反映各属性值在不同区间内变化对被评事物的影响程度。
在区间数多属性决策中,对一类需要进行点与区间数距离计算的多属性决策,应用可拓数学距的概念拓展了经典数学中点与区间的距离的概念,从而决策也更加科学。
在决策模型求解方面,根据可拓逆向思维方法对期望-方差决策的求解属性权重模型进行改进,提高了属性权重计算的精确度,决策更加合理。
在可拓层次分析法中,为了把可拓判断矩阵中的每个元素定量化,一般取可拓区间数的中值作为定量化的数字。但是有时候属性的权重的实际值可能在可拓区间数中值的左侧或者右侧,由于中值的选取可能使得属性权重的确定偏离实际。为了克服上述缺陷,对可拓判断矩阵定量化进行改进,使得属性权重的确定在实际应用中更加有效。
Extension mathematics is a new study which takes contradiction problems as research object, take the intelligent processing of contradiction problems as the main research contents and take the extension methodology as main research method. Based on the extension mathematics theory and multi-attribute decision-making theory, this paper mainly studied the following problem.
In the study of extension correlation function, this paper introduce a new correlation function, non-linear parabolic of Kth order. This non-linear correlation function can reflect not only the non-linear relationship between the attributes, but also the influence that the values of each attributes in different intervals exert on the things which are evaluated.
In the interval multi-attribute decision-making, for the kind of multi-attribute decision-making which need to calculate the distance between dot and interval, the distance in extension mathematics is introduced to expand the classical mathematical concept of distance between dot and interval, which make decision-making more scientific.
In the aspect of solving the model of decision-making, through improving the solving attribute weights in expectation-variance decision-making model using extension reverse thinking, make calculating more accurate and decision-making more rational.
In extension analytic hierarchy process (EAHP), in order to quantify every elements of the extension judgment matrix, generally take the median of extension interval as a quantitative number. But sometimes the actual value of attribute weights maybe on the left or right of median of extension interval, because the select of median may make the attribute weights deviate the actual value. To overcome these shortcomings, the quantification of the extension judgment matrix is improved. And this can make the selection of the attribute weights more effective in practical applications.
引文
[1]Fandel G, Gal T. Multiple criteria Decision Making.Theory and Applications.NewYork:Springer-Verlag,1980.
[2]Hwang C L and Yoon K. Multiple Attribute Decision Making-Methods and Applications. A State-of-the Art Survey. Springer-Verlag Berlin Herdelberg,1981.
[3]Chanjong,V,Haimes YY.Multi objective Decision Making Theory and Methodology. New York: North Holland,1983.
[4]李登峰.模糊多目标多人决策与对策.国防工业出版社.2003.
[5]ChenSJ,HwangCL. Fuzzy Multiple Attribute Decision Making methods and applications.Berlin: SPringer-Verlag.1992.
[6]康志荣,任平泉.对经典数学的思考与拓展-可拓数学产生及意义.科学技术与辩证法,2001,18(1)：57-61
[7]蔡文,杨春燕.可拓营销.北京：科学技术文献出版社,2000.
[8]蔡文,杨春艳,何斌,可拓逻辑初步.北京：科学出版社,2003：34-41.
[9]蔡文,杨春燕,林伟初.可拓工程方法.北京：科学出版社,2003.
[10]杨春燕.可拓集与数据挖掘.北京：科学出版社,2007.
[11]蔡文.物元模型及其应用.北京：科学技术文献出版社,1994.
[12]杨春燕,蔡文.可拓集合的新定义.广东工业大学学报,2001,18(1)：61-62.
[13]何斌,张应利.可拓集合的分类性质和信息开发的可拓方法.系统工程理论实践,1999.
[14]杨春燕,张拥军,蔡文.可拓集合及其应用研究.广州：全国第九届可拓工程年会报告,2001.
[15]Gao Fengji, Z Wenying. Multiple Attribute Decision Which Power Importance be Incomlete Defined, MCDM:Theory and Applications. SCI-TECH Information Service,1995.
[16]何保红,陈峻,崔洪军.停车设施规划方案的不确定多属性决策模型.交通运输工程与信息学报,2005,3(1)：63-66.
[17]樊治平,宫贤斌,张全.区间数多属性决策中决策矩阵的规范化方法.东北大学学报,1 999,20(3)：326-329.
[18]郭耀煌, 贾建民.综合评价与排序.系统工程理论与实践,1990,10(2)：26-30.
[19]王应明.基于加权法和线性分配法的有限方案多目标决策新方法.控制与决策,1992,7(4)：259-263.
[20]穆尔.综合排序的双基点法的改进及灵敏度分析.系统工程理论与实践,1993,13(5)
33-37.
[21]徐改丽,史文雷,郭欣荣.区间数排序的一种新方法.第四届中国不确定系统年会论文集[C].桂林：2006,321-328.
[22]胡宝清,王孝礼,何娟娟.区间上的可拓集及其关联函数.广东工业大学学报,2000,17(2)：101-108.
[23]胡宝清,何娟娟.区间论域上的区间可拓集及其关联函数.广东工业大学学报,2001,18(1)：48-54.
[24]李志林.区间关联函数的新定义及其应用研究.数学的实践与认识2006,36(2)：207-210.
[25]樊治平,张权.一种不确定性多属性决策模型的改进.系统工程理论与实践,1999,19(12)：42-47.
[26]高峰记.不完全信息下对方案有偏好的多指标决策.系统工程理论与实践,20004(20)：94-97.
[27]王登瀛.多目标决策方法优选的密切值法.系统工程,1989,7(1)：33-36.
[28]张吉军.区间数的排序方法研究.运筹与管理,2003,12(3)：18-22.
[29]徐泽水.求解不确定多属性决策问题的一种新方法.系统工程学报,2002,17(2)：176-181.
[30]Bryson N, Mobolurih A. A n action learning evaluation procedure for multiple criteria decision making problems-European Journal of Operational Research,1996,96:379-386.
[31]Yoon K. The propagation of errors in multiple-attribute decision analysis:a practical appro-ach. Journal of the Operational Research Society,1989,7:681-686.
[32]樊治平,郭亚军.误差分析理论在区间数多属性决策问题中的应用.东北大学学报,1997,5：550-560.
[33]樊治平.复杂多属性决策理论与方法的研究.沈阳：东北大学,1996.
[34]尤天慧,樊治平.区间数多指标决策的一种TOPSIS方法.东北大学学报(自然科学版),2002,9：840-843.
[35]Sajjad ZM. Incorporating the uncertainty of decision judgments in the analytic hierarchy process. European Journal of Operational Research,1991,53:206-216.
[36]Saaty T L.The analysis hierarchy process.New York:McGraw-Hill,1980.
[37]朱建军.层次分析法的若干问题研究及应用.东北大学博士学位论文.2005：20-25
[38]赵浪,王亮.层次分析法的两处缺陷改进及实例.2007,27(3)：507-510.
[39]肖四汉,樊治平,王梦光Fuzzy判断矩阵的一致性研究.系统工程报,2001,16(2)：142-145.
[40]高洁,盛昭瀚.可拓层次分析法研究.系统工程,2002,20(5)：6-9.
[41]Wang Y M, Yang J B, Xu D L. Interval weight generation approaches based on consistency test and interval comparison matrices. Applied Mathematics and Computation,2005,167 (1): 252-273.
[42]徐玖平,吴巍.多属性决策的理论与方法.北京：清华大学出版社,2006.
[43]Leung L C,Cao D.one consistency and ranking of alternatives in fuzzy AHP. European Jour-nal of Operational Research,2000,124(1):102-113.
[44]Xia Jun, Hu Baoqing. A Grey System Model for Predicting Trend Change of Urban Waste Water Load. J. Of Enviromental Hydrology,1997,5 (1):1-10.
[45]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,2002,10(2)：84-87.
[46]Wang W, Cui M M. Hybrid.multiple attribute decision making model based on entropy. Jour-nal of Systems Engineering and Electronics,2007,18(1):72-75.
[47]Yager R R. OWA aggregation over a continuous interval argument with applications to decision making.IEEE Transaction on Systems, Man, and Cybernetics-Part B,2004,34(5):1952-1963.
[48]周光明,刘树人.不确定多属性决策中区间数的一种心排序法.系统工程2006,24(4)：115-117.
[49]蔡文,石勇.可拓学的科学意义与未来发展.哈尔滨工业大学学报,2006,7：1081-1082.
[50]徐泽水.不确定多属性决策方法及应用.北京：清华大学出版社,2004.
[51]刘宝碇,彭锦.不确定理论教程.清华大学出版社,2006,6.
[52]朱建军,王梦光,刘士新.一种新型不确定AHP的研究与应用.管理科学学报,2005,8(5)：15-20
[53]王石青,邱林,王志良,韩晓军.确定隶属函数的统计分析法.户华北水利水电学院学报,2002,23：68-71.
[54]郭均鹏等.区间线性规划的标准及求解.系统工程,2003，2 1(2)：79-82.
[55]Xu Z S.Chen J. An interactive method for fuzzy multiple attribute group decision making. In-formation Science,2007,177(1):248-263.
[56]Islam R,Biswal M P,Alam S S. Preference programming and inconsistent interval judgments. European Journal of Operational Research,1997,97(1):53-62.
[57]Leung L,Cao D. On consistency and ranking of alternatives in fuzzy AHP[J]. European Journal of Operational Research,2000,124(1):102-113.
[58]Mikhailov L. A fuzzy approach to deriving priorities from interval pairwise comparison judgements. European Journal of Operational Research,2004,159(3):687-704.
[59]Wang Y M. On lexicographic goal programming method for generating weights from Inconsistent interval comparison matrices. Applied Mathematics and Computation, 2006,173(2):985-991.
[60]Wang Y M,Yang J B,Xu D L. A two-stage logarithmic goal programming method for generating weights from interval comparison matrices. Fuzzy Sets and Systems,2005,152(3):475-498.
[2]Hwang C L and Yoon K. Multiple Attribute Decision Making-Methods and Applications. A State-of-the Art Survey. Springer-Verlag Berlin Herdelberg,1981.
[3]Chanjong,V,Haimes YY.Multi objective Decision Making Theory and Methodology. New York: North Holland,1983.
[4]李登峰.模糊多目标多人决策与对策.国防工业出版社.2003.
[5]ChenSJ,HwangCL. Fuzzy Multiple Attribute Decision Making methods and applications.Berlin: SPringer-Verlag.1992.
[6]康志荣,任平泉.对经典数学的思考与拓展-可拓数学产生及意义.科学技术与辩证法,2001,18(1)：57-61
[7]蔡文,杨春燕.可拓营销.北京：科学技术文献出版社,2000.
[8]蔡文,杨春艳,何斌,可拓逻辑初步.北京：科学出版社,2003：34-41.
[9]蔡文,杨春燕,林伟初.可拓工程方法.北京：科学出版社,2003.
[10]杨春燕.可拓集与数据挖掘.北京：科学出版社,2007.
[11]蔡文.物元模型及其应用.北京：科学技术文献出版社,1994.
[12]杨春燕,蔡文.可拓集合的新定义.广东工业大学学报,2001,18(1)：61-62.
[13]何斌,张应利.可拓集合的分类性质和信息开发的可拓方法.系统工程理论实践,1999.
[14]杨春燕,张拥军,蔡文.可拓集合及其应用研究.广州：全国第九届可拓工程年会报告,2001.
[15]Gao Fengji, Z Wenying. Multiple Attribute Decision Which Power Importance be Incomlete Defined, MCDM:Theory and Applications. SCI-TECH Information Service,1995.
[16]何保红,陈峻,崔洪军.停车设施规划方案的不确定多属性决策模型.交通运输工程与信息学报,2005,3(1)：63-66.
[17]樊治平,宫贤斌,张全.区间数多属性决策中决策矩阵的规范化方法.东北大学学报,1 999,20(3)：326-329.
[18]郭耀煌, 贾建民.综合评价与排序.系统工程理论与实践,1990,10(2)：26-30.
[19]王应明.基于加权法和线性分配法的有限方案多目标决策新方法.控制与决策,1992,7(4)：259-263.
[20]穆尔.综合排序的双基点法的改进及灵敏度分析.系统工程理论与实践,1993,13(5)
33-37.
[21]徐改丽,史文雷,郭欣荣.区间数排序的一种新方法.第四届中国不确定系统年会论文集[C].桂林：2006,321-328.
[22]胡宝清,王孝礼,何娟娟.区间上的可拓集及其关联函数.广东工业大学学报,2000,17(2)：101-108.
[23]胡宝清,何娟娟.区间论域上的区间可拓集及其关联函数.广东工业大学学报,2001,18(1)：48-54.
[24]李志林.区间关联函数的新定义及其应用研究.数学的实践与认识2006,36(2)：207-210.
[25]樊治平,张权.一种不确定性多属性决策模型的改进.系统工程理论与实践,1999,19(12)：42-47.
[26]高峰记.不完全信息下对方案有偏好的多指标决策.系统工程理论与实践,20004(20)：94-97.
[27]王登瀛.多目标决策方法优选的密切值法.系统工程,1989,7(1)：33-36.
[28]张吉军.区间数的排序方法研究.运筹与管理,2003,12(3)：18-22.
[29]徐泽水.求解不确定多属性决策问题的一种新方法.系统工程学报,2002,17(2)：176-181.
[30]Bryson N, Mobolurih A. A n action learning evaluation procedure for multiple criteria decision making problems-European Journal of Operational Research,1996,96:379-386.
[31]Yoon K. The propagation of errors in multiple-attribute decision analysis:a practical appro-ach. Journal of the Operational Research Society,1989,7:681-686.
[32]樊治平,郭亚军.误差分析理论在区间数多属性决策问题中的应用.东北大学学报,1997,5：550-560.
[33]樊治平.复杂多属性决策理论与方法的研究.沈阳：东北大学,1996.
[34]尤天慧,樊治平.区间数多指标决策的一种TOPSIS方法.东北大学学报(自然科学版),2002,9：840-843.
[35]Sajjad ZM. Incorporating the uncertainty of decision judgments in the analytic hierarchy process. European Journal of Operational Research,1991,53:206-216.
[36]Saaty T L.The analysis hierarchy process.New York:McGraw-Hill,1980.
[37]朱建军.层次分析法的若干问题研究及应用.东北大学博士学位论文.2005：20-25
[38]赵浪,王亮.层次分析法的两处缺陷改进及实例.2007,27(3)：507-510.
[39]肖四汉,樊治平,王梦光Fuzzy判断矩阵的一致性研究.系统工程报,2001,16(2)：142-145.
[40]高洁,盛昭瀚.可拓层次分析法研究.系统工程,2002,20(5)：6-9.
[41]Wang Y M, Yang J B, Xu D L. Interval weight generation approaches based on consistency test and interval comparison matrices. Applied Mathematics and Computation,2005,167 (1): 252-273.
[42]徐玖平,吴巍.多属性决策的理论与方法.北京：清华大学出版社,2006.
[43]Leung L C,Cao D.one consistency and ranking of alternatives in fuzzy AHP. European Jour-nal of Operational Research,2000,124(1):102-113.
[44]Xia Jun, Hu Baoqing. A Grey System Model for Predicting Trend Change of Urban Waste Water Load. J. Of Enviromental Hydrology,1997,5 (1):1-10.
[45]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,2002,10(2)：84-87.
[46]Wang W, Cui M M. Hybrid.multiple attribute decision making model based on entropy. Jour-nal of Systems Engineering and Electronics,2007,18(1):72-75.
[47]Yager R R. OWA aggregation over a continuous interval argument with applications to decision making.IEEE Transaction on Systems, Man, and Cybernetics-Part B,2004,34(5):1952-1963.
[48]周光明,刘树人.不确定多属性决策中区间数的一种心排序法.系统工程2006,24(4)：115-117.
[49]蔡文,石勇.可拓学的科学意义与未来发展.哈尔滨工业大学学报,2006,7：1081-1082.
[50]徐泽水.不确定多属性决策方法及应用.北京：清华大学出版社,2004.
[51]刘宝碇,彭锦.不确定理论教程.清华大学出版社,2006,6.
[52]朱建军,王梦光,刘士新.一种新型不确定AHP的研究与应用.管理科学学报,2005,8(5)：15-20
[53]王石青,邱林,王志良,韩晓军.确定隶属函数的统计分析法.户华北水利水电学院学报,2002,23：68-71.
[54]郭均鹏等.区间线性规划的标准及求解.系统工程,2003，2 1(2)：79-82.
[55]Xu Z S.Chen J. An interactive method for fuzzy multiple attribute group decision making. In-formation Science,2007,177(1):248-263.
[56]Islam R,Biswal M P,Alam S S. Preference programming and inconsistent interval judgments. European Journal of Operational Research,1997,97(1):53-62.
[57]Leung L,Cao D. On consistency and ranking of alternatives in fuzzy AHP[J]. European Journal of Operational Research,2000,124(1):102-113.
[58]Mikhailov L. A fuzzy approach to deriving priorities from interval pairwise comparison judgements. European Journal of Operational Research,2004,159(3):687-704.
[59]Wang Y M. On lexicographic goal programming method for generating weights from Inconsistent interval comparison matrices. Applied Mathematics and Computation, 2006,173(2):985-991.
[60]Wang Y M,Yang J B,Xu D L. A two-stage logarithmic goal programming method for generating weights from interval comparison matrices. Fuzzy Sets and Systems,2005,152(3):475-498.