属性值为区间数的决策对象相对相似规划模型
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摘要
对于属性值是区间数的不确定多属性决策问题,首先在界定区间数相对相似度的基础上给出两种新的供选决策对象Max型与Min型相对相似度定义,提出区间数相对相似度与比较优势关系理论并得到一些优良性质关系和结论;其次借鉴合作博弈中可能度最大化算法构建一种确定属性权重向量的区间数型决策对象相对相似规划模型,通过集结所有决策对象比较的总体相对相似度值便于对方案对象集进行优劣筛选和次序排定,以此得到一种新的区间数多属性决策对象的相对相似规划模型算法;最后通过算例分析说明该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 interval number, two new type definition of the Max-relative and Min-relative similarity degree of decision-making alternatives for the election is given based on defying the relative similarity degree of interval number, firstly, the relative similarity degree and comparative advantage relation theories of interval number are put forward, and some good properties, relations and conclusions are derived. Secondly, by using the idea of maximizing possibility degree algorithm rules in the cooperative game theory,an interval number-based decision making object relative similarity programming model to determine the attribute weight vector is constructed. Then by aggregating the comparison overall relative similarity degree values of all decision-making objects, it is convenient to select and schedule the set of alternative objects, and obtain a new model algorithm for the relative similarity programming of interval number-based multiple criteria decision making objects. Finally, an example is given to illustrate the feasibility and practicability of the model algorithm proposed in this paper.
For the problem of uncertain multiple criteria decision making(UMCDM) of which the attribute value is interval number, two new type definition of the Max-relative and Min-relative similarity degree of decision-making alternatives for the election is given based on defying the relative similarity degree of interval number, firstly, the relative similarity degree and comparative advantage relation theories of interval number are put forward, and some good properties, relations and conclusions are derived. Secondly, by using the idea of maximizing possibility degree algorithm rules in the cooperative game theory,an interval number-based decision making object relative similarity programming model to determine the attribute weight vector is constructed. Then by aggregating the comparison overall relative similarity degree values of all decision-making objects, it is convenient to select and schedule the set of alternative objects, and obtain a new model algorithm for the relative similarity programming of interval number-based multiple criteria decision making objects. Finally, an example is given to illustrate the feasibility and practicability of the model algorithm proposed in this paper.
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.Xu Z S. Uncertain multiple attribute decision making methods and applications[M]. Beijing:Tsinghua University Press, 2004.
[2] Wang P, Meng P, Song B W. Response surface method using grey relational analysis for decision making in weapon system selection[J]. Journal of Systems Engineering and Electronics, 2014, 25(2):265-272.
[3] Wu L F, Liu S F, Yang Y J. A model to determine OWA weights and its application in energy technology evaluation[J]. International Journal of Intelligent Systems, 2015, 30(7):798-806.
[4] Ju Y B, Wang A H. Extension of VIKOR method for multi-criteria group decision making problem with linguistic information[J]. Applied Mathematical Modeling, 2013, 37(5):3112-3125.
[5]阚洪生,陆云波,乐云,等.基于Agent的项目交易治理计算模型研究[J].系统工程理论与实践,2017, 37(4):972-981.Kan H S, Lu Y B, Le Y, et al. Agent-based computational model for project transaction governance[J]. Systems Engineering—Theory Practice, 2017, 37(4):972-981.
[6] Tian L, Luo J, Zeng Y F, et al. Modeling and algorithms for multiagent communication through interactive dynamic influence diagrams[J]. Applied Artificial Intelligence, 2016, 30(4):352-377.
[7]程呈,高敏,程旭德,等.基于组合赋权的反坦克导弹武器系统作战效能评估研究[J].系统工程理论与实践,2018, 38(1):241-251.Cheng C, Gao M, Cheng X D, et al. Research on operational efficiency evaluation of anti-tank missile weapon system based on combination weighting[J]. Systems Engineering—Theory&Practice, 2018, 38(1):241-251.
[8]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,2016.Huang Z L. Study on interval number-based and triangular fuzzy number-based uncertain multi-attribute decision-making[D]. Xiamen:Xiamen University, 2016.
[9]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 inmulti-mission planning of near space system[J]. Systems Engineering一Theory&Practice, 2014, 34(2):421-427.
[10]周漩,张凤鸣,惠晓滨,等.基于信息熵的专家聚类赋权方法[J].控制与决策,2011,26(1):153-156.Zhou X, Zhang F M, Hui X B, et al. Method for determining experts'weights based on entropy and cluster analysis[J]. Control and Decision, 2011, 26(1):153-156.
[11] Wang Y M, Luo Y. Area ranking of fuzzy numbers based on positive and negative ideal points[J]. Computers and Mathematics with Applications, 2009, 58(9):1769-1779.
[12] Sayadi M K, Heydari M, Shahanaghi K. Extension of VIKOR method for decision making problem with interval numbers[J]. Applied Mathematical Modelling, 2009, 33(5):2257-2262.
[13] Rezaie K, Ramiyani S S,Nazari-Shirkouhi S, et al. Evaluating performance of Iranian cement firms using an integrated fuzzy AHP-VIKOR method[J]. Applied Mathematical Modelling, 2014, 38(21-22):5033-5046.
[14] Wei G W. Grey relational analysis method for 2-tuple linguistic multiple attribute group decision making with incomplete weight information[J]. Expert Systems with Applications, 2011, 38(5):4824-4828.
[15]刘勇,Forrest Jeffrey,刘思峰,等.基于前景理论的多目标灰靶决策方法[J].控制与决策,2013, 28(3):345-350.Liu Y, Forrest J, Liu S F, et al. Multi-objective grey target decision-making based on prospect theory[J]. Control and Decision, 2013, 28(3):345-350.
[16]孙昱,姚佩阳,万路军,等.基于权重集结和相对优势关系的多属性决策方法[J].控制与决策,2017, 32(2):317-322.Sun Y,Yao P Y,Wan L J,et al. Multiple attribute decision making method based on weights aggregation and relative dominance relation[J]. Control and Decision, 2017, 32(2):317-322.
[17]黄智力,罗键.不确定多指标决策问题的相对相似关系法研究[J]·系统工程理论与实践,2015, 35(11):2917-2924.Huang Z L, Luo J. Study on relative similarity relation method for uncertain multi-attribute decision making problem[J]. Systems Engineering—Theory&Practice, 2015, 35(11):2917-2924.
[18]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.
[19]周宏安,刘三阳.基于二次规划与相对优势度的不确定多属性决策法[J].系统工程与电子技术,2007, 29(4):555-562.Zhou H A, Liu S Y. Method of uncertain multi-attribute decision-making based on quadratic programming and relative superiority degree[J]. Systems Engineering and Electronics, 2007, 29(4):555-562.
[20] Peng X, Yang Y. Fundamental properties of interval-valued pythagorean fuzzy aggregation operators[J]. International Journal of Intelligent Systems, 2016, 31(5):444-487.
[21] Gou X, Xu Z, Ren P. The properties of continuous pythagorean fuzzy information[J]. International Journal of Intelligent Systems, 2016, 31(5):401-424.
[22]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.
[23]刘健,刘思峰,周献中,等.基于相似关系的多属性决策问题研究[J].系统工程与电子技术,2011, 33(5):1069-1072.Liu J, Liu S F, Zhou X Z, et al. Research on multiple-attribute decision making problems based on the similarity relationship[J], Systems Engineering and Electronics,2011,33(5):1069-1072.
[24]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.Ding C M, Li F, Qi H. Technique of hybrid multiple attribute decision making based on similarity degree to ideal solution[J]. Systems Engineering and Electronics, 2007, 29(5):737-740.
[25] Van Laarhoven P J M, Pedrycz W. A fuzzy extension of Satty's priority theory[J]. Fuzzy Sets and Systems, 1983,11(1-3):229-241.
[26]李登峰.模糊多目标多人决策与对策[M].北京:国防工业出版社,2003.Li D F. Fuzzy multi-object multi-person decision making and countermeasure[M]. Beijing:National Defense Industry Press,2003.
[2] Wang P, Meng P, Song B W. Response surface method using grey relational analysis for decision making in weapon system selection[J]. Journal of Systems Engineering and Electronics, 2014, 25(2):265-272.
[3] Wu L F, Liu S F, Yang Y J. A model to determine OWA weights and its application in energy technology evaluation[J]. International Journal of Intelligent Systems, 2015, 30(7):798-806.
[4] Ju Y B, Wang A H. Extension of VIKOR method for multi-criteria group decision making problem with linguistic information[J]. Applied Mathematical Modeling, 2013, 37(5):3112-3125.
[5]阚洪生,陆云波,乐云,等.基于Agent的项目交易治理计算模型研究[J].系统工程理论与实践,2017, 37(4):972-981.Kan H S, Lu Y B, Le Y, et al. Agent-based computational model for project transaction governance[J]. Systems Engineering—Theory Practice, 2017, 37(4):972-981.
[6] Tian L, Luo J, Zeng Y F, et al. Modeling and algorithms for multiagent communication through interactive dynamic influence diagrams[J]. Applied Artificial Intelligence, 2016, 30(4):352-377.
[7]程呈,高敏,程旭德,等.基于组合赋权的反坦克导弹武器系统作战效能评估研究[J].系统工程理论与实践,2018, 38(1):241-251.Cheng C, Gao M, Cheng X D, et al. Research on operational efficiency evaluation of anti-tank missile weapon system based on combination weighting[J]. Systems Engineering—Theory&Practice, 2018, 38(1):241-251.
[8]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,2016.Huang Z L. Study on interval number-based and triangular fuzzy number-based uncertain multi-attribute decision-making[D]. Xiamen:Xiamen University, 2016.
[9]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 inmulti-mission planning of near space system[J]. Systems Engineering一Theory&Practice, 2014, 34(2):421-427.
[10]周漩,张凤鸣,惠晓滨,等.基于信息熵的专家聚类赋权方法[J].控制与决策,2011,26(1):153-156.Zhou X, Zhang F M, Hui X B, et al. Method for determining experts'weights based on entropy and cluster analysis[J]. Control and Decision, 2011, 26(1):153-156.
[11] Wang Y M, Luo Y. Area ranking of fuzzy numbers based on positive and negative ideal points[J]. Computers and Mathematics with Applications, 2009, 58(9):1769-1779.
[12] Sayadi M K, Heydari M, Shahanaghi K. Extension of VIKOR method for decision making problem with interval numbers[J]. Applied Mathematical Modelling, 2009, 33(5):2257-2262.
[13] Rezaie K, Ramiyani S S,Nazari-Shirkouhi S, et al. Evaluating performance of Iranian cement firms using an integrated fuzzy AHP-VIKOR method[J]. Applied Mathematical Modelling, 2014, 38(21-22):5033-5046.
[14] Wei G W. Grey relational analysis method for 2-tuple linguistic multiple attribute group decision making with incomplete weight information[J]. Expert Systems with Applications, 2011, 38(5):4824-4828.
[15]刘勇,Forrest Jeffrey,刘思峰,等.基于前景理论的多目标灰靶决策方法[J].控制与决策,2013, 28(3):345-350.Liu Y, Forrest J, Liu S F, et al. Multi-objective grey target decision-making based on prospect theory[J]. Control and Decision, 2013, 28(3):345-350.
[16]孙昱,姚佩阳,万路军,等.基于权重集结和相对优势关系的多属性决策方法[J].控制与决策,2017, 32(2):317-322.Sun Y,Yao P Y,Wan L J,et al. Multiple attribute decision making method based on weights aggregation and relative dominance relation[J]. Control and Decision, 2017, 32(2):317-322.
[17]黄智力,罗键.不确定多指标决策问题的相对相似关系法研究[J]·系统工程理论与实践,2015, 35(11):2917-2924.Huang Z L, Luo J. Study on relative similarity relation method for uncertain multi-attribute decision making problem[J]. Systems Engineering—Theory&Practice, 2015, 35(11):2917-2924.
[18]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.
[19]周宏安,刘三阳.基于二次规划与相对优势度的不确定多属性决策法[J].系统工程与电子技术,2007, 29(4):555-562.Zhou H A, Liu S Y. Method of uncertain multi-attribute decision-making based on quadratic programming and relative superiority degree[J]. Systems Engineering and Electronics, 2007, 29(4):555-562.
[20] Peng X, Yang Y. Fundamental properties of interval-valued pythagorean fuzzy aggregation operators[J]. International Journal of Intelligent Systems, 2016, 31(5):444-487.
[21] Gou X, Xu Z, Ren P. The properties of continuous pythagorean fuzzy information[J]. International Journal of Intelligent Systems, 2016, 31(5):401-424.
[22]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.
[23]刘健,刘思峰,周献中,等.基于相似关系的多属性决策问题研究[J].系统工程与电子技术,2011, 33(5):1069-1072.Liu J, Liu S F, Zhou X Z, et al. Research on multiple-attribute decision making problems based on the similarity relationship[J], Systems Engineering and Electronics,2011,33(5):1069-1072.
[24]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.Ding C M, Li F, Qi H. Technique of hybrid multiple attribute decision making based on similarity degree to ideal solution[J]. Systems Engineering and Electronics, 2007, 29(5):737-740.
[25] Van Laarhoven P J M, Pedrycz W. A fuzzy extension of Satty's priority theory[J]. Fuzzy Sets and Systems, 1983,11(1-3):229-241.
[26]李登峰.模糊多目标多人决策与对策[M].北京:国防工业出版社,2003.Li D F. Fuzzy multi-object multi-person decision making and countermeasure[M]. Beijing:National Defense Industry Press,2003.