灰色多属性决策方法研究
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摘要
灰色系统理论研究“部分信息已知、部分信息未知”的不确定性系统,把具有贫信息特征的事物作为研究对象,利用部分已知信息去发现和认识事物的发展规律。由于贫信息不确定性系统的普遍存在,决定了这一新理论具有十分广阔的发展前景。不确定灰色多属性决策是现代决策科学的一个重要领域,它在社会、经济、管理、军事和工程中具有广泛的应用。本文分别对属性值为区间灰数,或区间灰数与自然语言的灰色多属性决策问题进行了研究。本文的主要研究结果概括为以下几个方面:
(1)对于属性值为区间灰数且属性权重完全已知或部分已知的不确定灰色多属性(群)决策问题,利用标准区间灰数的运算法则,求出每个方案的区间灰数型综合属性值,在决策者不能给出承担风险态度的情况下,提出了基于最小最大悔值法的灰色多属性决策方法;引入了区间灰数型正、负理想点的概念,将多属性决策的逼近理想点方法推广到灰色多属性决策情形。
(2)根据规范化后的区间灰数的本质,给出了两区间灰数相离度的一个新的计算公式。提出了基于相离度的灰色区间关联系数公式和灰色区间相对关联系数公式。对属性权重部分已知的情况,提出了决策者对所有方案的偏好值为区间灰数的灰色关联决策方法;将多属性群体决策的TOPSIS方法推广到灰色多属性群体决策情形。对属性权重完全未知且决策者对方案有偏好和无偏好两种情形,分别建立了确定属性权重的非线性优化模型,给出了灰色关联决策方法;对属性权重完全未知的灰色多属性(群)决策问题,根据灰色区间关联系数的意义,提出了方案间优势度、方案间相对优势度和方案集中方案间优势比较矩阵等概念及计算公式,建立了基于灰色区间关联系数的模糊互补判断矩阵排序方法;引入了理想专家、群体关联度评分矩阵、方案间群体优势度和方案集中方案间群体优势比较矩阵等概念及计算公式,建立了基于投影的特征向量法和模糊互补判断矩阵排序方法的两种决策算法,这些方法使属性权重完全未知的决策问题摆脱了依赖权重的束缚。
(3)对于属性权重完全已知的情形,针对属性值为区间灰数和自然语言的混合型灰色多属性(群)决策问题,提出了基于证据推理解析算法的决策方法;针对属性值为区间灰数和不确定自然语言的混合型灰色多属性决策问题,提出了区间灰数转换成相应的等级区间的信任度计算公式,建立了基于等级区间证据推理递归算法的决策方法。对于属性权重部分已知的情形,针对属性值为区间灰数和自然语言,或区间灰数和不确定自然语言的混合型灰色多属性决策问题,通过证据推理的解析算法或等级区间证据推理的递归算法和期望效用分别建立了非线性规划模型。提出了利用遗传算法求解的新思路,并给出了实现过程。决策者还可根据自己的风险偏好选择最优决策方案,其中风险偏好是指灰色信息的白化方法,或评价等级的效用取法。
(4)研究了取折衷解的方法在混合型灰色多属性决策的应用。首次将目前应用较少的VIKOR方法拓展应用于混合型灰色多属性决策当中,分别对属性权重已知和未知的混合型多属性决策问题,利用VIKOR方法给出了决策方法。
The researching objective of grey systems theory is the uncertain system whose information is partly knowable and partly unknowable. Its character is missing information. We can find its regularity using the knowable information. Due to the ubiquity of missing information uncertain systems, Grey system theories are more prosperous in the future. Furthermore, grey multiple attribute decision making is an important field in present decision sciences, and it can be applied widely to society, economics, management, military affairs and engineering. This paper is to do a research on problems of grey multiple attribute decision making with interval grey numbers, or interval grey numbers and linguistic variables, respectively. The research results are below:
(1) Using the operation principle of the standard interval gery number and computing interval grey numbers of overall value of alternatives, ranking method based on the minimax regret approach is proposed for grey multiple attribute decision making problems, including grey multiple attribute group decision making problems, in which the attribute values take interval grey numbers, and the weight information is known, or known partially.Concepts of interval grey number of positive ideal point and negative ideal point are introduced and multiple attribute decision making method marching on ideal point is generalized to grey multiple attribute decision making.
(2) The definition of deviation degree between two interval grey numbers is given from the essence of normalized interval grey number as well as the concept and formula. The incidence degree coefficient formula and relative incidence degree coefficient formula are constructed from an analytical technique based on deviation degree for interval grey numbers. Incidence degree decision making approach is put, in which decision-maker’preferences to alternatives are interval grey number with partial weight information.The TOPSIS method of multiple attribute group decision making is generalized to grey multiple attribute group decision making. Two nonlinear programming models and incidence degree decision making approach are established under the situations where decision maker has (or has no) preference information on alternatives for the case of the unknown attribute weight. For grey multiple attribute decision making problems without the attribute weight, according to essence of grey incidence coefficient, the concepts and formulas for predominance strength and predominance comparative matrix between alternatives are introduced and the alternative is ranked according to the priority method of fuzzy complementary judgment matrix. For grey multiple attribute group decision making problems without the attribute weight, according to essence of grey incidence degree, ideal expert, assessment matrix of group incidence degree, and formulas for group predominance strength and group predominance comparative matrix between alternatives are introduced and two methods of ranking alternatives are given by the priority method of fuzzy complementary judgment matrix and by the eigenvector algorithm based on projection.
(3) For the case of the known attribute weight, the evidential reasoning approaches are proposed for hybrid grey multiple attribute (or group) decision making problems in which the attribute values are interval grey numbers and linguistic variables, respectively; the grade interval evidential reasoning approach is proposed for hybrid grey multiple attribute decision making problems in which the attribute values are interval grey numbers and uncertain linguistic variables. For hybrid grey multiple attribute decision making problems, in which the information on the attribute’s weight is known partially and the attribute values are interval grey numbers and linguistic variables, or the attribute values are interval grey numbers and uncertain linguistic variables, the approaches based on the evidential reasoning are proposed, respectively. In these approaches, through evidential reasoning algorithms, the attribute values are aggregated and two nonlinear programming models are developed. Because classic programming methods are hard to solve the nonlinear programming models, using genetic algorithms to solve the nonlinear programming models, the attribute’s weight, the maximum, minimum, and average expected values are gained. So the ranking of the alternatives can be attained. Also, selecting the risk-preferences of the decision maker is a very important, because changing the points of discontinuity in the piecewise linear utility function and choosing whitenization methods of grey information may affect the choice of the best alternative.
(4) The research on the application of compromise method for hybrid grey multiple attribute decision making is given.For hybrid grey multiple attribute decision making problems, in which the information on the attribute’s weight is unknown,or known and the attribute values are interval grey numbers and linguistic variables, VIKOR method is proposed. Meanwhile, the range of VIKOR is developed.
(1)对于属性值为区间灰数且属性权重完全已知或部分已知的不确定灰色多属性(群)决策问题,利用标准区间灰数的运算法则,求出每个方案的区间灰数型综合属性值,在决策者不能给出承担风险态度的情况下,提出了基于最小最大悔值法的灰色多属性决策方法;引入了区间灰数型正、负理想点的概念,将多属性决策的逼近理想点方法推广到灰色多属性决策情形。
(2)根据规范化后的区间灰数的本质,给出了两区间灰数相离度的一个新的计算公式。提出了基于相离度的灰色区间关联系数公式和灰色区间相对关联系数公式。对属性权重部分已知的情况,提出了决策者对所有方案的偏好值为区间灰数的灰色关联决策方法;将多属性群体决策的TOPSIS方法推广到灰色多属性群体决策情形。对属性权重完全未知且决策者对方案有偏好和无偏好两种情形,分别建立了确定属性权重的非线性优化模型,给出了灰色关联决策方法;对属性权重完全未知的灰色多属性(群)决策问题,根据灰色区间关联系数的意义,提出了方案间优势度、方案间相对优势度和方案集中方案间优势比较矩阵等概念及计算公式,建立了基于灰色区间关联系数的模糊互补判断矩阵排序方法;引入了理想专家、群体关联度评分矩阵、方案间群体优势度和方案集中方案间群体优势比较矩阵等概念及计算公式,建立了基于投影的特征向量法和模糊互补判断矩阵排序方法的两种决策算法,这些方法使属性权重完全未知的决策问题摆脱了依赖权重的束缚。
(3)对于属性权重完全已知的情形,针对属性值为区间灰数和自然语言的混合型灰色多属性(群)决策问题,提出了基于证据推理解析算法的决策方法;针对属性值为区间灰数和不确定自然语言的混合型灰色多属性决策问题,提出了区间灰数转换成相应的等级区间的信任度计算公式,建立了基于等级区间证据推理递归算法的决策方法。对于属性权重部分已知的情形,针对属性值为区间灰数和自然语言,或区间灰数和不确定自然语言的混合型灰色多属性决策问题,通过证据推理的解析算法或等级区间证据推理的递归算法和期望效用分别建立了非线性规划模型。提出了利用遗传算法求解的新思路,并给出了实现过程。决策者还可根据自己的风险偏好选择最优决策方案,其中风险偏好是指灰色信息的白化方法,或评价等级的效用取法。
(4)研究了取折衷解的方法在混合型灰色多属性决策的应用。首次将目前应用较少的VIKOR方法拓展应用于混合型灰色多属性决策当中,分别对属性权重已知和未知的混合型多属性决策问题,利用VIKOR方法给出了决策方法。
The researching objective of grey systems theory is the uncertain system whose information is partly knowable and partly unknowable. Its character is missing information. We can find its regularity using the knowable information. Due to the ubiquity of missing information uncertain systems, Grey system theories are more prosperous in the future. Furthermore, grey multiple attribute decision making is an important field in present decision sciences, and it can be applied widely to society, economics, management, military affairs and engineering. This paper is to do a research on problems of grey multiple attribute decision making with interval grey numbers, or interval grey numbers and linguistic variables, respectively. The research results are below:
(1) Using the operation principle of the standard interval gery number and computing interval grey numbers of overall value of alternatives, ranking method based on the minimax regret approach is proposed for grey multiple attribute decision making problems, including grey multiple attribute group decision making problems, in which the attribute values take interval grey numbers, and the weight information is known, or known partially.Concepts of interval grey number of positive ideal point and negative ideal point are introduced and multiple attribute decision making method marching on ideal point is generalized to grey multiple attribute decision making.
(2) The definition of deviation degree between two interval grey numbers is given from the essence of normalized interval grey number as well as the concept and formula. The incidence degree coefficient formula and relative incidence degree coefficient formula are constructed from an analytical technique based on deviation degree for interval grey numbers. Incidence degree decision making approach is put, in which decision-maker’preferences to alternatives are interval grey number with partial weight information.The TOPSIS method of multiple attribute group decision making is generalized to grey multiple attribute group decision making. Two nonlinear programming models and incidence degree decision making approach are established under the situations where decision maker has (or has no) preference information on alternatives for the case of the unknown attribute weight. For grey multiple attribute decision making problems without the attribute weight, according to essence of grey incidence coefficient, the concepts and formulas for predominance strength and predominance comparative matrix between alternatives are introduced and the alternative is ranked according to the priority method of fuzzy complementary judgment matrix. For grey multiple attribute group decision making problems without the attribute weight, according to essence of grey incidence degree, ideal expert, assessment matrix of group incidence degree, and formulas for group predominance strength and group predominance comparative matrix between alternatives are introduced and two methods of ranking alternatives are given by the priority method of fuzzy complementary judgment matrix and by the eigenvector algorithm based on projection.
(3) For the case of the known attribute weight, the evidential reasoning approaches are proposed for hybrid grey multiple attribute (or group) decision making problems in which the attribute values are interval grey numbers and linguistic variables, respectively; the grade interval evidential reasoning approach is proposed for hybrid grey multiple attribute decision making problems in which the attribute values are interval grey numbers and uncertain linguistic variables. For hybrid grey multiple attribute decision making problems, in which the information on the attribute’s weight is known partially and the attribute values are interval grey numbers and linguistic variables, or the attribute values are interval grey numbers and uncertain linguistic variables, the approaches based on the evidential reasoning are proposed, respectively. In these approaches, through evidential reasoning algorithms, the attribute values are aggregated and two nonlinear programming models are developed. Because classic programming methods are hard to solve the nonlinear programming models, using genetic algorithms to solve the nonlinear programming models, the attribute’s weight, the maximum, minimum, and average expected values are gained. So the ranking of the alternatives can be attained. Also, selecting the risk-preferences of the decision maker is a very important, because changing the points of discontinuity in the piecewise linear utility function and choosing whitenization methods of grey information may affect the choice of the best alternative.
(4) The research on the application of compromise method for hybrid grey multiple attribute decision making is given.For hybrid grey multiple attribute decision making problems, in which the information on the attribute’s weight is unknown,or known and the attribute values are interval grey numbers and linguistic variables, VIKOR method is proposed. Meanwhile, the range of VIKOR is developed.
引文
[1]黄孟藩等.决策的科学方法[M].北京:海洋出版社,1983.
[2]陈珽.决策分析[M].北京:科学出版社,1987.
[3]Sen A. Collective choice and social welfare[M].Holden-Day, San Francisco,CA,1970.
[4]Keeny R L, Raiffa H. Decisions with multiple objectives: preferences and value trade-offs[M]. Wiley, New York,1976.
[5]Holloway C A. Decision making under uncertainly: models and choice[M].Prentice-Hill, Englewood Cliffs, 1979.
[6]Saaty T L. The analytic hierarchy process[M]. McGraw-Hill, New York, 1981.
[7]Hwang C L, Yoon K. Multiple attribute decision making[M]. Spriger-Verlag, Berlin, 1981.
[8]Hwang C L, Lin M J. Group decision making under multiple criteria: methods and applications[M].Spriger,Berlin,1987.
[9]Chen S J, Hwang C L. Fuzzy multiple attribute decision making[M].Spriger,Berlin, 1992.
[10]Zeeny M. Multiple criteria decision making[M]. McGraw-Hill, New York, 1982.
[11]徐南荣,仲伟俊.科学决策理论与方法[M].南京:东南大学出版社,1996.
[12]徐泽水.不确定多属性决策方法及应用[M].北京:清华大学出版社,2004.
[13]徐玖平,吴巍.多属性决策理论与方法[M].北京:清华大学出版社,2006.
[14]卫民堂.决策理论与技术[M].西安:西安交通大学出版社,2002.
[15]邱宛华.管理决策与应用熵学[M].北京:机械工业出版社,2002.
[16]段新生.证据理论与决策、人工智能[M].北京:中国人民大学出版社,1993.
[17]李荣钧.模糊多准则决策理论方法与应用[M].北京:科学出版社,2003.
[18]Deng Julong. Control problems of unknown system[J].Proceedings of the Bilateral Meeting on Control systems.1981,156–171.
[19]Deng Julong. Control problems of grey systems[J].Systems&Control Letters,1982,1(5):288–294.
[20]Deng Julong. Zhou Chaoshun. Sufficient conditions for stability of a class of interconnected dynamic systems[J].Systems&Control Letters,1986,5(2):105–108.
[21]Deng Julong. Introduction to Grey System Theory[J].The Journal of Grey System, 1989,l(1):1–24.
[22]Deng Julong. Grey Hazy Sets[J].The Journal of Grey System,1992.4(1):13–30.
[23]Deng Julong. Extent Information Cover Grey System Theory[J].The Journal of Grey System,1995.7(2):131–138.
[24]邓聚龙.灰色控制系统[M].武汉:华中理工大学出版社,1993.
[25]邓聚龙.灰预测与灰决策[M].武汉:华中科技大学出版社,2002.
[26]王子亮.灰色建模技术理论[D].武汉:华中科技大学博士论文,1998.
[27]罗党.灰色决策问题的分析方法研究[D].南京航空航天大学博士论文,2005.
[28]党耀国.灰色不确定性分析与决策模型研究[D].南京航空航天大学博士论文,2006.
[29]Liu Sifeng.On Perron-Frobenius theorem of grey non-negative matrix and its proof[J].The Journal of Grey System,1989,1(2):157–166.
[30]Liu Sifeng,Lin Yi.An introduction to grey systems theory[M].Grove City:IIGSS Academic Publisher, 1998.
[31]李孜军.92–2001年我国灰色系统理论应用研究进展[J].系统工程,2003,21(5):8–12.
[32]刘思峰.灰色系统理论的产生与发展[J].南京航空航天大学学报(自然科学版),2004,36(2):267–272.
[33]邓聚龙.灰色系统理论与应用进展的若干问题.武汉:华中理工大学出版社,1996,1–10.
[34]刘思峰.走向世界的灰色系统理论[A].第十届全国灰色系统学术讨论会[C].北京,2002.
[35]刘思峰,史本广.灰色系统理论在科学发展中的作用和地位[J].农业系统科学与综合研究,2000,16(3):168–170.
[36]刘思峰,党耀国,方志耕等.灰色系统理论及其应用[M].北京:科学出版社,2004.
[37]肖新平,宋中民,李峰.灰技术基础及其应用[M].北京:科学出版社,2005.
[38]李荣均.模糊多准则决策理论与应用[M].北京:科学出版社,2002.
[39]魏世孝,周献中.多属性决策理论方法及其在C3I系统中的应用〔M〕.北京:国防工业出版社,1998.
[40]何波.不完全信息下的基于证据理论的多属性决策方法研究[D].中南大学硕士学位论文,2003
[41]Yager R. Uncertainty Modeling and Decision Support[J].Reliability Engineering & System Safety,2004,85(1):341-354.
[42]Savage L.The foundations of statistic[M].John Wiley and Sons, New York,1954.
[43]潘介人.决策分析中的效用理论[M].上海:上海交通大学出版社,2000.
[44]成盛超,谢如贤,吴健中.效用理论的历史与现状[J].系统工程理论与实践,1994,14(12):16-21.
[45]Keun Tae Cho. Multi-criteria Decision Methods: An attempt to evaluate and unify[J]. Mathematical and Computer Modelling,2003,37:1099-1119.
[46]Keeney R L. Creativity in decision making with value-focused thinking[J].Sloan ManagementReview,1994,35(4):33-41.
[47]Mangasarian O L. Misclassification minimization[J].Journal of Global Optimization 1994,5(4):309-323.
[48]Constantin Zopounidis, Michael Doumpos. A Multicriteria Decision Aid Methodology for Sorting Decision Problems:The Case of Financial Distress[J].Computational Economics,1999,14(3): 197-218.
[49]Roy B. The outranking approach and the foundations of ELECTRE methods[J].Theory and Decision,1991,31:49-73.
[50]Mousseau V, Rlowinski R. Infering an ELECTRE TRI model from assignment examples[]. Journal of Global Optimization,1998,9(12):157-174.
[51]Dias L C,Climaco J N. On computing ELECTRE's credibility indices under partial information[J].Journal of Multi-criteria Decision Analysis,1999,8:74-92.
[52]Figueira J,Roy B. Determining the weights of criteria in the ELECTRE type methods with a revised Simos’procedure[J].European Journal of Operational Research,2002,139: 317-326.
[53]Luis Dias,Vincent Mousseau,et al.An aggregation-disaggregation approach to obtain robust conclusions with ELECTRE TRI[J]. European Journal of Operational Research,2002, 138:332-348.
[54]Leyva-Lopez J C,Frenandez-Gonzalez E F.A new method for group decision support based on ELECTRE III methodlogy[J]. European Journal of Operational Research,2003,148: 14-27.
[55]Brans J P,Mareschal B,Vincke P. PROMETHEE:A new family of outranking methods in multi-criteria analysis[C].In:MCDM,IFORS’84.Amsterdam,North-Holland,1984,447-490.
[56]Brans J P,Mareschal B,Vincke P.A preference ranking organization method: The PROMETHEE method for MCDM[J].Management Science,1985,31(6):647-656.
[57]吴冀平.多准则评价方法的评价[J].决策与决策支持系统,1994,4(1):74-80.
[58]史本山.序偏好条件下多准则问题的分析方法[J].西安交通大学学报,1996,10:494-500.
[59]张秋明,史庆端,姚建民.采用多准则决策分析技术评估技改项目[J].中国软科学,1997,2:70-73.
[60]Li D F. An approach to fuzzy multi-attribute decision making under uncertainty[J]. Information Sciences,2005,169(l-2):97-112.
[61]王绪柱,单静.模糊量排序综述[J].模糊系统和数学,2002,16(4):25-34.
[62]Yao J S,Wu W M. Ranking fuzzy numbers based on decomposition principle and signed distance[J].Fuzzy Sets and Systems,2000,116:275-288.
[63]Dubois P,Prade H. Ranking fuzzy numbers in the setting of possibility theory[J]. Information Science,1983,30:183-224.
[64]Fortemps P,Roubens M. Ranking and defuzzification methods based on area compensation[J]. Fuzzy Sets and Systems,1996,82:319-330.
[65]Liouts,Wang M J. Ranking fuzzy numbers with integral value[J].Fuzzy Sets and Systems,1992,50:247-255.
[66]Iskander M G. Comparison of fuzzy number using possibility programming: comments and new concepts[J]. Computer Mathematics Application,2002,43:833-840.
[67]Tran L,Duckstein L. Comparison of fuzzy number using a fuzzy distance measure[J].Fuzzy sets and systems,2002,130:331-341.
[68]Chen L H,Lu H W. The Preference order of fuzzy number[J].Computer Mathematics Application,2002,44:1455-1465.
[69]Modarres M,Soheil S N. Ranking fuzzy numbers by preference ratio[J].Fuzzy Sets and Systems,2001,118:429-436.
[70]Chu Tachung. Ranking fuzzy numbers with an area between the centroid point and original point[J].Computer Mathematics Application,2002,43:111-117.
[71]吕翔昊,李登峰.基于模糊信息的群体多维偏好分析决策模型[J].系统工程与电子技术,2004,5:605-608.
[72]Nibin Chang, Wen C G, Chen Y L, Yong Y C.A grey fuzzy multi-objective programming approach for the optimal planning of a reservoir watershed[J]. Part A: Theoretical development. Wat. Res., 1996,30(10):2329–2334.
[73]罗党,刘思峰.一类灰色模糊决策问题的熵权分析方法[J].中国工程科学,2004,Vol.6(10):48-51.
[74]Huang G H, Baetz B W , Party G G. A grey fuzzy linear programming approach for municipal solid wasted management planning under uncertainty[J].Civil Engineering Systems , 1993 ,10:123–146.
[75]Yoping Huang, Shengfang Wang. The application of multiple grey models to the control problems[J].The Journal of Grey System,1995,7(4):299–313.
[76]Yoping Huang, Chichang Huang. The application of fuzzy and gradient descent methods to the grey prediction control[J].The Journal of Grey System,1995,7(1):9–22.
[77]Chinming Hong, Sinncheng Lin, Chihtang Chiang. Control of dynamic systems by fuzzy based grey prediction controller[J].The Journal of Grey System,1995,7(1):23–44.
[78]Lin Y H, Chew J M, Chen J M,Chen J Y and Tsi P S. Fuzzy self-tuning via grey prediction of PID controllers[J].EUFIT’95,1995:1095–1100.
[79]Hong Chinming, Lin Chenghung, Ted Tao. Grey cerebella model articulation controller[J]. The Journal of Grey System,1997,9(3):199–218.
[80]B.Kosko. Neural Networks and Fuzzy Systems[M].Prentice-Hill Inc.,USA,1992.
[81]L.X.Wang and J.M.Mendel. Generating fuzzy rules by learning from examples[J].IEEE Trams. Systems, Man, and Cybernation,1992,22(6):1414–1427.
[82]Y.M.Park, U.C.Moon, and K.Lee. A self-organizing fuzzy logic controller for dynamic systems using a fuzzy auto-regressive moving average(FARMA)model[J].IEEE Trams. Fuzzy Systems,1995, 3(1):75–82.
[83]S.Z.He, S.H.Tan and F.L.Xu. Fuzzy self-tuning of PID controllers[J].Fuzzy Sets and Systems, 1993,56:37–46.
[84]Delgado M,Verdegay J L,Vila MA. Linguistic decision making models[J].International Journal of Intelligent Systems,1992,7:479-492.
[85]Delgado M,Verdegay J L,Vila MA. A model for linguistic partial information in decision making problem[J]. International Journal of Intelligent Systems,1992,7: 479-492.
[86]胡应平.基于语言偏好的群体决策的软方法[J].系统工程学报,1996,11(4):53-60.
[87]徐泽水.纯语言多属性决策方法研究[J].控制与决策,2004,7:778-783.
[88]Herrera F, Herrera-Viedma E, Verdegay J L.A sequential selection process in group decision making with a linguistic assessment approach[J].Information Sciences,1995, 85:223-229.
[89]Herrera F, Herrera-Viedma E, Martnez L.A fusion approach for managing multi-granularity linguistic term sets in decision making[J].Fuzzy Sets and Systems,2000,114:43-58.
[90]Herrera F, Herrera-Viedma E. Aggregation operators for linguistic weighted information[J].IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans,1997,27(5):646-656.
[91]Herrera F, Herrera-Viedma E. Linguistic decision analysis: Steps for solving decision problems under linguistic information[J].Fuzzy Sets and Systems,2000,115:67-82.
[92]刘爱学,李永明,史忠科.一种基于语言变量的MCDM问题的决策方法[J].系统工程,2001,19(5):28-32.
[93]王欣荣,樊治平.群决策中基于语言信息处理的一种理想点法[J].中国管理科学,2002,10(6):84-87.
[94]王欣荣,樊治平.一种基于语言信息的多指标群决策方法[J].系统工程学报,2003,18(2):173-176.
[95]陈岩,樊治平.群决策中基于语言评价信息的TOPSIS方法[J].南京工业大学学报,2004,26(3):27-30.
[96]Xu Zeshui. Uncertain linguistic aggregation operations based approach to multiple attribute group decision making under uncertain linguistic environment[J].Information Sciences,2004,168: 171-184.
[97] Xu Zeshui. A method based on linguistic aggregation operators for group decision making with linguistic preference relations[J]. Information Sciences,2004,166: 19-30.
[98]Herrera F, Lopez E,Cristina Mendafia,Rodriugez M A. A linguistic decision model for personnel management solved with a linguistic biobjective genetic algorithm[J].Fuzzy Sets and Systems,2001,118:47-64.
[99]Herrera F, Lopez E,Rodriugez M A.A linguistic decision model for promotion mix management solved with genetic algorithms[J]. Fuzzy Sets and Systems,2001,131:47-61.
[100]Herrera F, Martnez L. A 2-tuple fuzzy linguistic representation model for computing with words[J].IEEE Transactions on Fuzzy Systems,2000,8(6):746-775.
[101]李洪燕,樊治平.一种基于语言判断矩阵的群决策问题的二元语义解法[J].系统工程,2003,21(5):104-108.
[102]王欣荣,樊治平.基于二元语义信息处理的一种语言群决策方法[J].管理科学学报,2003,6(5):1-5.
[103]徐泽水.基于语言信息的决策理论与方法[M].北京:科学出版社,2008.
[104]杨晓莉.混合多属性决策理论方法与应用研究[D].华中师范大学硕士学位论文,2007.
[105]宋业新,张曙红,陈绵云.基于模糊模式识别的时序混合多指标决策闭.系统工程与电子技术,2002,24(4):1-4.
[106]夏勇其,吴祈宗.一种混合型多属性决策问题的TOPSIS方法[J1.系统工程学报,2004,19(6):630-634.
[107]闫书丽,杨万才,肖新平.混合型多属性决策的一种新方法[J].数学的实践与认识,2007,37(16):111-116.
[108]丁传明,黎放,齐欢.一种基于相似度的混合型多属性决策方法[J].系统工程与电子技术,2007,29(5):737-740.
[109]梁昌勇,吴坚,陆文星,丁勇.一种新的混合型多属性决策方法及在供应商选择中的应用[J].中国管理科学,2006,14(6):71-76.
[110]Yang J B,Singh M G. An evidential reasoning approach for multiple attribute decision making with uncertainty[J].IEEE Trans. Systems,Man,and Cybernetics,1994,24(1):l-18.
[111]Yang J B , Sen P. A general multi-level evaluation process for hybrid MADM with uncertainty[J].IEEE Trans. Systems,Man,and Cybernetics,1994,24(10):1458一1473.
[112]Wang J,Yang J B,Sen P. Safety analysis and synthesis using fuzzy sets and evidentialreasoning[J].Reliability Engineering & System Safety,1995,47(2):103-118.
[113]Wang J,Yang J B,Sen P. Multi-person and multi-attribute design evaluations using evidential reasoning based on subjective safety and cost analyses[J].Reliability Engineering & System Safety,1996,52(2):113-128.
[114]Yang J B. Rule and utility-based evidential reasoning approach for complex decision analysis[J].European Journal of Operational Research,2001,131(l):31-61.
[115]Yang J B,Xu D L. On the evidential reasoning algorithm for multi-attribute decision analysis with uncertainty[J].IEEE Trans. Systems,Man,Cybernetics. A,2002,32(3):289-304.
[116]Van-Nam Huynh,Yoshiteru Nakamori,Tu-Bao Ho. Assessment Aggregation in the Evidential Reasoning Approach to MADM Under Uncertainty: orthogonal Versus Weighted Sum[J].Advances in Computer Seienee-ASIAN2004:Higher-Level Decision Making. 2004, 9th Asian Computing Science Conference,Chiang Mai,Thailand,December 8-10.
[117]何兵,郝爱民,赵沁平.一种基于不确定信息的决策方法[J].计算机学报,2004,2:281-85.
[118]Huynh V N,Tetsuya N. Multiple Attribute Decision Making under uncertainty: The Evidential Reasoning Approach Revisited[J].IEEE Trans. on Systems,Man and Cybernetics part A: Systems and Humans,2006,36(4):804-822.
[119]何波,任鸣鸣,王坚强.一种基于证据推理的信息不完全的多准则决策方法[J].数学的实践与认识,2006,36(3):58-62.
[120]王坚强,何波.基于证据推理的信息不完全的多准则决策方法及应用[J].系统工程与电子技术,2005(4):659-661.
[121]王坚强,孙超,吴小月.基于证据推理的信息不完全的多准则分类决策方法[J].武汉理工大学学报,2005,27(6):86-89.
[122]Yang J B,Wang Y M,Xu D L, Chin K S. The evidential reasoning approach for MADA under both probabilistic and fuzzy uncertainties[J].European Journal of Operational Research,2006,171(l):309-343.
[123]Wang Y M,Yang J B,Xu D L. Environmental impact assessment using the evidential reasoning approach[J].European Journal of Operational Research,2006,174(3): 1885- 1913.
[124]Xu D L, Yang J B,Wang Y M. The evidential reasoning approach for multi-attribute decision analysis under interval uncertainty[J]. European Journal of Operational Research , 2006 ,174(l):1914-1943.
[125]Wang Y M, Yang J B, Xu D L, Chin K S. The evidential reasoning approach for multiple attribute decision analysis using interval belief degrees[J]. European Journal of Operational Research,2006,175(l):35-66.
[126]王坚强.几种信息不完全确定的多准则决策方法研究[D].长沙:中南大学博士学位论文,2005.
[127]廖琳武,李垣,雷宏振.确定多属性群决策协调权的模型和方法闭.管理科学学报,2006,9(4):33-39.
[128]Park K.S. Mathematical Programming models for characterizing dominance and Potential optimality when multi-criteria alternatives values and weights are simultaneously incomplete[J].IEEE Transactions on System,Man,and Cybernetics,2004,5:601-614.
[129]Kim S.H.,Choi S.H.,Ahn B.S. Interactive group decision process with evolutionary database[J].Decision Support System,1998,23:333-345.
[130]Kim S.H.,Choi S.H. A utility range-based information group support system for multi- attribute decision making[J].Computers & Operations Research,2001,28:485-505.
[131]王坚强、孙超.基于语言判断矩阵的信息不完全的群体决策方法[J].系统工程与电子技术,2006,28(9):1345-1352.
[132]Salo A.A. Interactive decision aiding for group decision support[J].European Journal of Operational Research,1995,84:131-149.
[133]Yan H,Wei Q. Determining compromise weights for group decision making[J].Journal of the Operational Research Society,2002,53:680-687.
[134]罗党,刘思峰.灰色多指标风险型决策方法研究[J].系统工程与电子技术,2004,Vol.22(8):29-32.
[135]罗党,刘思峰.灰色动态规划研究[J].系统工程理论与实践,2004,Vol.24(4):56-62.
[136]罗党,刘思峰.灰色多目标规划算法研究[J].系统工程,2004,Vol.22(6):12-15.
[137]Deng Julong. Applications of tacit consent rationale to grey analysis[J].The Journal of Grey System,1997,9(1):82-88.
[138]Deng Julong. Tacit consent rationale in grey inference[J].The Journal of Grey System, 1997, 9(1):1-8.
[139]Deng Julong. Grey group decision in grey rationale space[J].The Journal of Grey System, 1998, 10(3):177-182.
[140]Deng Julong. The foundation of grey system theory[J]. The Journal of Grey System, 1997, 9(1):40-48.
[141]Deng Julong. Grey decision making of group, Grey System[M].China Ocean Press,1998: 115-129.2006,175(l):35-66.
[126]王坚强.几种信息不完全确定的多准则决策方法研究[D].长沙:中南大学博士学位论文,2005.
[127]廖琳武,李垣,雷宏振.确定多属性群决策协调权的模型和方法闭.管理科学学报,2006,9(4):33-39.
[128]Park K.S. Mathematical Programming models for characterizing dominance and Potential optimality when multi-criteria alternatives values and weights are simultaneously incomplete[J].IEEE Transactions on System,Man,and Cybernetics,2004,5:601-614.
[129]Kim S.H.,Choi S.H.,Ahn B.S. Interactive group decision process with evolutionary database[J].Decision Support System,1998,23:333-345.
[130]Kim S.H.,Choi S.H. A utility range-based information group support system for multi- attribute decision making[J].Computers & Operations Research,2001,28:485-505.
[131]王坚强、孙超.基于语言判断矩阵的信息不完全的群体决策方法[J].系统工程与电子技术,2006,28(9):1345-1352.
[132]Salo A.A. Interactive decision aiding for group decision support[J].European Journal of Operational Research,1995,84:131-149.
[133]Yan H,Wei Q. Determining compromise weights for group decision making[J].Journal of the Operational Research Society,2002,53:680-687.
[134]罗党,刘思峰.灰色多指标风险型决策方法研究[J].系统工程与电子技术,2004,Vol.22(8):29-32.
[135]罗党,刘思峰.灰色动态规划研究[J].系统工程理论与实践,2004,Vol.24(4):56-62.
[136]罗党,刘思峰.灰色多目标规划算法研究[J].系统工程,2004,Vol.22(6):12-15.
[137]Deng Julong. Applications of tacit consent rationale to grey analysis[J].The Journal of Grey System,1997,9(1):82-88.
[138]Deng Julong. Tacit consent rationale in grey inference[J].The Journal of Grey System, 1997, 9(1):1-8.
[139]Deng Julong. Grey group decision in grey rationale space[J].The Journal of Grey System, 1998, 10(3):177-182.
[140]Deng Julong. The foundation of grey system theory[J]. The Journal of Grey System, 1997, 9(1):40-48.
[141]Deng Julong. Grey decision making of group, Grey System[M].China Ocean Press,1998: 115-129.seasonal time series[J].Technological Forecasting and Social Change,2001,67:291-302.
[161]Fan Z P,Ma J,Zhang Q. An approach to multiple attribute decision making based fuzzy preference information on alternatives[J]. Fuzzy Sets andSystems,2002,131(1):101-106.
[162]徐泽水.求解不确定型多属性决策问题的一种新方法[J].系统工程学报,2002,17(2):177-181.
[163]Wang Juite, Lin Yungi. A fuzzy multicriteria group decision making approach to select configuration item for software development[J].Fuzzy Sets and Systems,2003,134(3):343-363.
[164]Lee Hsuan-Shih . Optimal consensus of fuzzy opinions under group decision making environment[J]. Fuzzy Sets and Systems, 2002, 132(3):303-315.
[165]Chen Chen-Tung . Extensions of the TOPSIS for group decision-making under fuzzy environment[J]. Fuzzy Sets and Systems,2000,114(1):1-9.
[166]张新波.多目标群体决策问题的灰色分析方法[J].信息与控制,2004,33(2):223-226.
[167]罗党,刘思峰.一类灰色群决策问题的分析方法[J].南京航空航天大学学报,2005, 37 (3):395-398.
[168]徐泽水,孙在东一类不确定性多属性决策问题的排序方法[J]管理科学学报,2002,5(3):35-39
[169]Xu Z S, Da Q L. The uncertain QWA operator[J].International Journal of intelligent Systems, 2002,17:569-575.
[170]Delgado M, Herrera F, Herrera-Viedma E, et al. Combining numerical and linguistic information in group decision making[J].Information Sciences,1998, 107(3):177-194.
[171]邱菀华.群组决策特征根法[J].应用数学与力学,1997,18(11):1027-1033.
[172]方卫国,周泓.逼近群体理想点的多目标群体决策算法[J].管理科学学报,1998,1(4):34-38.
[173]李洪燕,樊治平.群体决策中两种不同偏好信息的集成方法[J].东北大学学报(自然科学版),2000,21(3):336-338.
[174]朱建军.群决策中两类不确定偏好信息的集结方法研究[J].控制与决策,2006,21(8):889-892.
[175]LIU Si-feng, LIN Yi. Grey information: theory and practical applications[M].Spinger-Verlag London,2006,1-138,315-366.
[176]陈孝新.灰色多属性群决策的TOPSIS法[J].江西财经大学学报,2008,55(1):22-25.
[177]陈孝新,刘思峰.一种部分权重信息的灰色多属性群决策方法[J].系统工程与电子技术,2009,31(4):843-846.
[178]Varga,R.S. Matrix Iterative Analysis[M]. Prentice-Hall,Englewood Cliffs,New Jersey,1962.
[179]种晓丽.混合型多属性灰决策与模型的矩阵理论[D].武汉:武汉理工大学硕士论文,2006.
[180]Shafer G A. Mathematical Theory of Evidence[M].Princeton, N J, Princeton U P,1976.
[181]周光明,刘树人.不确定多属性决策中区间数的一种新排序法[J].系统工程,2006,24(4):115-117.
[182]王坚强.一种信息不完全确定的多准则语言群决策方法[J].控制与决策,2007,22(4):394-398.
[183]王坚强.一种多准则纯语言群决策方法[J].控制与决策,2007,22(5):545-553.
[184]Mareschal B. Weight stability intervals in multi-criteria decision[J]. European Journal of Operational Research,1998,109(1):54-64.
[185]Saaty T L. A scaling method for priorities in hierachical structures[J].Journal of Mathemathical Psychology,1997,33(15):234-281.
[186]罗庆成.灰色系统新方法[J].浙江:农业出版社,1992:157-161.
[187]崔杰,党耀国,刘思峰.基于灰色关联度求解指标权重的改进方法[J].中国管理科学,2008,16(5):141-145.
[188]玄光男,程润伟.遗传算法与工程优化[M].北京:清华大学出版社,2004.
[189]倪金林.遗传算法求解约束非线性规划及MATLAB实现[J].大学数学,2005,21(1):91-95.
[190]Opricovic S. Multi-criteria optimization of civil engineering systems[M]. Belgrade: Faculty of Civil Engineering,1998.
[191]Opricovic S, Tzeng G H. Comparative solution by MCDM methods: A comparative analysis of VIKOR and TOPSIS[J]. European Journal of Operational Research,2004,156(2):445-455.
[192]王坚强,张忠.信息不完全确定的多准则直觉模糊决策的折衷解法[C].2006中国控制与决策学术年会论文集,1195-1198.
[193]卫贵武,罗玉军,姚恒申.权重信息不完全的混合多属性决策方法[C].2006中国控制与决策学术年会论文集,1161-1164.
[2]陈珽.决策分析[M].北京:科学出版社,1987.
[3]Sen A. Collective choice and social welfare[M].Holden-Day, San Francisco,CA,1970.
[4]Keeny R L, Raiffa H. Decisions with multiple objectives: preferences and value trade-offs[M]. Wiley, New York,1976.
[5]Holloway C A. Decision making under uncertainly: models and choice[M].Prentice-Hill, Englewood Cliffs, 1979.
[6]Saaty T L. The analytic hierarchy process[M]. McGraw-Hill, New York, 1981.
[7]Hwang C L, Yoon K. Multiple attribute decision making[M]. Spriger-Verlag, Berlin, 1981.
[8]Hwang C L, Lin M J. Group decision making under multiple criteria: methods and applications[M].Spriger,Berlin,1987.
[9]Chen S J, Hwang C L. Fuzzy multiple attribute decision making[M].Spriger,Berlin, 1992.
[10]Zeeny M. Multiple criteria decision making[M]. McGraw-Hill, New York, 1982.
[11]徐南荣,仲伟俊.科学决策理论与方法[M].南京:东南大学出版社,1996.
[12]徐泽水.不确定多属性决策方法及应用[M].北京:清华大学出版社,2004.
[13]徐玖平,吴巍.多属性决策理论与方法[M].北京:清华大学出版社,2006.
[14]卫民堂.决策理论与技术[M].西安:西安交通大学出版社,2002.
[15]邱宛华.管理决策与应用熵学[M].北京:机械工业出版社,2002.
[16]段新生.证据理论与决策、人工智能[M].北京:中国人民大学出版社,1993.
[17]李荣钧.模糊多准则决策理论方法与应用[M].北京:科学出版社,2003.
[18]Deng Julong. Control problems of unknown system[J].Proceedings of the Bilateral Meeting on Control systems.1981,156–171.
[19]Deng Julong. Control problems of grey systems[J].Systems&Control Letters,1982,1(5):288–294.
[20]Deng Julong. Zhou Chaoshun. Sufficient conditions for stability of a class of interconnected dynamic systems[J].Systems&Control Letters,1986,5(2):105–108.
[21]Deng Julong. Introduction to Grey System Theory[J].The Journal of Grey System, 1989,l(1):1–24.
[22]Deng Julong. Grey Hazy Sets[J].The Journal of Grey System,1992.4(1):13–30.
[23]Deng Julong. Extent Information Cover Grey System Theory[J].The Journal of Grey System,1995.7(2):131–138.
[24]邓聚龙.灰色控制系统[M].武汉:华中理工大学出版社,1993.
[25]邓聚龙.灰预测与灰决策[M].武汉:华中科技大学出版社,2002.
[26]王子亮.灰色建模技术理论[D].武汉:华中科技大学博士论文,1998.
[27]罗党.灰色决策问题的分析方法研究[D].南京航空航天大学博士论文,2005.
[28]党耀国.灰色不确定性分析与决策模型研究[D].南京航空航天大学博士论文,2006.
[29]Liu Sifeng.On Perron-Frobenius theorem of grey non-negative matrix and its proof[J].The Journal of Grey System,1989,1(2):157–166.
[30]Liu Sifeng,Lin Yi.An introduction to grey systems theory[M].Grove City:IIGSS Academic Publisher, 1998.
[31]李孜军.92–2001年我国灰色系统理论应用研究进展[J].系统工程,2003,21(5):8–12.
[32]刘思峰.灰色系统理论的产生与发展[J].南京航空航天大学学报(自然科学版),2004,36(2):267–272.
[33]邓聚龙.灰色系统理论与应用进展的若干问题.武汉:华中理工大学出版社,1996,1–10.
[34]刘思峰.走向世界的灰色系统理论[A].第十届全国灰色系统学术讨论会[C].北京,2002.
[35]刘思峰,史本广.灰色系统理论在科学发展中的作用和地位[J].农业系统科学与综合研究,2000,16(3):168–170.
[36]刘思峰,党耀国,方志耕等.灰色系统理论及其应用[M].北京:科学出版社,2004.
[37]肖新平,宋中民,李峰.灰技术基础及其应用[M].北京:科学出版社,2005.
[38]李荣均.模糊多准则决策理论与应用[M].北京:科学出版社,2002.
[39]魏世孝,周献中.多属性决策理论方法及其在C3I系统中的应用〔M〕.北京:国防工业出版社,1998.
[40]何波.不完全信息下的基于证据理论的多属性决策方法研究[D].中南大学硕士学位论文,2003
[41]Yager R. Uncertainty Modeling and Decision Support[J].Reliability Engineering & System Safety,2004,85(1):341-354.
[42]Savage L.The foundations of statistic[M].John Wiley and Sons, New York,1954.
[43]潘介人.决策分析中的效用理论[M].上海:上海交通大学出版社,2000.
[44]成盛超,谢如贤,吴健中.效用理论的历史与现状[J].系统工程理论与实践,1994,14(12):16-21.
[45]Keun Tae Cho. Multi-criteria Decision Methods: An attempt to evaluate and unify[J]. Mathematical and Computer Modelling,2003,37:1099-1119.
[46]Keeney R L. Creativity in decision making with value-focused thinking[J].Sloan ManagementReview,1994,35(4):33-41.
[47]Mangasarian O L. Misclassification minimization[J].Journal of Global Optimization 1994,5(4):309-323.
[48]Constantin Zopounidis, Michael Doumpos. A Multicriteria Decision Aid Methodology for Sorting Decision Problems:The Case of Financial Distress[J].Computational Economics,1999,14(3): 197-218.
[49]Roy B. The outranking approach and the foundations of ELECTRE methods[J].Theory and Decision,1991,31:49-73.
[50]Mousseau V, Rlowinski R. Infering an ELECTRE TRI model from assignment examples[]. Journal of Global Optimization,1998,9(12):157-174.
[51]Dias L C,Climaco J N. On computing ELECTRE's credibility indices under partial information[J].Journal of Multi-criteria Decision Analysis,1999,8:74-92.
[52]Figueira J,Roy B. Determining the weights of criteria in the ELECTRE type methods with a revised Simos’procedure[J].European Journal of Operational Research,2002,139: 317-326.
[53]Luis Dias,Vincent Mousseau,et al.An aggregation-disaggregation approach to obtain robust conclusions with ELECTRE TRI[J]. European Journal of Operational Research,2002, 138:332-348.
[54]Leyva-Lopez J C,Frenandez-Gonzalez E F.A new method for group decision support based on ELECTRE III methodlogy[J]. European Journal of Operational Research,2003,148: 14-27.
[55]Brans J P,Mareschal B,Vincke P. PROMETHEE:A new family of outranking methods in multi-criteria analysis[C].In:MCDM,IFORS’84.Amsterdam,North-Holland,1984,447-490.
[56]Brans J P,Mareschal B,Vincke P.A preference ranking organization method: The PROMETHEE method for MCDM[J].Management Science,1985,31(6):647-656.
[57]吴冀平.多准则评价方法的评价[J].决策与决策支持系统,1994,4(1):74-80.
[58]史本山.序偏好条件下多准则问题的分析方法[J].西安交通大学学报,1996,10:494-500.
[59]张秋明,史庆端,姚建民.采用多准则决策分析技术评估技改项目[J].中国软科学,1997,2:70-73.
[60]Li D F. An approach to fuzzy multi-attribute decision making under uncertainty[J]. Information Sciences,2005,169(l-2):97-112.
[61]王绪柱,单静.模糊量排序综述[J].模糊系统和数学,2002,16(4):25-34.
[62]Yao J S,Wu W M. Ranking fuzzy numbers based on decomposition principle and signed distance[J].Fuzzy Sets and Systems,2000,116:275-288.
[63]Dubois P,Prade H. Ranking fuzzy numbers in the setting of possibility theory[J]. Information Science,1983,30:183-224.
[64]Fortemps P,Roubens M. Ranking and defuzzification methods based on area compensation[J]. Fuzzy Sets and Systems,1996,82:319-330.
[65]Liouts,Wang M J. Ranking fuzzy numbers with integral value[J].Fuzzy Sets and Systems,1992,50:247-255.
[66]Iskander M G. Comparison of fuzzy number using possibility programming: comments and new concepts[J]. Computer Mathematics Application,2002,43:833-840.
[67]Tran L,Duckstein L. Comparison of fuzzy number using a fuzzy distance measure[J].Fuzzy sets and systems,2002,130:331-341.
[68]Chen L H,Lu H W. The Preference order of fuzzy number[J].Computer Mathematics Application,2002,44:1455-1465.
[69]Modarres M,Soheil S N. Ranking fuzzy numbers by preference ratio[J].Fuzzy Sets and Systems,2001,118:429-436.
[70]Chu Tachung. Ranking fuzzy numbers with an area between the centroid point and original point[J].Computer Mathematics Application,2002,43:111-117.
[71]吕翔昊,李登峰.基于模糊信息的群体多维偏好分析决策模型[J].系统工程与电子技术,2004,5:605-608.
[72]Nibin Chang, Wen C G, Chen Y L, Yong Y C.A grey fuzzy multi-objective programming approach for the optimal planning of a reservoir watershed[J]. Part A: Theoretical development. Wat. Res., 1996,30(10):2329–2334.
[73]罗党,刘思峰.一类灰色模糊决策问题的熵权分析方法[J].中国工程科学,2004,Vol.6(10):48-51.
[74]Huang G H, Baetz B W , Party G G. A grey fuzzy linear programming approach for municipal solid wasted management planning under uncertainty[J].Civil Engineering Systems , 1993 ,10:123–146.
[75]Yoping Huang, Shengfang Wang. The application of multiple grey models to the control problems[J].The Journal of Grey System,1995,7(4):299–313.
[76]Yoping Huang, Chichang Huang. The application of fuzzy and gradient descent methods to the grey prediction control[J].The Journal of Grey System,1995,7(1):9–22.
[77]Chinming Hong, Sinncheng Lin, Chihtang Chiang. Control of dynamic systems by fuzzy based grey prediction controller[J].The Journal of Grey System,1995,7(1):23–44.
[78]Lin Y H, Chew J M, Chen J M,Chen J Y and Tsi P S. Fuzzy self-tuning via grey prediction of PID controllers[J].EUFIT’95,1995:1095–1100.
[79]Hong Chinming, Lin Chenghung, Ted Tao. Grey cerebella model articulation controller[J]. The Journal of Grey System,1997,9(3):199–218.
[80]B.Kosko. Neural Networks and Fuzzy Systems[M].Prentice-Hill Inc.,USA,1992.
[81]L.X.Wang and J.M.Mendel. Generating fuzzy rules by learning from examples[J].IEEE Trams. Systems, Man, and Cybernation,1992,22(6):1414–1427.
[82]Y.M.Park, U.C.Moon, and K.Lee. A self-organizing fuzzy logic controller for dynamic systems using a fuzzy auto-regressive moving average(FARMA)model[J].IEEE Trams. Fuzzy Systems,1995, 3(1):75–82.
[83]S.Z.He, S.H.Tan and F.L.Xu. Fuzzy self-tuning of PID controllers[J].Fuzzy Sets and Systems, 1993,56:37–46.
[84]Delgado M,Verdegay J L,Vila MA. Linguistic decision making models[J].International Journal of Intelligent Systems,1992,7:479-492.
[85]Delgado M,Verdegay J L,Vila MA. A model for linguistic partial information in decision making problem[J]. International Journal of Intelligent Systems,1992,7: 479-492.
[86]胡应平.基于语言偏好的群体决策的软方法[J].系统工程学报,1996,11(4):53-60.
[87]徐泽水.纯语言多属性决策方法研究[J].控制与决策,2004,7:778-783.
[88]Herrera F, Herrera-Viedma E, Verdegay J L.A sequential selection process in group decision making with a linguistic assessment approach[J].Information Sciences,1995, 85:223-229.
[89]Herrera F, Herrera-Viedma E, Martnez L.A fusion approach for managing multi-granularity linguistic term sets in decision making[J].Fuzzy Sets and Systems,2000,114:43-58.
[90]Herrera F, Herrera-Viedma E. Aggregation operators for linguistic weighted information[J].IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans,1997,27(5):646-656.
[91]Herrera F, Herrera-Viedma E. Linguistic decision analysis: Steps for solving decision problems under linguistic information[J].Fuzzy Sets and Systems,2000,115:67-82.
[92]刘爱学,李永明,史忠科.一种基于语言变量的MCDM问题的决策方法[J].系统工程,2001,19(5):28-32.
[93]王欣荣,樊治平.群决策中基于语言信息处理的一种理想点法[J].中国管理科学,2002,10(6):84-87.
[94]王欣荣,樊治平.一种基于语言信息的多指标群决策方法[J].系统工程学报,2003,18(2):173-176.
[95]陈岩,樊治平.群决策中基于语言评价信息的TOPSIS方法[J].南京工业大学学报,2004,26(3):27-30.
[96]Xu Zeshui. Uncertain linguistic aggregation operations based approach to multiple attribute group decision making under uncertain linguistic environment[J].Information Sciences,2004,168: 171-184.
[97] Xu Zeshui. A method based on linguistic aggregation operators for group decision making with linguistic preference relations[J]. Information Sciences,2004,166: 19-30.
[98]Herrera F, Lopez E,Cristina Mendafia,Rodriugez M A. A linguistic decision model for personnel management solved with a linguistic biobjective genetic algorithm[J].Fuzzy Sets and Systems,2001,118:47-64.
[99]Herrera F, Lopez E,Rodriugez M A.A linguistic decision model for promotion mix management solved with genetic algorithms[J]. Fuzzy Sets and Systems,2001,131:47-61.
[100]Herrera F, Martnez L. A 2-tuple fuzzy linguistic representation model for computing with words[J].IEEE Transactions on Fuzzy Systems,2000,8(6):746-775.
[101]李洪燕,樊治平.一种基于语言判断矩阵的群决策问题的二元语义解法[J].系统工程,2003,21(5):104-108.
[102]王欣荣,樊治平.基于二元语义信息处理的一种语言群决策方法[J].管理科学学报,2003,6(5):1-5.
[103]徐泽水.基于语言信息的决策理论与方法[M].北京:科学出版社,2008.
[104]杨晓莉.混合多属性决策理论方法与应用研究[D].华中师范大学硕士学位论文,2007.
[105]宋业新,张曙红,陈绵云.基于模糊模式识别的时序混合多指标决策闭.系统工程与电子技术,2002,24(4):1-4.
[106]夏勇其,吴祈宗.一种混合型多属性决策问题的TOPSIS方法[J1.系统工程学报,2004,19(6):630-634.
[107]闫书丽,杨万才,肖新平.混合型多属性决策的一种新方法[J].数学的实践与认识,2007,37(16):111-116.
[108]丁传明,黎放,齐欢.一种基于相似度的混合型多属性决策方法[J].系统工程与电子技术,2007,29(5):737-740.
[109]梁昌勇,吴坚,陆文星,丁勇.一种新的混合型多属性决策方法及在供应商选择中的应用[J].中国管理科学,2006,14(6):71-76.
[110]Yang J B,Singh M G. An evidential reasoning approach for multiple attribute decision making with uncertainty[J].IEEE Trans. Systems,Man,and Cybernetics,1994,24(1):l-18.
[111]Yang J B , Sen P. A general multi-level evaluation process for hybrid MADM with uncertainty[J].IEEE Trans. Systems,Man,and Cybernetics,1994,24(10):1458一1473.
[112]Wang J,Yang J B,Sen P. Safety analysis and synthesis using fuzzy sets and evidentialreasoning[J].Reliability Engineering & System Safety,1995,47(2):103-118.
[113]Wang J,Yang J B,Sen P. Multi-person and multi-attribute design evaluations using evidential reasoning based on subjective safety and cost analyses[J].Reliability Engineering & System Safety,1996,52(2):113-128.
[114]Yang J B. Rule and utility-based evidential reasoning approach for complex decision analysis[J].European Journal of Operational Research,2001,131(l):31-61.
[115]Yang J B,Xu D L. On the evidential reasoning algorithm for multi-attribute decision analysis with uncertainty[J].IEEE Trans. Systems,Man,Cybernetics. A,2002,32(3):289-304.
[116]Van-Nam Huynh,Yoshiteru Nakamori,Tu-Bao Ho. Assessment Aggregation in the Evidential Reasoning Approach to MADM Under Uncertainty: orthogonal Versus Weighted Sum[J].Advances in Computer Seienee-ASIAN2004:Higher-Level Decision Making. 2004, 9th Asian Computing Science Conference,Chiang Mai,Thailand,December 8-10.
[117]何兵,郝爱民,赵沁平.一种基于不确定信息的决策方法[J].计算机学报,2004,2:281-85.
[118]Huynh V N,Tetsuya N. Multiple Attribute Decision Making under uncertainty: The Evidential Reasoning Approach Revisited[J].IEEE Trans. on Systems,Man and Cybernetics part A: Systems and Humans,2006,36(4):804-822.
[119]何波,任鸣鸣,王坚强.一种基于证据推理的信息不完全的多准则决策方法[J].数学的实践与认识,2006,36(3):58-62.
[120]王坚强,何波.基于证据推理的信息不完全的多准则决策方法及应用[J].系统工程与电子技术,2005(4):659-661.
[121]王坚强,孙超,吴小月.基于证据推理的信息不完全的多准则分类决策方法[J].武汉理工大学学报,2005,27(6):86-89.
[122]Yang J B,Wang Y M,Xu D L, Chin K S. The evidential reasoning approach for MADA under both probabilistic and fuzzy uncertainties[J].European Journal of Operational Research,2006,171(l):309-343.
[123]Wang Y M,Yang J B,Xu D L. Environmental impact assessment using the evidential reasoning approach[J].European Journal of Operational Research,2006,174(3): 1885- 1913.
[124]Xu D L, Yang J B,Wang Y M. The evidential reasoning approach for multi-attribute decision analysis under interval uncertainty[J]. European Journal of Operational Research , 2006 ,174(l):1914-1943.
[125]Wang Y M, Yang J B, Xu D L, Chin K S. The evidential reasoning approach for multiple attribute decision analysis using interval belief degrees[J]. European Journal of Operational Research,2006,175(l):35-66.
[126]王坚强.几种信息不完全确定的多准则决策方法研究[D].长沙:中南大学博士学位论文,2005.
[127]廖琳武,李垣,雷宏振.确定多属性群决策协调权的模型和方法闭.管理科学学报,2006,9(4):33-39.
[128]Park K.S. Mathematical Programming models for characterizing dominance and Potential optimality when multi-criteria alternatives values and weights are simultaneously incomplete[J].IEEE Transactions on System,Man,and Cybernetics,2004,5:601-614.
[129]Kim S.H.,Choi S.H.,Ahn B.S. Interactive group decision process with evolutionary database[J].Decision Support System,1998,23:333-345.
[130]Kim S.H.,Choi S.H. A utility range-based information group support system for multi- attribute decision making[J].Computers & Operations Research,2001,28:485-505.
[131]王坚强、孙超.基于语言判断矩阵的信息不完全的群体决策方法[J].系统工程与电子技术,2006,28(9):1345-1352.
[132]Salo A.A. Interactive decision aiding for group decision support[J].European Journal of Operational Research,1995,84:131-149.
[133]Yan H,Wei Q. Determining compromise weights for group decision making[J].Journal of the Operational Research Society,2002,53:680-687.
[134]罗党,刘思峰.灰色多指标风险型决策方法研究[J].系统工程与电子技术,2004,Vol.22(8):29-32.
[135]罗党,刘思峰.灰色动态规划研究[J].系统工程理论与实践,2004,Vol.24(4):56-62.
[136]罗党,刘思峰.灰色多目标规划算法研究[J].系统工程,2004,Vol.22(6):12-15.
[137]Deng Julong. Applications of tacit consent rationale to grey analysis[J].The Journal of Grey System,1997,9(1):82-88.
[138]Deng Julong. Tacit consent rationale in grey inference[J].The Journal of Grey System, 1997, 9(1):1-8.
[139]Deng Julong. Grey group decision in grey rationale space[J].The Journal of Grey System, 1998, 10(3):177-182.
[140]Deng Julong. The foundation of grey system theory[J]. The Journal of Grey System, 1997, 9(1):40-48.
[141]Deng Julong. Grey decision making of group, Grey System[M].China Ocean Press,1998: 115-129.2006,175(l):35-66.
[126]王坚强.几种信息不完全确定的多准则决策方法研究[D].长沙:中南大学博士学位论文,2005.
[127]廖琳武,李垣,雷宏振.确定多属性群决策协调权的模型和方法闭.管理科学学报,2006,9(4):33-39.
[128]Park K.S. Mathematical Programming models for characterizing dominance and Potential optimality when multi-criteria alternatives values and weights are simultaneously incomplete[J].IEEE Transactions on System,Man,and Cybernetics,2004,5:601-614.
[129]Kim S.H.,Choi S.H.,Ahn B.S. Interactive group decision process with evolutionary database[J].Decision Support System,1998,23:333-345.
[130]Kim S.H.,Choi S.H. A utility range-based information group support system for multi- attribute decision making[J].Computers & Operations Research,2001,28:485-505.
[131]王坚强、孙超.基于语言判断矩阵的信息不完全的群体决策方法[J].系统工程与电子技术,2006,28(9):1345-1352.
[132]Salo A.A. Interactive decision aiding for group decision support[J].European Journal of Operational Research,1995,84:131-149.
[133]Yan H,Wei Q. Determining compromise weights for group decision making[J].Journal of the Operational Research Society,2002,53:680-687.
[134]罗党,刘思峰.灰色多指标风险型决策方法研究[J].系统工程与电子技术,2004,Vol.22(8):29-32.
[135]罗党,刘思峰.灰色动态规划研究[J].系统工程理论与实践,2004,Vol.24(4):56-62.
[136]罗党,刘思峰.灰色多目标规划算法研究[J].系统工程,2004,Vol.22(6):12-15.
[137]Deng Julong. Applications of tacit consent rationale to grey analysis[J].The Journal of Grey System,1997,9(1):82-88.
[138]Deng Julong. Tacit consent rationale in grey inference[J].The Journal of Grey System, 1997, 9(1):1-8.
[139]Deng Julong. Grey group decision in grey rationale space[J].The Journal of Grey System, 1998, 10(3):177-182.
[140]Deng Julong. The foundation of grey system theory[J]. The Journal of Grey System, 1997, 9(1):40-48.
[141]Deng Julong. Grey decision making of group, Grey System[M].China Ocean Press,1998: 115-129.seasonal time series[J].Technological Forecasting and Social Change,2001,67:291-302.
[161]Fan Z P,Ma J,Zhang Q. An approach to multiple attribute decision making based fuzzy preference information on alternatives[J]. Fuzzy Sets andSystems,2002,131(1):101-106.
[162]徐泽水.求解不确定型多属性决策问题的一种新方法[J].系统工程学报,2002,17(2):177-181.
[163]Wang Juite, Lin Yungi. A fuzzy multicriteria group decision making approach to select configuration item for software development[J].Fuzzy Sets and Systems,2003,134(3):343-363.
[164]Lee Hsuan-Shih . Optimal consensus of fuzzy opinions under group decision making environment[J]. Fuzzy Sets and Systems, 2002, 132(3):303-315.
[165]Chen Chen-Tung . Extensions of the TOPSIS for group decision-making under fuzzy environment[J]. Fuzzy Sets and Systems,2000,114(1):1-9.
[166]张新波.多目标群体决策问题的灰色分析方法[J].信息与控制,2004,33(2):223-226.
[167]罗党,刘思峰.一类灰色群决策问题的分析方法[J].南京航空航天大学学报,2005, 37 (3):395-398.
[168]徐泽水,孙在东一类不确定性多属性决策问题的排序方法[J]管理科学学报,2002,5(3):35-39
[169]Xu Z S, Da Q L. The uncertain QWA operator[J].International Journal of intelligent Systems, 2002,17:569-575.
[170]Delgado M, Herrera F, Herrera-Viedma E, et al. Combining numerical and linguistic information in group decision making[J].Information Sciences,1998, 107(3):177-194.
[171]邱菀华.群组决策特征根法[J].应用数学与力学,1997,18(11):1027-1033.
[172]方卫国,周泓.逼近群体理想点的多目标群体决策算法[J].管理科学学报,1998,1(4):34-38.
[173]李洪燕,樊治平.群体决策中两种不同偏好信息的集成方法[J].东北大学学报(自然科学版),2000,21(3):336-338.
[174]朱建军.群决策中两类不确定偏好信息的集结方法研究[J].控制与决策,2006,21(8):889-892.
[175]LIU Si-feng, LIN Yi. Grey information: theory and practical applications[M].Spinger-Verlag London,2006,1-138,315-366.
[176]陈孝新.灰色多属性群决策的TOPSIS法[J].江西财经大学学报,2008,55(1):22-25.
[177]陈孝新,刘思峰.一种部分权重信息的灰色多属性群决策方法[J].系统工程与电子技术,2009,31(4):843-846.
[178]Varga,R.S. Matrix Iterative Analysis[M]. Prentice-Hall,Englewood Cliffs,New Jersey,1962.
[179]种晓丽.混合型多属性灰决策与模型的矩阵理论[D].武汉:武汉理工大学硕士论文,2006.
[180]Shafer G A. Mathematical Theory of Evidence[M].Princeton, N J, Princeton U P,1976.
[181]周光明,刘树人.不确定多属性决策中区间数的一种新排序法[J].系统工程,2006,24(4):115-117.
[182]王坚强.一种信息不完全确定的多准则语言群决策方法[J].控制与决策,2007,22(4):394-398.
[183]王坚强.一种多准则纯语言群决策方法[J].控制与决策,2007,22(5):545-553.
[184]Mareschal B. Weight stability intervals in multi-criteria decision[J]. European Journal of Operational Research,1998,109(1):54-64.
[185]Saaty T L. A scaling method for priorities in hierachical structures[J].Journal of Mathemathical Psychology,1997,33(15):234-281.
[186]罗庆成.灰色系统新方法[J].浙江:农业出版社,1992:157-161.
[187]崔杰,党耀国,刘思峰.基于灰色关联度求解指标权重的改进方法[J].中国管理科学,2008,16(5):141-145.
[188]玄光男,程润伟.遗传算法与工程优化[M].北京:清华大学出版社,2004.
[189]倪金林.遗传算法求解约束非线性规划及MATLAB实现[J].大学数学,2005,21(1):91-95.
[190]Opricovic S. Multi-criteria optimization of civil engineering systems[M]. Belgrade: Faculty of Civil Engineering,1998.
[191]Opricovic S, Tzeng G H. Comparative solution by MCDM methods: A comparative analysis of VIKOR and TOPSIS[J]. European Journal of Operational Research,2004,156(2):445-455.
[192]王坚强,张忠.信息不完全确定的多准则直觉模糊决策的折衷解法[C].2006中国控制与决策学术年会论文集,1195-1198.
[193]卫贵武,罗玉军,姚恒申.权重信息不完全的混合多属性决策方法[C].2006中国控制与决策学术年会论文集,1161-1164.