基于证据理论的多属性决策关联问题研究
|
摘要
多属性决策是决策科学的一个重要组成部分,工程、经济和管理领域中诸多问题均可以抽象为多属性决策问题,由于客观事物的复杂性、不确定性以及人类思维的模糊性,经典的多属性决策理论与方法不能完全满足人们的需求,一些不确定多属性决策方法相继提出。由于证据理论在表示及融合不确定信息方面的优势,基于证据理论的多属性决策方法日益受到人们的关注。然而,这些方法大多未考虑决策中存在的关联问题,忽略这些关联问题可能导致决策结果不合理,甚至决策失误,因此,对多属性决策的证据理论方法中存在的关联问题进行研究具有重要的理论意义与实际意义。论文针对基于证据理论的多属性决策中常见的若干关联问题展开研究,具体研究内容如下：
(1)证据关联问题。在多属性决策中,由于对属性的评价可能基于部分或完全相同的事实、数据、经验等,这样形成的证据是相关的,若直接用Dempster规则合成会产生过估计的合成结果。针对证据关联问题,首先分析了已有的相关证据合成方法,指出了一些不足之处。对于相关源证据己知的情况,提出一种相关证据的合成规则,在已知相关源证据的情况下能够得到准确的合成结果；对于相关源证据未知时,提出多证据的平均融合规则,以同时融合多个相关证据。考虑多专家意见的综合,由于专家意见存在关联,提出了基于平均融合规则的证据合成方法综合多专家的意见,并给出了一种确定专家权值的方法。
(2)层次关联问题。较复杂的多属性决策问题的指标往往具有递阶层次结构,在递阶层次结构中可能存在某属性与上层多个属性相关,这种情况下需要考虑属性的综合权值。在基于证据推理的多属性决策方法中,对多层次的属性集结是分层递归完成的,这一过程并未考虑属性的层次关联问题,不能准确反映基本属性在指标体系中的相对重要性,在解决递阶层次结构问题时仅能获得近似结果,因此建议采取综合权值表示属性的相对重要性,并给出确定综合属性权值的方法,将其应用于层次关联的多属性决策问题,将多层次结构转化为两个层次的决策问题,从而消除层次关联的影响。
(3)信任优势准则。基于信任累积分布的分析,解释和验证了一阶信任优势准则,在随机优势理论的指导下建立了二阶、三阶信任优势及近似信任优势准则。在信任优势准则的基础上,给出了定量的信任优势度定义,分析了信任优势度的性质。根据信任优势与信任优势度概念,结合级别优先序理论,分别提出了不同的多属性决策方法,为基于证据理论的多属性决策提供了新的研究思路。
(4)属性关联问题。多属性决策中属性相互作用的关联问题已逐渐受到人们的关注,但已有的基于证据理论的多属性决策方法均未考虑属性关联问题。针对属性关联问题,分析了属性关联的表现,基于信任优势和信任优势度的概念,提出了属性关联的信任优势决策方法,两种方法均考虑了属性关联时权值的处理,能够更好地满足人们实际决策的需求。
Multiple attribute decision making (MADM) is an important part of decision science, and many problems invovled in engineering, economic and managerial areas can be abstracted to MADM problems. Because of the complexity and uncertainty in the real world and the ambiguity in the human thoughts, the classical MADM theory cannot completely meet the demand of people, thus decision making methods under uncertainty was advanced one after another. Due to the advantages in representing and fusing uncertain information of evidence theory, people are increasingly concerned about MADM methods based on evidence theory. However, most of the approaches do not consider the dependent issues in the process of decision making, and it will cause the unreasonable results even fail to decision making if ignoring the issues. So, research on the dependent issues existed in these approaches has greatly theoretical and practical significance. The thesis focuses on various dependent issues. Specific contents are as follows:
(1) Evidence dependence. The evaluation of attributes may be partly or totally based on the same facts, data and experiences, thus it can be seen that the evidences are dependent. If Dempster rule is applied directly to dependent evidences, over-estimate will be resulted. For the evidence dependence issue, the existing combination methods as well as their deficiency are analyzed. If the dependent original evidence is known, the combination method for dependent evidence is proposed and exact result will be got; while the dependent orginal evidence is unknown, the average combination method is generalized so as to intergrate multiple dependent evidences. Since experts'opinions are related in general, the way to combine multiple experts opinions based on average fusion rule and to determine the weights of each expert are proposed.
(2) Hierarchical dependence. The hierarchical structure always existes in relatively complex multi-attribute decision making problems, that there may be some attributes related to more than one attribute in upper level within hierarchical structure. For this case, synthetical weights of the attributes should be concerned. Since attributes integration of evidential reasoning method is completed by the way of recursion in which the attributes ralationship between different levels is ignored, it can not tell the relative importance among the attributes in the index system and only get approximate results in dealing with such prolems. So it is suggested to represent the attributes' relative importance by synthetical weight, and an approach of how to determine the weights is proposed. In this way, the multi-level problems can be converted to double-level problems and the effect of hierarchical dependent from hierarchical structure could be eliminated.
(3) Belief dominance principle. By analyzing belief cumulative distribution, first-degree belief dominance principle is explained and verified, whereafter second-degree and third-degree belief dominance principle as well as almost belief dominance principle are also established guided by stochastic dominance theory. The definition of quantitative belief dominance degree is given and its characteristics are also analyzed. According to the concepts of belief dominance principle and belief dominance degree, different MADM methods are introduced inspired by outranking theory, which provide new perspective into MADM based on evidence theory.
(4) Attribute dependence. The dependent issue arised from interaction between attributes in MADM has been gradually concerned by more and more people, but the existing MADM methods based on evidence theory has never taken the problem of attribute dependence into consideration. The author analyzes the behaviour of attribute dependence, and proposes two approaches for attribute dependence which are based on the concept of belief dominance principle and belief dominance degree. By taking the weights of dependent attributes into account, the proposed approaches will better reflect the people's desire of decision making.
(1)证据关联问题。在多属性决策中,由于对属性的评价可能基于部分或完全相同的事实、数据、经验等,这样形成的证据是相关的,若直接用Dempster规则合成会产生过估计的合成结果。针对证据关联问题,首先分析了已有的相关证据合成方法,指出了一些不足之处。对于相关源证据己知的情况,提出一种相关证据的合成规则,在已知相关源证据的情况下能够得到准确的合成结果；对于相关源证据未知时,提出多证据的平均融合规则,以同时融合多个相关证据。考虑多专家意见的综合,由于专家意见存在关联,提出了基于平均融合规则的证据合成方法综合多专家的意见,并给出了一种确定专家权值的方法。
(2)层次关联问题。较复杂的多属性决策问题的指标往往具有递阶层次结构,在递阶层次结构中可能存在某属性与上层多个属性相关,这种情况下需要考虑属性的综合权值。在基于证据推理的多属性决策方法中,对多层次的属性集结是分层递归完成的,这一过程并未考虑属性的层次关联问题,不能准确反映基本属性在指标体系中的相对重要性,在解决递阶层次结构问题时仅能获得近似结果,因此建议采取综合权值表示属性的相对重要性,并给出确定综合属性权值的方法,将其应用于层次关联的多属性决策问题,将多层次结构转化为两个层次的决策问题,从而消除层次关联的影响。
(3)信任优势准则。基于信任累积分布的分析,解释和验证了一阶信任优势准则,在随机优势理论的指导下建立了二阶、三阶信任优势及近似信任优势准则。在信任优势准则的基础上,给出了定量的信任优势度定义,分析了信任优势度的性质。根据信任优势与信任优势度概念,结合级别优先序理论,分别提出了不同的多属性决策方法,为基于证据理论的多属性决策提供了新的研究思路。
(4)属性关联问题。多属性决策中属性相互作用的关联问题已逐渐受到人们的关注,但已有的基于证据理论的多属性决策方法均未考虑属性关联问题。针对属性关联问题,分析了属性关联的表现,基于信任优势和信任优势度的概念,提出了属性关联的信任优势决策方法,两种方法均考虑了属性关联时权值的处理,能够更好地满足人们实际决策的需求。
Multiple attribute decision making (MADM) is an important part of decision science, and many problems invovled in engineering, economic and managerial areas can be abstracted to MADM problems. Because of the complexity and uncertainty in the real world and the ambiguity in the human thoughts, the classical MADM theory cannot completely meet the demand of people, thus decision making methods under uncertainty was advanced one after another. Due to the advantages in representing and fusing uncertain information of evidence theory, people are increasingly concerned about MADM methods based on evidence theory. However, most of the approaches do not consider the dependent issues in the process of decision making, and it will cause the unreasonable results even fail to decision making if ignoring the issues. So, research on the dependent issues existed in these approaches has greatly theoretical and practical significance. The thesis focuses on various dependent issues. Specific contents are as follows:
(1) Evidence dependence. The evaluation of attributes may be partly or totally based on the same facts, data and experiences, thus it can be seen that the evidences are dependent. If Dempster rule is applied directly to dependent evidences, over-estimate will be resulted. For the evidence dependence issue, the existing combination methods as well as their deficiency are analyzed. If the dependent original evidence is known, the combination method for dependent evidence is proposed and exact result will be got; while the dependent orginal evidence is unknown, the average combination method is generalized so as to intergrate multiple dependent evidences. Since experts'opinions are related in general, the way to combine multiple experts opinions based on average fusion rule and to determine the weights of each expert are proposed.
(2) Hierarchical dependence. The hierarchical structure always existes in relatively complex multi-attribute decision making problems, that there may be some attributes related to more than one attribute in upper level within hierarchical structure. For this case, synthetical weights of the attributes should be concerned. Since attributes integration of evidential reasoning method is completed by the way of recursion in which the attributes ralationship between different levels is ignored, it can not tell the relative importance among the attributes in the index system and only get approximate results in dealing with such prolems. So it is suggested to represent the attributes' relative importance by synthetical weight, and an approach of how to determine the weights is proposed. In this way, the multi-level problems can be converted to double-level problems and the effect of hierarchical dependent from hierarchical structure could be eliminated.
(3) Belief dominance principle. By analyzing belief cumulative distribution, first-degree belief dominance principle is explained and verified, whereafter second-degree and third-degree belief dominance principle as well as almost belief dominance principle are also established guided by stochastic dominance theory. The definition of quantitative belief dominance degree is given and its characteristics are also analyzed. According to the concepts of belief dominance principle and belief dominance degree, different MADM methods are introduced inspired by outranking theory, which provide new perspective into MADM based on evidence theory.
(4) Attribute dependence. The dependent issue arised from interaction between attributes in MADM has been gradually concerned by more and more people, but the existing MADM methods based on evidence theory has never taken the problem of attribute dependence into consideration. The author analyzes the behaviour of attribute dependence, and proposes two approaches for attribute dependence which are based on the concept of belief dominance principle and belief dominance degree. By taking the weights of dependent attributes into account, the proposed approaches will better reflect the people's desire of decision making.
引文
[1]Hwang C L, Yoon K. Multiple Attribute Decision Making Methods and Applications[M]. Berlin:Springer-Verlag,1981.
[2]刘树林.多属性决策理论方法与应用研究[D].北京航空航天大学博士学位论文,1997.
[3]徐玖平,吴巍.多属性决策的理论与方法[M].北京：清华大学出版社,2006.
[4]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.
[5]Chen S J, Hwang C L. Fuzzy multiple attribute decision making:Methods and applications[M]. New York:Springer-Verlag,1992.
[6]Martel J M, Zaras K. Stochastic dominance in multicriterion analysis under risk[J]. Theory and Decision,1995,39(1):31-49.
[7]Salvatore G. Rough set theory for multicriterial decision analysis[J]. European Journal of Operational Research,2001,129(1):1-47.
[8]Xu D L, Yang J B. Introduction to multi-criteria decision making and the evidential reasoning approach[R]. Working Paper Series No.0106, Manchester School of Management, University of Manchester Institute and Technology, ISBN:1 86115 111 X,2001.
[9]Amor S B, Jabeur K, J. Martel M. Multiple criteria analysis in the context of information imperfections:Processing of additional information[J]. Operational Research,2005,5(3):395-417.
[10]Amor S B, Jabeur K, J. Martel M. Multiple criteria aggregation procedure for mixed evaluations[J]. European Journal of Operational Research,2007,181(3): 1506-1515.
[11]Yager R R, Liu·Liping(Eds.). Classic works of the Dempster-Shafer theory of belief functions[M]. Springer,2008.
[12]Saaty T L. The Analytic Hierarchy Process[M]. New York:McGraw-Hill, 1980.
[13]Stewart T J. Relationships between data envelopment analysis and multicriteria decision analysis[J]. Journal of the Operations Research Society,1996,47(5): 654-665.
[14]杨春.证据理论在决策评价中的应用研究[D].西安交通大学博士学位论文,1998.
[15]Shenoy P P. Valuation-based systems:A framework for managing uncertainty in expert systems[A]. In L. A. Zadeh & J. Kacprzyk(eds), Fuzzy Logic for the Management of Uncertainty, John Wiley, New York,1992:83-104.
[16]Shenoy P P. Valuation-based systems for Bayesian decision analysis[J]. Operations Research,1992,40(3):463-484.
[17]Xu H. Valuation-based systems for decision analysis using belief functions[J]. Decision Support Systems,1997,20(2):165-184.
[18]Liu L P, Shenoy P P. Representing asymmetric decision problems using coarse valuations[J]. Decision Support Systems,2004,37(1):119-135.
[19]Yager R R. Decision Making Under Dempster-Shafer Uncertainties [J]. International Journal of General Systems,1992,20(3):233-245.
[20]Engemann K J, Miller H E, Yager R R. Decision making with belief structures: an application in risk management[J]. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems,1996,4(1):1-25.
[21]Merigo J M, Casanovas M. Decision making with Dempster-Shafer theory of evidence using geometric operators [J]. International Journal of Computational Intelligence,2008,4(4):261-268.
[22]Boujelben M A, Smet Y D, Frikha A, et al. The first belief dominance:a new approach in evidence theory for comparing basic belief assignments[R]. CoDE-SMG Technical report series:TR/SMG/2009-001,2009.
[23]Boujelben M A, Smet Y D, Frikha A, et al. Building a binary outranking relation in uncertain, imprecise and multi-experts contexts:The application of evidence theory [J]. International Journal of Approximate Reasoning,2009,50(8): 1259-1278.
[24]Beynon M, Curry B, Morgan P. The Dempster-Shafer theory of evidence:an alternative approach to multicriteria decision modelling[J]. Omega,2000, 28(1):37-50.
[25]Beynon M. DS/AHP method:A mathematical analysis including an understanding of uncertainty[J]. European Journal of Operational Research,2002, 140(1):148-164.
[26]Beynon M. Understanding local ignorance and non-specificity within the DS/AHP method of multi-criteria decision making[J]. European Journal of Operational Research,2005,163(2):403-417.
[27]Hua Z S, Gong B G, Xu X. Y. A DS-AHP approach for multi-attribute decision making problem with incomplete information[J]. Expert Systems with Applications, 2008,34(3):2221-2227.
[28]Utkin L V, Simanova N V. Multi-criteria Decision Making by Incomplete Preferences[J]. Journal of Uncertain Systems,2008,2(4):255-266.
[29]梁昌勇,陈增明,丁勇.基于DS/AHP的供应商选择方法[J].运筹与管理,2005,14(6)：33-38.
[30]Yang J B, Singh M G. An evidential reasoning approach for multiple attribute decision making with uncertainty [J]. IEEE Transactions on Systems, Man, and Cybernetics,1994,24(1):1-18.
[31]Yang J B, Sen P. A general multi-level evaluation process for hybrid MADM with uncertainty[J]. IEEE Transactions on Systems, Man, and Cybernetics,1994, 24(10):1458-1473.
[32]Yang J B. Rule and utility based evidential reasoning approach for multiattribute decision analysis under uncertainties[J]. European Journal of Operational Research,2001,131(1):31-61.
[33]Sonmez M. Data transformation in the evidential reasoning-based decision making process[J], International Transactions in Operational Research,2007, 14(5):411-429.
[34]Yang J B, Xu D L. On the evidential reasoning algorithm for multiattribute decision analysis under uncertainty[J]. IEEE Transactions on Systems, Man and Cybernetics Part A:Systems and Humans,2002,32(3):289-304.
[35]Yang J B, Xu D L. Nonlinear information aggregation via evidential reasoning in multiattribute decision analysis under uncertainty [J]. IEEE Transactions on Systems, Man, and Cybernetics Part A:Systems and Humans,2002,32(3):376-393.
[36]Yang J B, Liu J, Wang J, et al. Belief Rule-Base Inference Methodology Using the Evidential Reasoning Approach-RIMER[J]. IEEE Transactions on Systems, Man, and Cybernetics Part A:Systems and Humans,2006,36(2):266-285.
[37]Yang J B, Liu J, Xu D L, et al. Optimization Models for Training Belief-Rule-Based Systems[J]. IEEE Transactions on Systems, Man, and Cybernetics Part A:Systems and Humans,2007,37(4):569-585.
[38]Xu D L, Liu J, Yang J B, et al. Inference and learning methodology of belief-rule-based expert system for pipeline leak detection[J]. Expert Systems with Applications,2007,32(1):103-113.
[39]Yang J B, Wang Y M, Xu D L, et al. The evidential reasoning approach for MADA under both probabilistic and fuzzy uncertainties[J]. European Journal of Operational Research,2006,171(1):309-343.
[40]Wang Y M, Yang J B, Xu D L, et al. The evidential reasoning approach for multiple attribute decision analysis using interval belief degrees[J]. European Journal of Operational Research,2006,175(1):35-66.
[41]Guo M, Yang J B, Chin K S, et al. Evidential reasoning based preference programming for multiple attribute decision analysis under uncertainty [J]. European Journal of Operational Research,2007,182(3):1294-1312.
[42]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(3):1914-1943.
[43]Guo M, Yang J B, Chin K S, et al. Evidential Reasoning Approach for Multiattribute Decision Analysis Under Both Fuzzy and Interval Uncertainty [J]. IEEE Transactions on Fuzzy Systems,2009,17(3):683-697.
[44]王坚强,何波.基于证据推理的信息不完全确定的MCDM方法[J].系统工程与电子技术,2005,27(4)：659-661.
[45]王坚强.一种信息不完全确定的多准则分类决策方法[J].控制与决策,2006,21(8)：863-867.
[46]王坚强.基于证据推理的信息不完全的多准则排序方法[J].系统工程学报, 2006,21(4):419-423.
[47]Xu D L, Yang J B. Intelligent decision system based on the evidential reasoning approach and its applications[J]. Journal of Telecommunications and Information Technology,2005, (3):73-80.
[48]Yang J B, Sen P. Multiple attribute design evaluation of large engineering products using the evidential reasoning approach[J]. Journal of Engineering Design, 1997,8(3):211-230.
[49]Li M, Yang J B. A decision model for self-assessment of business process based on the EFQM excellence model[J]. International Journal of Quality and Reliability Mangement,2003,20(2):163-187.
[50]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.
[51]Xu D L, McCarthy G, Yang J B. Intelligent decision system and its application in business innovation self assessment[J]. Decision Support Systems,2006,42(2): 664-673.
[52]江兵,潘洁琴,方军.基于证据推理的企业自主创新能力评价[J].系统管理学报,2009,18(4)：416-420.
[53]Chin K S, Xu D L, Yang J B, et al. Group-based ER-AHP system for product project screening[J]. Expert Systems with Applications,2008,35(4):1909-1929.
[54]Chin K. S, Yang J. B, Guo M, et al. Evidential-Reasoning-Interval-Based Method for New Product Design Assessment[J], IEEE Transactions on Engineering Management,2009,56(1):142-156.
[55]Zhou M, Liu X B, Yang J B, et al. Assessment of strategic R&D projects for car manufacturers based on the evidential reasoning approach[J]. International Journal of Intelligent Systems,2009,25(1):31-58.
[56]张全,樊治平,孟军.D-S理论在不确定性多属性决策中的应用[J].系统工程与电子技术,1999,21(11)：7-10.
[57]杨春,李怀祖.一个证据推理模型及其在专家意见综合中的应用[J].系统工程理论与实践,2001,(4)：43-48.
[58]杨萍,刘卫东.基于证据理论的群决策层次评价方法研究[J].系统工程与电子技术,2002,24(2)：42-44.
[59]吕文红,吴祈宗,郭银景.基于D-S证据理论的群决策专家意见集结方法[J].运筹与管理,2005,14(2)：10-13.
[60]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.
[61]陈增明.群决策环境下证据理论决策方法研究与应用[D].合肥工业大学博士学位论文,2006.
[62]付超.基于置信信念函数的群决策过程研究[D].合肥工业大学博士学位论文,2009.
[63]龚本刚.基于证据理论的不完全信息多属性决策方法研究[D].中国科学技术大学博士学位论文,2007.
[64]周谧.基于证据推理的多属性决策中若干问题的研究[D].合肥工业大学博士学位论文,2009.
[65]Zadeh L. A simple view of the Dempster-Shafer theory of evidence and its implication for the rule of combination[J]. AI Magazine,1986,7(2):85-90.
[66]郭华伟,施文康,邓勇等.证据冲突：丢弃,发现或化解?[J].系统工程与电子技术,2007,29(6)：890-898.
[67]Smets P. Analyzing the combination of conflicting belief functions[J]. Information Fusion,2007,8(4):387-412.
[68]孙怀江,杨静宇.一种相关证据合成方法[J].计算机学报,1999,22(9)：1004-1007.
[69]王明文,吴根秀,孙永强.相关证据合成方法[J].江西师范大学学报(自然科学版),2002,26(2)：135-137.
[70]Zhang Y, Bai B L. The Study and Improvement of Dependent Evidence Combining Method[C]. In:4th IEEE Conference on Industrial Electronics and Applications, Xi'an, China,2009:3750-3752.
[71]肖人彬,王雪,费奇等.相关证据合成方法的研究[J].模式识别与人工智能,1993,(9)：227-234.
[72]Wu Y G, Yang J Y, Liu K, et al. On the evidence inference theory[J]. Information Sciences,1996,89(3-4):245-260.
[73]罗志增,叶明.用证据理论实现相关信息的融合[J],电子与信息学报,2001,23(10)：970-974.
[74]杨善林,朱卫东,任明仑.基于可变参数优化的相关证据合成方法研究[J].管理科学学报,2003,6(5)：12-16.
[75]陈莉.基于粒子群神经网络优化的相关证据合成及应用[J].系统仿真学报,2009,21(3)：711-715.
[76]Yager R R. On the fusion of non-independent belief structures[J]. International Journal of General Systems,2009,38(5):505-531.
[77]Cattaneo M. Combining belief functions issued from dependent sources[C]. In Proc. Third International Symposium on Imprecise Probabilities and Their Application, Lugano, Switzerland,2003:133-147.
[78]Destercke S, Dubois D, Chojnacki E. Cautious conjunctive merging of belief functions[J]. Lecture Notes in Computer Science,2007,4724:332-343.
[79]Denoeux T. Conjunctive and disjunctive combination of belief functions induced by non distinct bodies of evidence[J]. Artificial Intelligence, 2008,172(2-3):234-264.
[80]Huynh V N, Nakamori Y, Ho T B. Assessment Aggregation in the Evidential Reasoning Approach to MADM Under Uncertainty:Orthogonal Sum Versus Weighted Sum[A]. In:Advances in Computer Science-ASIAN 2004:Higher-Level Decision Making[C],2004:109-127.
[81]Huynh V N, Nakamori Y, Ho T B, et al. Multiple attribute decision making under uncertainty:the evidential reasoning approach revisited[J]. IEEE Transactions on Systems, Man, and Cybernetics-Part A:Systems and Humans,2006,36(4): 804-822.
[82]J(?)sang A, Elouedi Z. Interpreting belief functions as Dirichlet distributions[C]. In the Proceedings of the 9th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU), Hammamet, Tunisia,2007.
[83]J(?)sang A, Diaz J, Rifqi M. Cumulative and averaging fusion of beliefs[J]. Information Fusion,2010,11(2):192-200.
[84]章玲,周德群基于关联的多属性决策分析理论研究综述[J].管理评论,2008,20(5)：51-57.
[85]Grabisch M, Labreuchea C. A decade of application of the Choquet and Sugeno integrals in multi-criteria decision aid[J].4OR A Quarterly Journal of Operations Research,2008,6(1):1-44.
[86]Siebert J. Aggregate Utility Factor Model:A Concept for Modeling Pair-wise Dependent Attributes in Multiattribute Utility Theory. Working paper, ISSN 1611-3837,2010.
[87]Figueira J R, Greco S, Roy B. ELECTRE methods with interaction between criteria:an extension of the concordance index[J]. European Journal of Operational Research 2009,199(2):478-495.
[88]章玲.基于关联的多属性决策分析理论及其应用研究[D].南京航空航天大学博士学位论文,2007.
[89]Dempster A P. Upper and lower probabilities induced by multivalued mapping [J]. Annals of Mathematical Statistics,1967,38(2):325-339.
[90]Dempster, A P. A generalization of Bayesian inference (with discussion)[J]. Journal of the Royal Statistical Society Series B,1968,30(2):205-247.
[91]Shafer G. A mathematical theory of evidence [M]. Princeton:Princeton University Press,1976.
[92]Srivastava R P, Liu L P. Applications of belief functions in business decisions: Areview[J], Information Systems Frontiers,2003,5(4):359-378.
[93]Smets P. What is Dempster-Shafer's model?[A]. In:Yager R R, Kacprzyk J, Fedrizzi M, ed. Advances in the Dempster-Shafer theory of evidence, New York: Wiley,1994:5-34.
[94]Kohlas J, Monney P A. A mathematical theory of hints:An appproach to Dempster-Shafer theory of evidence[M]. Lecture Notes in Economics and Mathematical Systems No.425. Springer-Verlage,1995.
[95]Smets P, Kennes R. The transferable belief model[J], Artificial Intelligence, 1994,66 (2):191-234.
[96]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.
[97]Orponen P. Dempster's rule of combination is#P-complete[J]. Artificial Intelligence,1990,44(1-2):245-253.
[98]Bauer M. Approximation algorithms and decision making in the Dempster-Shafer theory of evidence-An empirical study[J]. International Journal of Approximate Reasoning,1997,17(2-3):217237.
[99]Srivastava R. Alternative form of Dempster's rule for binary variables[J]. International Journal Intelligent System,2005,20(8):789-797.
[100]Bi Y X. An efficient triplet-based algorithm for evidential reasoning[J], International Journal of Intelligent Systems,2008,23(4):483-516.
[101]Smets P. Decision making in the TBM:the necessity of the pignistic transformation[J], International Journal of Approximate Reasoning,2005,38(2): 133-147.
[102]Cobb B R,, Shenoy P P. On the plausibility transformation method for translating belief function models to probability models[J]. International Journal of Approximate Reasoning,2006,41(3):314-330.
[103]Strat T M. Decision analysis using belief functions[J]. International Journal of Approximate Reasoning,1990,4(5):391-417.
[104]Shenoy P P. No double counting semantics for conditional independence[C]. In: 4th International Symposium on Imprecise Probabilities and Their Applications, Pittsburgh, Pennsylvania,2005:306-314.
[105]Smets P. The canonical decomposition of a weighted belief[C]. In: International Joint Conference on Artificial Intelligence, Morgan Kaufman, San Mateo, CA,1995:1896-1901.
[106]Walley P. Inferences from multinomial data:learning about a bag of marbles[J], Journal of the Royal Statistical Society,1996,58(1):3-57.
[107]Smets P. The concept of distinct evidence[C]. International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems,1992:789-794.
[108]贺金凤,徐济超,吴卫东.不确定性多属性决策中的ER方法改进[J].控制与决策,2006,21(4)：385-390.
[109]高斌,周雷,倪明放.不确定多属性决策中的改进ER算法[J].系统工程,2007,25(7)：105-107.
[110]岳超源.决策理论与方法[M].北京：科学出版社,2003.
[111]Jousselme A L, Grenier D, Bosse E. A new distance between two bodies of evidence[J]. Information Fusion,2001,2(2):91-101.
[112]陆文星,梁昌勇,丁勇.一种基于证据距离的客观权重确定方法[J].中国管理科学,2008,16(6)：95-99.
[113]Jiang W, Zhang A, Yang Q. A New Method to Determine Evidence Discounting Coefficient[C]. In D. S. Huang et al. (Eds.), ICIC 2008, LNCS 5226,2008:882-887.
[114]Murphy C.K. Combining belief functions when evidence conflicts [J]. Decision Support Systems,2000,29(1):1-9.
[115]毛荐其,霍保世,杨海山.高新技术项目投资的风险评价[J].数量经济技术经济研究,2002：29(8)：37-40.
[116]Levy H, Sarnat M. Portfolio and Investment Selection:Theory and Practice[M]. Prentice-Hall,1984.
[117]Yager R R. Cumulative distribution functions from Dempster-Shafer belief structures[J]. IEEE Transactions on Systems, Man and Cybernetics Part B: Cybernetics,2004,34(5):2080-2087.
[118]Smets P. Decision Making in a Context where Uncertainty is Represented by Belief Functions[A], In:Srivastava R P. & Mock T J. (Eds.):Belief functions in business decisions, Physica-Verlag, Heidelberg, Germany,2002:17-61.
[119]Schubert J. On p in a Decision-Theoretic apparatus of Dempster-Shafer theory[J]. International Journal of Approximate Reasoning,1995,13(3):185-200.
[120]Leshno M, Levy H. Preferred by "All" and Preferred by "Most" Decision Makers:Almost Stochastic Dominance[J]. Management Science,2002,48(8): 1074-1085.
[121]Levy H. Almost Stochastic Dominance[A]. In:Studies in Risk and Uncertainty, Springer,2006,12:331-351.
[122]张立清,解林,屠仁寿.随机优势指标方法及其应用[J].控制与决策,1995,10(1)：80-84.
[123]韩敏,孙昭旭,邱菀华等.基于随机占优关系的ELECTRE Ⅲ方法[J].系统工程,2006,24(5)：118-121.
[124]姚升保.基于随机优势与概率优势的风险型多属性决策方法[J].预测,2007,26(3)：33-38.
[125]任剑,高阳,王坚强等.随机多准则决策的PROMETHEEⅡ方法[J].管理学报,2009,6(10)：1319-1322.
[126]Zhang Y, Fan Z. P, Liu Y. A method based on stochastic dominance degrees for stochastic multiple criteria decision making[J]. Computers & Industrial Engineering, 2010,58(4):544-552.
[127]孙威武.技术创新项目选择综合评价[J].数量经济技术经济研究,2003,20(4)：88-91.
[128]Carlsson C, Fuller R. Multiple criteria decision makingrthe case for interdependence[J]. Computers & Operations Research,1995,22(3):251-260.
[2]刘树林.多属性决策理论方法与应用研究[D].北京航空航天大学博士学位论文,1997.
[3]徐玖平,吴巍.多属性决策的理论与方法[M].北京：清华大学出版社,2006.
[4]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.
[5]Chen S J, Hwang C L. Fuzzy multiple attribute decision making:Methods and applications[M]. New York:Springer-Verlag,1992.
[6]Martel J M, Zaras K. Stochastic dominance in multicriterion analysis under risk[J]. Theory and Decision,1995,39(1):31-49.
[7]Salvatore G. Rough set theory for multicriterial decision analysis[J]. European Journal of Operational Research,2001,129(1):1-47.
[8]Xu D L, Yang J B. Introduction to multi-criteria decision making and the evidential reasoning approach[R]. Working Paper Series No.0106, Manchester School of Management, University of Manchester Institute and Technology, ISBN:1 86115 111 X,2001.
[9]Amor S B, Jabeur K, J. Martel M. Multiple criteria analysis in the context of information imperfections:Processing of additional information[J]. Operational Research,2005,5(3):395-417.
[10]Amor S B, Jabeur K, J. Martel M. Multiple criteria aggregation procedure for mixed evaluations[J]. European Journal of Operational Research,2007,181(3): 1506-1515.
[11]Yager R R, Liu·Liping(Eds.). Classic works of the Dempster-Shafer theory of belief functions[M]. Springer,2008.
[12]Saaty T L. The Analytic Hierarchy Process[M]. New York:McGraw-Hill, 1980.
[13]Stewart T J. Relationships between data envelopment analysis and multicriteria decision analysis[J]. Journal of the Operations Research Society,1996,47(5): 654-665.
[14]杨春.证据理论在决策评价中的应用研究[D].西安交通大学博士学位论文,1998.
[15]Shenoy P P. Valuation-based systems:A framework for managing uncertainty in expert systems[A]. In L. A. Zadeh & J. Kacprzyk(eds), Fuzzy Logic for the Management of Uncertainty, John Wiley, New York,1992:83-104.
[16]Shenoy P P. Valuation-based systems for Bayesian decision analysis[J]. Operations Research,1992,40(3):463-484.
[17]Xu H. Valuation-based systems for decision analysis using belief functions[J]. Decision Support Systems,1997,20(2):165-184.
[18]Liu L P, Shenoy P P. Representing asymmetric decision problems using coarse valuations[J]. Decision Support Systems,2004,37(1):119-135.
[19]Yager R R. Decision Making Under Dempster-Shafer Uncertainties [J]. International Journal of General Systems,1992,20(3):233-245.
[20]Engemann K J, Miller H E, Yager R R. Decision making with belief structures: an application in risk management[J]. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems,1996,4(1):1-25.
[21]Merigo J M, Casanovas M. Decision making with Dempster-Shafer theory of evidence using geometric operators [J]. International Journal of Computational Intelligence,2008,4(4):261-268.
[22]Boujelben M A, Smet Y D, Frikha A, et al. The first belief dominance:a new approach in evidence theory for comparing basic belief assignments[R]. CoDE-SMG Technical report series:TR/SMG/2009-001,2009.
[23]Boujelben M A, Smet Y D, Frikha A, et al. Building a binary outranking relation in uncertain, imprecise and multi-experts contexts:The application of evidence theory [J]. International Journal of Approximate Reasoning,2009,50(8): 1259-1278.
[24]Beynon M, Curry B, Morgan P. The Dempster-Shafer theory of evidence:an alternative approach to multicriteria decision modelling[J]. Omega,2000, 28(1):37-50.
[25]Beynon M. DS/AHP method:A mathematical analysis including an understanding of uncertainty[J]. European Journal of Operational Research,2002, 140(1):148-164.
[26]Beynon M. Understanding local ignorance and non-specificity within the DS/AHP method of multi-criteria decision making[J]. European Journal of Operational Research,2005,163(2):403-417.
[27]Hua Z S, Gong B G, Xu X. Y. A DS-AHP approach for multi-attribute decision making problem with incomplete information[J]. Expert Systems with Applications, 2008,34(3):2221-2227.
[28]Utkin L V, Simanova N V. Multi-criteria Decision Making by Incomplete Preferences[J]. Journal of Uncertain Systems,2008,2(4):255-266.
[29]梁昌勇,陈增明,丁勇.基于DS/AHP的供应商选择方法[J].运筹与管理,2005,14(6)：33-38.
[30]Yang J B, Singh M G. An evidential reasoning approach for multiple attribute decision making with uncertainty [J]. IEEE Transactions on Systems, Man, and Cybernetics,1994,24(1):1-18.
[31]Yang J B, Sen P. A general multi-level evaluation process for hybrid MADM with uncertainty[J]. IEEE Transactions on Systems, Man, and Cybernetics,1994, 24(10):1458-1473.
[32]Yang J B. Rule and utility based evidential reasoning approach for multiattribute decision analysis under uncertainties[J]. European Journal of Operational Research,2001,131(1):31-61.
[33]Sonmez M. Data transformation in the evidential reasoning-based decision making process[J], International Transactions in Operational Research,2007, 14(5):411-429.
[34]Yang J B, Xu D L. On the evidential reasoning algorithm for multiattribute decision analysis under uncertainty[J]. IEEE Transactions on Systems, Man and Cybernetics Part A:Systems and Humans,2002,32(3):289-304.
[35]Yang J B, Xu D L. Nonlinear information aggregation via evidential reasoning in multiattribute decision analysis under uncertainty [J]. IEEE Transactions on Systems, Man, and Cybernetics Part A:Systems and Humans,2002,32(3):376-393.
[36]Yang J B, Liu J, Wang J, et al. Belief Rule-Base Inference Methodology Using the Evidential Reasoning Approach-RIMER[J]. IEEE Transactions on Systems, Man, and Cybernetics Part A:Systems and Humans,2006,36(2):266-285.
[37]Yang J B, Liu J, Xu D L, et al. Optimization Models for Training Belief-Rule-Based Systems[J]. IEEE Transactions on Systems, Man, and Cybernetics Part A:Systems and Humans,2007,37(4):569-585.
[38]Xu D L, Liu J, Yang J B, et al. Inference and learning methodology of belief-rule-based expert system for pipeline leak detection[J]. Expert Systems with Applications,2007,32(1):103-113.
[39]Yang J B, Wang Y M, Xu D L, et al. The evidential reasoning approach for MADA under both probabilistic and fuzzy uncertainties[J]. European Journal of Operational Research,2006,171(1):309-343.
[40]Wang Y M, Yang J B, Xu D L, et al. The evidential reasoning approach for multiple attribute decision analysis using interval belief degrees[J]. European Journal of Operational Research,2006,175(1):35-66.
[41]Guo M, Yang J B, Chin K S, et al. Evidential reasoning based preference programming for multiple attribute decision analysis under uncertainty [J]. European Journal of Operational Research,2007,182(3):1294-1312.
[42]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(3):1914-1943.
[43]Guo M, Yang J B, Chin K S, et al. Evidential Reasoning Approach for Multiattribute Decision Analysis Under Both Fuzzy and Interval Uncertainty [J]. IEEE Transactions on Fuzzy Systems,2009,17(3):683-697.
[44]王坚强,何波.基于证据推理的信息不完全确定的MCDM方法[J].系统工程与电子技术,2005,27(4)：659-661.
[45]王坚强.一种信息不完全确定的多准则分类决策方法[J].控制与决策,2006,21(8)：863-867.
[46]王坚强.基于证据推理的信息不完全的多准则排序方法[J].系统工程学报, 2006,21(4):419-423.
[47]Xu D L, Yang J B. Intelligent decision system based on the evidential reasoning approach and its applications[J]. Journal of Telecommunications and Information Technology,2005, (3):73-80.
[48]Yang J B, Sen P. Multiple attribute design evaluation of large engineering products using the evidential reasoning approach[J]. Journal of Engineering Design, 1997,8(3):211-230.
[49]Li M, Yang J B. A decision model for self-assessment of business process based on the EFQM excellence model[J]. International Journal of Quality and Reliability Mangement,2003,20(2):163-187.
[50]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.
[51]Xu D L, McCarthy G, Yang J B. Intelligent decision system and its application in business innovation self assessment[J]. Decision Support Systems,2006,42(2): 664-673.
[52]江兵,潘洁琴,方军.基于证据推理的企业自主创新能力评价[J].系统管理学报,2009,18(4)：416-420.
[53]Chin K S, Xu D L, Yang J B, et al. Group-based ER-AHP system for product project screening[J]. Expert Systems with Applications,2008,35(4):1909-1929.
[54]Chin K. S, Yang J. B, Guo M, et al. Evidential-Reasoning-Interval-Based Method for New Product Design Assessment[J], IEEE Transactions on Engineering Management,2009,56(1):142-156.
[55]Zhou M, Liu X B, Yang J B, et al. Assessment of strategic R&D projects for car manufacturers based on the evidential reasoning approach[J]. International Journal of Intelligent Systems,2009,25(1):31-58.
[56]张全,樊治平,孟军.D-S理论在不确定性多属性决策中的应用[J].系统工程与电子技术,1999,21(11)：7-10.
[57]杨春,李怀祖.一个证据推理模型及其在专家意见综合中的应用[J].系统工程理论与实践,2001,(4)：43-48.
[58]杨萍,刘卫东.基于证据理论的群决策层次评价方法研究[J].系统工程与电子技术,2002,24(2)：42-44.
[59]吕文红,吴祈宗,郭银景.基于D-S证据理论的群决策专家意见集结方法[J].运筹与管理,2005,14(2)：10-13.
[60]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.
[61]陈增明.群决策环境下证据理论决策方法研究与应用[D].合肥工业大学博士学位论文,2006.
[62]付超.基于置信信念函数的群决策过程研究[D].合肥工业大学博士学位论文,2009.
[63]龚本刚.基于证据理论的不完全信息多属性决策方法研究[D].中国科学技术大学博士学位论文,2007.
[64]周谧.基于证据推理的多属性决策中若干问题的研究[D].合肥工业大学博士学位论文,2009.
[65]Zadeh L. A simple view of the Dempster-Shafer theory of evidence and its implication for the rule of combination[J]. AI Magazine,1986,7(2):85-90.
[66]郭华伟,施文康,邓勇等.证据冲突：丢弃,发现或化解?[J].系统工程与电子技术,2007,29(6)：890-898.
[67]Smets P. Analyzing the combination of conflicting belief functions[J]. Information Fusion,2007,8(4):387-412.
[68]孙怀江,杨静宇.一种相关证据合成方法[J].计算机学报,1999,22(9)：1004-1007.
[69]王明文,吴根秀,孙永强.相关证据合成方法[J].江西师范大学学报(自然科学版),2002,26(2)：135-137.
[70]Zhang Y, Bai B L. The Study and Improvement of Dependent Evidence Combining Method[C]. In:4th IEEE Conference on Industrial Electronics and Applications, Xi'an, China,2009:3750-3752.
[71]肖人彬,王雪,费奇等.相关证据合成方法的研究[J].模式识别与人工智能,1993,(9)：227-234.
[72]Wu Y G, Yang J Y, Liu K, et al. On the evidence inference theory[J]. Information Sciences,1996,89(3-4):245-260.
[73]罗志增,叶明.用证据理论实现相关信息的融合[J],电子与信息学报,2001,23(10)：970-974.
[74]杨善林,朱卫东,任明仑.基于可变参数优化的相关证据合成方法研究[J].管理科学学报,2003,6(5)：12-16.
[75]陈莉.基于粒子群神经网络优化的相关证据合成及应用[J].系统仿真学报,2009,21(3)：711-715.
[76]Yager R R. On the fusion of non-independent belief structures[J]. International Journal of General Systems,2009,38(5):505-531.
[77]Cattaneo M. Combining belief functions issued from dependent sources[C]. In Proc. Third International Symposium on Imprecise Probabilities and Their Application, Lugano, Switzerland,2003:133-147.
[78]Destercke S, Dubois D, Chojnacki E. Cautious conjunctive merging of belief functions[J]. Lecture Notes in Computer Science,2007,4724:332-343.
[79]Denoeux T. Conjunctive and disjunctive combination of belief functions induced by non distinct bodies of evidence[J]. Artificial Intelligence, 2008,172(2-3):234-264.
[80]Huynh V N, Nakamori Y, Ho T B. Assessment Aggregation in the Evidential Reasoning Approach to MADM Under Uncertainty:Orthogonal Sum Versus Weighted Sum[A]. In:Advances in Computer Science-ASIAN 2004:Higher-Level Decision Making[C],2004:109-127.
[81]Huynh V N, Nakamori Y, Ho T B, et al. Multiple attribute decision making under uncertainty:the evidential reasoning approach revisited[J]. IEEE Transactions on Systems, Man, and Cybernetics-Part A:Systems and Humans,2006,36(4): 804-822.
[82]J(?)sang A, Elouedi Z. Interpreting belief functions as Dirichlet distributions[C]. In the Proceedings of the 9th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU), Hammamet, Tunisia,2007.
[83]J(?)sang A, Diaz J, Rifqi M. Cumulative and averaging fusion of beliefs[J]. Information Fusion,2010,11(2):192-200.
[84]章玲,周德群基于关联的多属性决策分析理论研究综述[J].管理评论,2008,20(5)：51-57.
[85]Grabisch M, Labreuchea C. A decade of application of the Choquet and Sugeno integrals in multi-criteria decision aid[J].4OR A Quarterly Journal of Operations Research,2008,6(1):1-44.
[86]Siebert J. Aggregate Utility Factor Model:A Concept for Modeling Pair-wise Dependent Attributes in Multiattribute Utility Theory. Working paper, ISSN 1611-3837,2010.
[87]Figueira J R, Greco S, Roy B. ELECTRE methods with interaction between criteria:an extension of the concordance index[J]. European Journal of Operational Research 2009,199(2):478-495.
[88]章玲.基于关联的多属性决策分析理论及其应用研究[D].南京航空航天大学博士学位论文,2007.
[89]Dempster A P. Upper and lower probabilities induced by multivalued mapping [J]. Annals of Mathematical Statistics,1967,38(2):325-339.
[90]Dempster, A P. A generalization of Bayesian inference (with discussion)[J]. Journal of the Royal Statistical Society Series B,1968,30(2):205-247.
[91]Shafer G. A mathematical theory of evidence [M]. Princeton:Princeton University Press,1976.
[92]Srivastava R P, Liu L P. Applications of belief functions in business decisions: Areview[J], Information Systems Frontiers,2003,5(4):359-378.
[93]Smets P. What is Dempster-Shafer's model?[A]. In:Yager R R, Kacprzyk J, Fedrizzi M, ed. Advances in the Dempster-Shafer theory of evidence, New York: Wiley,1994:5-34.
[94]Kohlas J, Monney P A. A mathematical theory of hints:An appproach to Dempster-Shafer theory of evidence[M]. Lecture Notes in Economics and Mathematical Systems No.425. Springer-Verlage,1995.
[95]Smets P, Kennes R. The transferable belief model[J], Artificial Intelligence, 1994,66 (2):191-234.
[96]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.
[97]Orponen P. Dempster's rule of combination is#P-complete[J]. Artificial Intelligence,1990,44(1-2):245-253.
[98]Bauer M. Approximation algorithms and decision making in the Dempster-Shafer theory of evidence-An empirical study[J]. International Journal of Approximate Reasoning,1997,17(2-3):217237.
[99]Srivastava R. Alternative form of Dempster's rule for binary variables[J]. International Journal Intelligent System,2005,20(8):789-797.
[100]Bi Y X. An efficient triplet-based algorithm for evidential reasoning[J], International Journal of Intelligent Systems,2008,23(4):483-516.
[101]Smets P. Decision making in the TBM:the necessity of the pignistic transformation[J], International Journal of Approximate Reasoning,2005,38(2): 133-147.
[102]Cobb B R,, Shenoy P P. On the plausibility transformation method for translating belief function models to probability models[J]. International Journal of Approximate Reasoning,2006,41(3):314-330.
[103]Strat T M. Decision analysis using belief functions[J]. International Journal of Approximate Reasoning,1990,4(5):391-417.
[104]Shenoy P P. No double counting semantics for conditional independence[C]. In: 4th International Symposium on Imprecise Probabilities and Their Applications, Pittsburgh, Pennsylvania,2005:306-314.
[105]Smets P. The canonical decomposition of a weighted belief[C]. In: International Joint Conference on Artificial Intelligence, Morgan Kaufman, San Mateo, CA,1995:1896-1901.
[106]Walley P. Inferences from multinomial data:learning about a bag of marbles[J], Journal of the Royal Statistical Society,1996,58(1):3-57.
[107]Smets P. The concept of distinct evidence[C]. International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems,1992:789-794.
[108]贺金凤,徐济超,吴卫东.不确定性多属性决策中的ER方法改进[J].控制与决策,2006,21(4)：385-390.
[109]高斌,周雷,倪明放.不确定多属性决策中的改进ER算法[J].系统工程,2007,25(7)：105-107.
[110]岳超源.决策理论与方法[M].北京：科学出版社,2003.
[111]Jousselme A L, Grenier D, Bosse E. A new distance between two bodies of evidence[J]. Information Fusion,2001,2(2):91-101.
[112]陆文星,梁昌勇,丁勇.一种基于证据距离的客观权重确定方法[J].中国管理科学,2008,16(6)：95-99.
[113]Jiang W, Zhang A, Yang Q. A New Method to Determine Evidence Discounting Coefficient[C]. In D. S. Huang et al. (Eds.), ICIC 2008, LNCS 5226,2008:882-887.
[114]Murphy C.K. Combining belief functions when evidence conflicts [J]. Decision Support Systems,2000,29(1):1-9.
[115]毛荐其,霍保世,杨海山.高新技术项目投资的风险评价[J].数量经济技术经济研究,2002：29(8)：37-40.
[116]Levy H, Sarnat M. Portfolio and Investment Selection:Theory and Practice[M]. Prentice-Hall,1984.
[117]Yager R R. Cumulative distribution functions from Dempster-Shafer belief structures[J]. IEEE Transactions on Systems, Man and Cybernetics Part B: Cybernetics,2004,34(5):2080-2087.
[118]Smets P. Decision Making in a Context where Uncertainty is Represented by Belief Functions[A], In:Srivastava R P. & Mock T J. (Eds.):Belief functions in business decisions, Physica-Verlag, Heidelberg, Germany,2002:17-61.
[119]Schubert J. On p in a Decision-Theoretic apparatus of Dempster-Shafer theory[J]. International Journal of Approximate Reasoning,1995,13(3):185-200.
[120]Leshno M, Levy H. Preferred by "All" and Preferred by "Most" Decision Makers:Almost Stochastic Dominance[J]. Management Science,2002,48(8): 1074-1085.
[121]Levy H. Almost Stochastic Dominance[A]. In:Studies in Risk and Uncertainty, Springer,2006,12:331-351.
[122]张立清,解林,屠仁寿.随机优势指标方法及其应用[J].控制与决策,1995,10(1)：80-84.
[123]韩敏,孙昭旭,邱菀华等.基于随机占优关系的ELECTRE Ⅲ方法[J].系统工程,2006,24(5)：118-121.
[124]姚升保.基于随机优势与概率优势的风险型多属性决策方法[J].预测,2007,26(3)：33-38.
[125]任剑,高阳,王坚强等.随机多准则决策的PROMETHEEⅡ方法[J].管理学报,2009,6(10)：1319-1322.
[126]Zhang Y, Fan Z. P, Liu Y. A method based on stochastic dominance degrees for stochastic multiple criteria decision making[J]. Computers & Industrial Engineering, 2010,58(4):544-552.
[127]孙威武.技术创新项目选择综合评价[J].数量经济技术经济研究,2003,20(4)：88-91.
[128]Carlsson C, Fuller R. Multiple criteria decision makingrthe case for interdependence[J]. Computers & Operations Research,1995,22(3):251-260.