属性值为三角模糊数的决策对象可能度关系模型
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摘要
对于属性值是三角模糊数的不确定多属性决策问题,首先研究几组三角模糊数比较可能度公式之间的等价关系,提出三角模糊数比较优势关系理论,并得到一些优良性质关系和结论;然后借鉴离差最大化思想构建一种确定属性权重向量的三角模糊数型比较可能度关系模型,通过集结所有决策对象比较的可能度值,并对方案对象集进行优劣筛选和次序排定,得到一种新的三角模糊数多属性决策对象的可能度关系模型算法;最后通过算例分析验证所提出模型算法的可行性和实用性.
For the problem of uncertain multiple criteria decision making(UMCDM) of which the attribute value is triangular fuzzy number, firstly equivalent relations between several groups comparison possibility degree formulas of triangular fuzzy numbers are studied, comparative advantage relation theories of triangular fuzzy numbers are proposed,and some good properties, relations and conclusions are obtained. Then, by using the idea of maximizing deviations algorithm rules, a triangular fuzzy number-based comparison possibility degree relation model to determine the attribute weight vector is constructed. By aggregating the comparison possibility degree values of all decision objects, the set of alternatives objects is selected and scheduled, and a new model algorithm for the possibility degree relation of triangular fuzzy number-based multiple criteria decision making objects is obtained. Finally, an example is given to illustrate the feasibility and practicability of the proposed algorithm.
For the problem of uncertain multiple criteria decision making(UMCDM) of which the attribute value is triangular fuzzy number, firstly equivalent relations between several groups comparison possibility degree formulas of triangular fuzzy numbers are studied, comparative advantage relation theories of triangular fuzzy numbers are proposed,and some good properties, relations and conclusions are obtained. Then, by using the idea of maximizing deviations algorithm rules, a triangular fuzzy number-based comparison possibility degree relation model to determine the attribute weight vector is constructed. By aggregating the comparison possibility degree values of all decision objects, the set of alternatives objects is selected and scheduled, and a new model algorithm for the possibility degree relation of triangular fuzzy number-based multiple criteria decision making objects is obtained. Finally, an example is given to illustrate the feasibility and practicability of the proposed algorithm.
引文
[1]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, 2004:161-178.(Xu Z S. Uncertain multiple attribute decision making methods and applications[M]. Beijing:Tsinghua University Press, 2004:161-178.)
[2]黄智力.区间数型与三角模糊数型不确定多指标决策研究[D].厦门:厦门大学航空航天学院, 2016.(Huang Z L. Study on interval number-based and triangular fuzzy number-based uncertain multi-attribute decision-making[D]. Xiamen:School of Aerospace Engineering, Xiamen University, 2016.)
[3]Hsieh C H, Chen S H. A model and algorithm of fuzzy product positioning[J]. Information Sciences, 1999,121(1):61-82.
[4]Kamran Rezaie, Sara Saeidi Ramiyani, Salman Nazari-Shirkouhi, et al. Evaluating performance of Iranian cement firms using an integrated fuzzy AHP-VIKOR method[J]. Applied Mathematical Modelling, 2014, 22(3):21-30.
[5]Wu L F, Liu S F, Yang Y J. A model to determine OWA weights and its application in energy technology evaluation[J]. Int J of Intelligent Systems, 2015, 30(7):798-806.
[6]Liu H C, Liu L, Liu N, et al. Risk evaluation in failure mode and effects analysis with extended VIKOR method under fuzzy environment[J]. Expert Systems with Applications, 2012, 39(17):12926-12934.
[7]Chang T H. Fuzzy VIKOR method:A case study of the hospital service evaluation in Taiwan[J]. Information Sciences, 2014, 271(1):196-212.
[8]Liu H C, You J X, Fan X J, et al. Site selection in waste management by the VIKOR method using linguistic assessment[J]. Applied Soft Computing, 2014, 21(1):684-696.
[9]Yim K K, Wong S C, Anthony Chen, et al. A reliability-based land use and transportation optimization model[J]. Transportation Research Part C, 2011, 19(2):351-362.
[10]Wang P, Meng P, Song B W. Response surface method using grey relational analysis for decision making in weapon system selection[J]. J of Systems Engineering and Electronics, 2014, 25(2):265-272.
[11]Van Laarhoven P J M, Pedrycz W. A fuzzy extension of satty’s priority theory[J]. Fuzzy Sets and Systems, 1983,11(1):229-241.
[12]Herrera-viedma E, Herrera F, Chiclana F, et al. Some issues on consistency of fuzzy preference relations[J].European J of Operational Research, 2004, 154(1):98-109.
[13]Wang Y M, Celik Parkan. Multiple attribute decision making based on fuzzy preference information on alternatives:Ranking and weighting[J]. Fuzzy Sets and Systems, 2005, 153(3):331-346.
[14]黄智力,罗键.三角模糊数型不确定多指标决策的相似规划模型及其应用[J].系统工程与电子技术, 2016,38(5):1100-1106.(Huang Z L, Luo J. Similarity programming model for triangular fuzzy number-based uncertain multi-attribute decision making and its application[J]. System Engineering and Electronics, 2016, 38(5):1100-1106.)
[15]陈雪,黄智力,罗键.基于相对相似度关系的三角模糊数型不确定多属性决策法[J].控制与决策, 2016,31(12):2232-2240.(Chen X, Huang Z L, Luo J. Approach for triangular fuzzy number-based uncertain multi-attribute decision making based on relative similarity degree relation[J]. Control and Decision, 2016, 31(12):2232-2240.)
[16]Li D F. TOPSIS-based nonlinear-programming methodology for multiattribute decision making with interval-valued intuitionistic fuzzy sets[J]. IEEE Trans on Fuzzy Systems, 2010, 18(2):299-311.
[17]李存林,张强.基于可能性测度的模糊对策[J].北京理工大学学报:自然科学版, 2011, 31(3):324-328.(Li C L, Zhang Q. Fuzzy games based on possibility measures[J]. J of Beijing Institute of Technology:Natural Science Edition, 2011, 31(3):324-328.)
[18]李亚利,李永明.可能性测度下计算树逻辑的若干性质[J].陕西师范大学学报:自然科学版, 2013, 41(6):6-11.(Li Y L, Li Y M. Some properties of computation tree logic under possibility measure[J]. J of Shaanxi Normal University:Natural Science Edition, 2013, 41(6):6-11.)
[19]John Drakopoulos A. Probabilities, possibilities, and fuzzy sets[J]. Fuzzy Sets and Systems, 1995, 75(1):1-15.
[20]Zadeh L A. Fuzzy sets as a basis for a theory of possibility[J]. Fuzzy Sets and Systems, 1978, 1(1):3-28.
[21]Wu Q, Law R. The complex fuzzy system forecasting model based on fuzzy SVM with triangular fuzzy number input and output[J]. Expert Systems with Applications,2011, 38(10):12085-12093.
[22]Jin J L, Wei Y M, Zou L L, et al. Risk evaluation of China’s natural disaster systems:An approach based on triangular fuzzy numbers and stochastic simulation[J].Natural Hazards, 2012, 62(1):129-139.
[23]Sadi-Nezhad S, Noroozi-Yadak A, Makui A. Fuzzy distance of triangular fuzzy numbers[J]. J of Intelligent&Fuzzy Systems, 2013, 25(4):845-852.
[24]Li D F. A fast approach to compute fuzzy values of matrix games with payoffs of triangular fuzzy numbers[J].European J of Operational Research, 2012, 223(2):421-429.
[25]Li D F. Linear programming models and methods of matrix games with payoffs of triangular fuzzy numbers[M]. Berlin:Springer Heidelberg, 2016:135-165.
[26]彭张林,张强,李珠瑞,等.改进的离差最大化决策模型及其在临近空间多任务规划中的应用[J].系统工程理论与实践, 2014, 34(2):421-427.(Peng Z L, Zhang Q, Li Z R, et al. Improved maximizing deviation decision-making model and its application in multi-mission planning of near space system[J].Systems Engineering—Theory&Practice, 2014, 34(2):421-427.)
[27]黄智力,罗键.三角模糊数型不确定多指标决策的可能度关系法[J].控制与决策, 2015, 30(8):1365-1371.(Huang Z L, Luo J. Possibility degree relation method for triangular fuzzy number-based uncertain multi-attribute decision making[J]. Control and Decision, 2015, 30(8):1365-1371.)
[28]胡凌云,袁宏俊,吴庆鹏.基于集对分析的三角模糊数多属性决策方法[J].武汉理工大学学报:信息与管理工程版, 2015, 37(1):108-111.(Hu L Y, Yuan H J, Wu Q P. Multiple attribute decision-making of triangular fuzzy number based on set pair analysis[J]. J of Wuhan University of Technology:Information&Management Engineering, 2015, 37(1):108-111.)
[2]黄智力.区间数型与三角模糊数型不确定多指标决策研究[D].厦门:厦门大学航空航天学院, 2016.(Huang Z L. Study on interval number-based and triangular fuzzy number-based uncertain multi-attribute decision-making[D]. Xiamen:School of Aerospace Engineering, Xiamen University, 2016.)
[3]Hsieh C H, Chen S H. A model and algorithm of fuzzy product positioning[J]. Information Sciences, 1999,121(1):61-82.
[4]Kamran Rezaie, Sara Saeidi Ramiyani, Salman Nazari-Shirkouhi, et al. Evaluating performance of Iranian cement firms using an integrated fuzzy AHP-VIKOR method[J]. Applied Mathematical Modelling, 2014, 22(3):21-30.
[5]Wu L F, Liu S F, Yang Y J. A model to determine OWA weights and its application in energy technology evaluation[J]. Int J of Intelligent Systems, 2015, 30(7):798-806.
[6]Liu H C, Liu L, Liu N, et al. Risk evaluation in failure mode and effects analysis with extended VIKOR method under fuzzy environment[J]. Expert Systems with Applications, 2012, 39(17):12926-12934.
[7]Chang T H. Fuzzy VIKOR method:A case study of the hospital service evaluation in Taiwan[J]. Information Sciences, 2014, 271(1):196-212.
[8]Liu H C, You J X, Fan X J, et al. Site selection in waste management by the VIKOR method using linguistic assessment[J]. Applied Soft Computing, 2014, 21(1):684-696.
[9]Yim K K, Wong S C, Anthony Chen, et al. A reliability-based land use and transportation optimization model[J]. Transportation Research Part C, 2011, 19(2):351-362.
[10]Wang P, Meng P, Song B W. Response surface method using grey relational analysis for decision making in weapon system selection[J]. J of Systems Engineering and Electronics, 2014, 25(2):265-272.
[11]Van Laarhoven P J M, Pedrycz W. A fuzzy extension of satty’s priority theory[J]. Fuzzy Sets and Systems, 1983,11(1):229-241.
[12]Herrera-viedma E, Herrera F, Chiclana F, et al. Some issues on consistency of fuzzy preference relations[J].European J of Operational Research, 2004, 154(1):98-109.
[13]Wang Y M, Celik Parkan. Multiple attribute decision making based on fuzzy preference information on alternatives:Ranking and weighting[J]. Fuzzy Sets and Systems, 2005, 153(3):331-346.
[14]黄智力,罗键.三角模糊数型不确定多指标决策的相似规划模型及其应用[J].系统工程与电子技术, 2016,38(5):1100-1106.(Huang Z L, Luo J. Similarity programming model for triangular fuzzy number-based uncertain multi-attribute decision making and its application[J]. System Engineering and Electronics, 2016, 38(5):1100-1106.)
[15]陈雪,黄智力,罗键.基于相对相似度关系的三角模糊数型不确定多属性决策法[J].控制与决策, 2016,31(12):2232-2240.(Chen X, Huang Z L, Luo J. Approach for triangular fuzzy number-based uncertain multi-attribute decision making based on relative similarity degree relation[J]. Control and Decision, 2016, 31(12):2232-2240.)
[16]Li D F. TOPSIS-based nonlinear-programming methodology for multiattribute decision making with interval-valued intuitionistic fuzzy sets[J]. IEEE Trans on Fuzzy Systems, 2010, 18(2):299-311.
[17]李存林,张强.基于可能性测度的模糊对策[J].北京理工大学学报:自然科学版, 2011, 31(3):324-328.(Li C L, Zhang Q. Fuzzy games based on possibility measures[J]. J of Beijing Institute of Technology:Natural Science Edition, 2011, 31(3):324-328.)
[18]李亚利,李永明.可能性测度下计算树逻辑的若干性质[J].陕西师范大学学报:自然科学版, 2013, 41(6):6-11.(Li Y L, Li Y M. Some properties of computation tree logic under possibility measure[J]. J of Shaanxi Normal University:Natural Science Edition, 2013, 41(6):6-11.)
[19]John Drakopoulos A. Probabilities, possibilities, and fuzzy sets[J]. Fuzzy Sets and Systems, 1995, 75(1):1-15.
[20]Zadeh L A. Fuzzy sets as a basis for a theory of possibility[J]. Fuzzy Sets and Systems, 1978, 1(1):3-28.
[21]Wu Q, Law R. The complex fuzzy system forecasting model based on fuzzy SVM with triangular fuzzy number input and output[J]. Expert Systems with Applications,2011, 38(10):12085-12093.
[22]Jin J L, Wei Y M, Zou L L, et al. Risk evaluation of China’s natural disaster systems:An approach based on triangular fuzzy numbers and stochastic simulation[J].Natural Hazards, 2012, 62(1):129-139.
[23]Sadi-Nezhad S, Noroozi-Yadak A, Makui A. Fuzzy distance of triangular fuzzy numbers[J]. J of Intelligent&Fuzzy Systems, 2013, 25(4):845-852.
[24]Li D F. A fast approach to compute fuzzy values of matrix games with payoffs of triangular fuzzy numbers[J].European J of Operational Research, 2012, 223(2):421-429.
[25]Li D F. Linear programming models and methods of matrix games with payoffs of triangular fuzzy numbers[M]. Berlin:Springer Heidelberg, 2016:135-165.
[26]彭张林,张强,李珠瑞,等.改进的离差最大化决策模型及其在临近空间多任务规划中的应用[J].系统工程理论与实践, 2014, 34(2):421-427.(Peng Z L, Zhang Q, Li Z R, et al. Improved maximizing deviation decision-making model and its application in multi-mission planning of near space system[J].Systems Engineering—Theory&Practice, 2014, 34(2):421-427.)
[27]黄智力,罗键.三角模糊数型不确定多指标决策的可能度关系法[J].控制与决策, 2015, 30(8):1365-1371.(Huang Z L, Luo J. Possibility degree relation method for triangular fuzzy number-based uncertain multi-attribute decision making[J]. Control and Decision, 2015, 30(8):1365-1371.)
[28]胡凌云,袁宏俊,吴庆鹏.基于集对分析的三角模糊数多属性决策方法[J].武汉理工大学学报:信息与管理工程版, 2015, 37(1):108-111.(Hu L Y, Yuan H J, Wu Q P. Multiple attribute decision-making of triangular fuzzy number based on set pair analysis[J]. J of Wuhan University of Technology:Information&Management Engineering, 2015, 37(1):108-111.)