动态不确定评价问题的随机聚合求解及应用
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摘要
面向区间数形式的多阶段动态不确定综合评价问题,在传统绝对形式排序结论的基础上,进一步从随机模拟的视角讨论该问题的随机聚合求解方法及其他形式的评价结论.首先对体现被评价对象之间两两比较的优胜度概率矩阵进行了介绍,并给出了其模拟求解算法及简化算法;然后基于优胜度概率矩阵,发展出了带有概率特征的可能性排序及用于反映被评价对象不同时期发展状态的动态估值等评价结论.最后,通过武器组装自动化流水线运转情况的动态评价算例对上述多种形式的评价结论进行了求解与分析.多种形式的评价结论,不仅更加吻合动态不确定性评价问题的背景,而且进一步丰富了评价结论的形式,从而可使评价需求方从不同侧面更加全面地了解被评价对象的发展动态.
To the dynamic evaluation problems with interval uncertainties, we further discuss the stochastic clustered solution from the aspect of stochastic simulation and develop other types of evaluation results.Firstly, the preference ratio matrix, representing the degree of which one alternative is superior to another one, is introduced, and the simulation solution and the associated simplified method for this matrix is developed. Then other types of results, including the possible ranking with preference probability, the dynamic estimated value for alternatives indicating their development trend, are provided based on the preference ratio matrix. At last, an example related to the dynamic evaluation of the automated assembly line for weapon building is introduced to illustrate the solution of these different types of results and give some analysis. This research can not only be more consistent with the dynamic uncertainty environment,but also further enrich the evaluation results, which can provide more information for the understanding of the alternatives' development trend from different aspects.
To the dynamic evaluation problems with interval uncertainties, we further discuss the stochastic clustered solution from the aspect of stochastic simulation and develop other types of evaluation results.Firstly, the preference ratio matrix, representing the degree of which one alternative is superior to another one, is introduced, and the simulation solution and the associated simplified method for this matrix is developed. Then other types of results, including the possible ranking with preference probability, the dynamic estimated value for alternatives indicating their development trend, are provided based on the preference ratio matrix. At last, an example related to the dynamic evaluation of the automated assembly line for weapon building is introduced to illustrate the solution of these different types of results and give some analysis. This research can not only be more consistent with the dynamic uncertainty environment,but also further enrich the evaluation results, which can provide more information for the understanding of the alternatives' development trend from different aspects.
引文
[1]王宗军.综合评价的方法、问题及其研究趋势[J].管理科学学报,1998, 1(1):73-79.Wang Z J. On the methods, problems and research trends of comprehensive evaluation[J]. Journal of Management Sciences in China, 1998, 1(1):73-79.
[2]郭亚军.综合评价理论、方法及应用[M].北京:科学出版社,2002.Guo Y J. Comprehensive evaluation theory, methods and application[M]. Beijing:Science Press, 2002.
[3]陈衍泰,陈国宏,李美娟.综合评价方法分类及研究进展[J].管理科学学报,2004, 7(2):69-79.Chen Y T, Chen G H, Li M J. Classification&research advancement of comprehensive evaluation methods[J].Journal of Management Sciences in China, 2004, 7(2):69-79.
[4] Liu J P, Chen H Y, Zhou L G, et al. On the properties of the generalized OWHA operators and their application to group decision making[J]. Journal of Intelligent&Fuzzy Systems, 2014, 27(4):2077-2089.
[5] Kou G, Wu W S, Zhao Y Y, et al. A dynamic assessment method for urban eco-environmental quality evaluation[J]. Journal of Multi-Criteria Decision Analysis, 2011, 18(1):23-38.
[6] Tura T, Harmaakorpi V, Pekkola S. Breaking inside the black box:Towards a dynamic evaluation framework for regional innovative capability[J]. Science and Public Policy, 2008, 5(10):733-744.
[7]金菊良,王淑娟,魏一鸣.动态多指标决策问题的投影寻踪模型[J].中国管理科学,2004, 12(1):64-67.Jin J L, Wang S J, Wei Y M. Projection pursuit model for dynamic multiple attribute decision problems[J].Chinese Journal of Management Science, 2004, 12(1):64-67.
[8]王欣荣,樊治平.上市公司财务状况的动态多指标综合评价方法[J].系统工程理论与实践,2002, 22(4):54-57.Wang X R, Fan Z P. Dynamic multiple index synthetical evaluation for financial condition of public corporations[J]. Systems Engineering—Theory&Practice, 2002, 22(4):54-57.
[9]王雪荣.一种基于证据理论的动态综合效绩评价实用方法[J].中国管理科学,2006, 14(4):121-127.Wang X R. The practical method of dynamically evaluating the comprehensive performance based on evidentialreasoning[J]. Chinese Journal of Management Science, 2006, 14(4):121-127.
[10]李美娟,陈国宏,林志炳,等.基于理想解法的动态评价方法研究[J].中国管理科学,2015, 23(10):156-161.Li M J, Chen G H, Lin Z B, et al. Dynamic evaluation method based on TOPSIS[J]. Chinese Journal of Management Science, 2015, 23(10):156-161.
[11]易平涛,郭亚军,张丹宁.基于双激励控制线的多阶段信息集结方法[J].预测,2007,26(3):39-43.Yi P T, Guo Y J, Zhang D N. A multi-phase information aggregation method based on double inspiriting control lines[J]. Forecasting, 2007, 26(3):39-43.
[12]易平涛,张丹宁,郭亚军.基于泛激励控制线的多阶段信息集结方法[J].运筹与管理,2010, 19(1):49-55.Yi P T, Zhang D N, Guo Y J. A multi-phase information aggregation method based on extensive inspiriting control lines[J]. Operations Research and Management Science, 2010, 19(1):49-55.
[13]刘薇薇,石春生,赵圣斌.具有速度特征的动态综合评价模型[J].系统工程理论与实践,2013, 33(3):705-710.Liu W W, Shi C S, Zhao S B. Dynamic comprehensive evaluation model with the feature of speed[J]. Systems Engineering-Theory&Practice, 2013, 33(3):705-710.
[14] Zhang F M, Tadikamalla P R, Shang J. Corporate credit-risk evaluation system:Integrating explicit and implicit financial performances[J]. International Journal of Production Economics, 2016, 177:77-100.
[15] Xu Z S, Yager R R. Dynamic intuitionistic fuzzy multi-attribute decision making[J]. International Journal of Approximate Reasoning, 2008, 48(1):246-262.
[16] Xu Z S. Multi-period multi-attribute group decision-making under linguistic assessments[J]. International Journal of General Systems, 2009, 38(8):823-850.
[17] Lin Y H, Lee P C, Ting H I. Dynamic multi-attribute decision making model with grey number evaluations[J].Expert Systems with Application, 2008, 35(4):1638-1644.
[18] Bali O, Gumus S, Kaya I. A multi-period decision making procedure based on intuitionistic fuzzy sets for selection among third-party logistics providers[J]. Journal of Multiple-Valued Logic&Soft Computing, 2015,24(5-6):547-569.
[19] Peng D H, Wang H. Dynamic hesitant fuzzy aggregation operators in multi-period decision making[J]. Kybernetes,2014, 43(5):715-736.
[20]郝晶晶,朱建军,刘思峰.基于Orness测度的多阶段不确定语言信息优化集结[J].系统工程理论与实践,2013, 33(11):2866-2873.Hao J J, Zhu J J, Liu S F. Aggregation of multi-stage uncertain linguistic evaluation information based on Orness[J]. Systems Engineering—Theory&Practice, 2013, 33(11):2866-2873.
[21]金菊良,吴开亚,李如忠.水环境风险评价的随机模拟与三角模糊数耦合模型[J].水利学报,2008, 39(11):1257-1261.Jin J L, Wu K Y, Li R Z. Damage analysis of reinforced concrete surrounding the spiral case under the action of repeated water pressure[J]. Journal of Hydraulic Engineering, 2008, 39(11):1257-1261.
[22]陈耀宁,智国铮,袁兴中,等.基于三角随机模拟和ArcGIS的河流水环境健康风险评价模型[J].环境工程学报,2016,10(4):1799-1806.Chen Y N, Zhi G Z, Yuan X Z, et al. Assessment model of water environmental health risk based on stochastic simulation-triangular fuzzy numbers and ArcGIS[J]. Chinese Journal of Environmental Engineering, 2016, 10(4):1799-1806.
[23]易平涛,李伟伟,郭亚军.随机模拟型综合评价模式及其求解算法[J].运筹与管理,2014, 23(6):222-228.Yi P T, Li W W, Guo Y J. Stochastic simulation model of comprehensive evaluation and the solution[J].Operations Research and Management Science, 2014, 23(6):222-228.
[24]徐泽水,达庆利.区间数排序的可能度法及其应用[J].系统工程学报,2003, 18(1):67-70.Xu Z S, Da Q L. Possibility degree method for ranking interval numbers and its application[J]. Journal of Systems Engineering, 2003, 18(1):67-70.
[25] Nakahara Y, Sasaki M, Gen M. On the linear programming problems with interval coefficients[J]. Computer&Industrial Engineering, 1992, 23:301-304.
[26]高峰记.可能度及区间数综合排序[J].系统工程理论与实践,2013, 33(8):2033-2040.Gao F J. Possibility degree and comprehensive priority of interval numbers[J]. Systems Engineering—Theory&Practice, 2013, 33(8):2033-2040.
[27]易平涛,张丹宁,郭亚军.综合评价的随机模拟求解算法及应用[J].运筹与管理,2009, 18(5):97-106.Yi P T, Zhan D N, Guo Y J. The study on a stochastic simulation solution method of comprehensive evaluation and application[J]. Operations Research and Management Science, 2009, 18(5):97-106.
[28]孙清岩.股票价格指数编制理论、方法与创新[M].大连:东北财经大学出版社,2010:77-78.Sun Q Y. The making of security index:Theory, methodology and innovation[M]. Dalian:Dongbei University of Finance&Economics Press, 2010:77-78.
[29]徐选华,蔡晨光,梁栋.基于混合多属性信息的复杂多阶段决策方法[J].系统工程与电子技术,2015, 37(10):2315-2321.Xu X H, Cai C G, Liang D. Complex multi-stage decision making method based on mixed multi-attribute information[J]. Systems Engineering and Electronics, 2015, 37(10):2315-2321.
[2]郭亚军.综合评价理论、方法及应用[M].北京:科学出版社,2002.Guo Y J. Comprehensive evaluation theory, methods and application[M]. Beijing:Science Press, 2002.
[3]陈衍泰,陈国宏,李美娟.综合评价方法分类及研究进展[J].管理科学学报,2004, 7(2):69-79.Chen Y T, Chen G H, Li M J. Classification&research advancement of comprehensive evaluation methods[J].Journal of Management Sciences in China, 2004, 7(2):69-79.
[4] Liu J P, Chen H Y, Zhou L G, et al. On the properties of the generalized OWHA operators and their application to group decision making[J]. Journal of Intelligent&Fuzzy Systems, 2014, 27(4):2077-2089.
[5] Kou G, Wu W S, Zhao Y Y, et al. A dynamic assessment method for urban eco-environmental quality evaluation[J]. Journal of Multi-Criteria Decision Analysis, 2011, 18(1):23-38.
[6] Tura T, Harmaakorpi V, Pekkola S. Breaking inside the black box:Towards a dynamic evaluation framework for regional innovative capability[J]. Science and Public Policy, 2008, 5(10):733-744.
[7]金菊良,王淑娟,魏一鸣.动态多指标决策问题的投影寻踪模型[J].中国管理科学,2004, 12(1):64-67.Jin J L, Wang S J, Wei Y M. Projection pursuit model for dynamic multiple attribute decision problems[J].Chinese Journal of Management Science, 2004, 12(1):64-67.
[8]王欣荣,樊治平.上市公司财务状况的动态多指标综合评价方法[J].系统工程理论与实践,2002, 22(4):54-57.Wang X R, Fan Z P. Dynamic multiple index synthetical evaluation for financial condition of public corporations[J]. Systems Engineering—Theory&Practice, 2002, 22(4):54-57.
[9]王雪荣.一种基于证据理论的动态综合效绩评价实用方法[J].中国管理科学,2006, 14(4):121-127.Wang X R. The practical method of dynamically evaluating the comprehensive performance based on evidentialreasoning[J]. Chinese Journal of Management Science, 2006, 14(4):121-127.
[10]李美娟,陈国宏,林志炳,等.基于理想解法的动态评价方法研究[J].中国管理科学,2015, 23(10):156-161.Li M J, Chen G H, Lin Z B, et al. Dynamic evaluation method based on TOPSIS[J]. Chinese Journal of Management Science, 2015, 23(10):156-161.
[11]易平涛,郭亚军,张丹宁.基于双激励控制线的多阶段信息集结方法[J].预测,2007,26(3):39-43.Yi P T, Guo Y J, Zhang D N. A multi-phase information aggregation method based on double inspiriting control lines[J]. Forecasting, 2007, 26(3):39-43.
[12]易平涛,张丹宁,郭亚军.基于泛激励控制线的多阶段信息集结方法[J].运筹与管理,2010, 19(1):49-55.Yi P T, Zhang D N, Guo Y J. A multi-phase information aggregation method based on extensive inspiriting control lines[J]. Operations Research and Management Science, 2010, 19(1):49-55.
[13]刘薇薇,石春生,赵圣斌.具有速度特征的动态综合评价模型[J].系统工程理论与实践,2013, 33(3):705-710.Liu W W, Shi C S, Zhao S B. Dynamic comprehensive evaluation model with the feature of speed[J]. Systems Engineering-Theory&Practice, 2013, 33(3):705-710.
[14] Zhang F M, Tadikamalla P R, Shang J. Corporate credit-risk evaluation system:Integrating explicit and implicit financial performances[J]. International Journal of Production Economics, 2016, 177:77-100.
[15] Xu Z S, Yager R R. Dynamic intuitionistic fuzzy multi-attribute decision making[J]. International Journal of Approximate Reasoning, 2008, 48(1):246-262.
[16] Xu Z S. Multi-period multi-attribute group decision-making under linguistic assessments[J]. International Journal of General Systems, 2009, 38(8):823-850.
[17] Lin Y H, Lee P C, Ting H I. Dynamic multi-attribute decision making model with grey number evaluations[J].Expert Systems with Application, 2008, 35(4):1638-1644.
[18] Bali O, Gumus S, Kaya I. A multi-period decision making procedure based on intuitionistic fuzzy sets for selection among third-party logistics providers[J]. Journal of Multiple-Valued Logic&Soft Computing, 2015,24(5-6):547-569.
[19] Peng D H, Wang H. Dynamic hesitant fuzzy aggregation operators in multi-period decision making[J]. Kybernetes,2014, 43(5):715-736.
[20]郝晶晶,朱建军,刘思峰.基于Orness测度的多阶段不确定语言信息优化集结[J].系统工程理论与实践,2013, 33(11):2866-2873.Hao J J, Zhu J J, Liu S F. Aggregation of multi-stage uncertain linguistic evaluation information based on Orness[J]. Systems Engineering—Theory&Practice, 2013, 33(11):2866-2873.
[21]金菊良,吴开亚,李如忠.水环境风险评价的随机模拟与三角模糊数耦合模型[J].水利学报,2008, 39(11):1257-1261.Jin J L, Wu K Y, Li R Z. Damage analysis of reinforced concrete surrounding the spiral case under the action of repeated water pressure[J]. Journal of Hydraulic Engineering, 2008, 39(11):1257-1261.
[22]陈耀宁,智国铮,袁兴中,等.基于三角随机模拟和ArcGIS的河流水环境健康风险评价模型[J].环境工程学报,2016,10(4):1799-1806.Chen Y N, Zhi G Z, Yuan X Z, et al. Assessment model of water environmental health risk based on stochastic simulation-triangular fuzzy numbers and ArcGIS[J]. Chinese Journal of Environmental Engineering, 2016, 10(4):1799-1806.
[23]易平涛,李伟伟,郭亚军.随机模拟型综合评价模式及其求解算法[J].运筹与管理,2014, 23(6):222-228.Yi P T, Li W W, Guo Y J. Stochastic simulation model of comprehensive evaluation and the solution[J].Operations Research and Management Science, 2014, 23(6):222-228.
[24]徐泽水,达庆利.区间数排序的可能度法及其应用[J].系统工程学报,2003, 18(1):67-70.Xu Z S, Da Q L. Possibility degree method for ranking interval numbers and its application[J]. Journal of Systems Engineering, 2003, 18(1):67-70.
[25] Nakahara Y, Sasaki M, Gen M. On the linear programming problems with interval coefficients[J]. Computer&Industrial Engineering, 1992, 23:301-304.
[26]高峰记.可能度及区间数综合排序[J].系统工程理论与实践,2013, 33(8):2033-2040.Gao F J. Possibility degree and comprehensive priority of interval numbers[J]. Systems Engineering—Theory&Practice, 2013, 33(8):2033-2040.
[27]易平涛,张丹宁,郭亚军.综合评价的随机模拟求解算法及应用[J].运筹与管理,2009, 18(5):97-106.Yi P T, Zhan D N, Guo Y J. The study on a stochastic simulation solution method of comprehensive evaluation and application[J]. Operations Research and Management Science, 2009, 18(5):97-106.
[28]孙清岩.股票价格指数编制理论、方法与创新[M].大连:东北财经大学出版社,2010:77-78.Sun Q Y. The making of security index:Theory, methodology and innovation[M]. Dalian:Dongbei University of Finance&Economics Press, 2010:77-78.
[29]徐选华,蔡晨光,梁栋.基于混合多属性信息的复杂多阶段决策方法[J].系统工程与电子技术,2015, 37(10):2315-2321.Xu X H, Cai C G, Liang D. Complex multi-stage decision making method based on mixed multi-attribute information[J]. Systems Engineering and Electronics, 2015, 37(10):2315-2321.