考虑决策者行为的概率不确定语言决策方法
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摘要
针对属性权重未知的不确定语言多属性群决策问题,提出一种考虑决策者行为的概率不确定语言决策方法.首先,定义概率不确定语言的海明距离,根据与负理想方案的距离偏差最大建立模型,从而确定属性权重.其次,改进经典TODIM方法适用于概率不确定语言决策环境中,得到了方案排序.最后,通过实例验证了所给方法的可行性,并对比传统的TOPSIS方法进行敏感度分析,进一步验证所提方法的有效性.
Based on probabilistic uncertain linguistic term set(PULTS), a group decisionmaking approach is proposed considering the behavior of decision makers, which is used for dealing with uncertain linguistic multi-attribute group decision-making problem with completely unknown attribute weights. First, the hamming distance between any two probabilistic uncertain linguistic term sets(PULTSs) is defined. A maximum deviation model is established based on the distance between each alternative and the negative ideal solution.All the attribute weights are obtained by solving the model. Second, the classical TODIM(an acronym in Portuguese for interactive and multi-criteria decision-making) method is extended and improved, and the rank of all the initiative is gotten by calculating the prospect value of each initiative based on the established TODIM method. Finally, a selection problem of the initiatives is presented to illustrate the practicality of the proposed method. Analyzing the sensitivity of the parameter and comparing it with the TOPSIS(the technique for order of preference by similarity to ideal solution) method, it was revealed to be more effective.
Based on probabilistic uncertain linguistic term set(PULTS), a group decisionmaking approach is proposed considering the behavior of decision makers, which is used for dealing with uncertain linguistic multi-attribute group decision-making problem with completely unknown attribute weights. First, the hamming distance between any two probabilistic uncertain linguistic term sets(PULTSs) is defined. A maximum deviation model is established based on the distance between each alternative and the negative ideal solution.All the attribute weights are obtained by solving the model. Second, the classical TODIM(an acronym in Portuguese for interactive and multi-criteria decision-making) method is extended and improved, and the rank of all the initiative is gotten by calculating the prospect value of each initiative based on the established TODIM method. Finally, a selection problem of the initiatives is presented to illustrate the practicality of the proposed method. Analyzing the sensitivity of the parameter and comparing it with the TOPSIS(the technique for order of preference by similarity to ideal solution) method, it was revealed to be more effective.
引文
[1] Rohan K. Gavade. Multi-Criteria Decision Making:An overview of different selection problems and methods[J]. International Journal of Computer Science&Information Technology, 2014, 5(4):5643-5646.
[2] Ramanathan R, Ravindran A R, Mathirajan M. Multi-Criteria Decision Making:An Overview and a Comparative Discussion[M]//Big Data Analytics Using Multiple Criteria Decision-Making Models. 2017.
[3] Xu Z, Wang H. Managing multi-granularity linguistic information in qualitative group decision making:an overview[J]. Granular Computing, 2016, 1(1):21-35.
[4] Xu Z. Uncertain linguistic aggregation operators based approach to multiple attribute group decision making under uncertain linguistic environment[J]. Information Sciences, 2004, 168(1-4):171-184.
[5] Xu Z. Induced uncertain linguistic OWA operators applied to group decision making[J]. Information Fusion, 2006, 7(2):231-238.
[6] GUI-WU WEI. Uncertain Linguistic Hybrid geometric mean operator and its application to group decision making under uncertain linguistic environment[J]. International Journal of Uncertainty,Fuzziness and Knowledge-Based Systems, 2009, 17(02):251-267.
[7] Fan Z P, Liu Y. A method for group decision-making based on multi-granularity uncertain linguistic information[J]. Expert Systems with Applications, 2010, 37(5):4000-4008.
[8] Rodríguez R M, MartíNez L, Herrera F. A group decision making model dealing with comparative linguistic expressions based on hesitant fuzzy linguistic term sets[J]. Information Sciences, 2013,241(12):28-42.
[9]魏翠萍,葛淑娜.犹豫模糊语言幂均算子及其在群决策中的应用[J].系统科学与数学,2016, 36(8):1308-1317.
[10]于倩,候福均.犹豫模糊语言Heronian平均算子在多属性决策中的应用[J].运筹与管理,2016, 25(2):90-97.
[11] Lin M, Xu Z, Zhai Y, et al. Multi-attribute group decision-making under probabilistic uncertain linguistic environment[J]. Journal of the Operational Research Society, 2017(22):1-15.
[12] Peide Liu. Multi-attribute decision-making method research based on interval vague set and TOPSIS method[J]. Ukio Technologinis ir Ekonominis Vystymas, 2009, 15(3):453-463.
[13] Yue Z. Yue Z. An extended TOPSIS for determining weights of decision makers with interval numbers. Knowledge-Based Systems 24, 146-153[J]. Knowledge-Based Systems, 2011, 24(1):146-153.
[14] Opricovic S, Tzeng G H. Compromise solution by MCDM methods:A comparative analysis of VIKOR and TOPSIS[J]. European Journal of Operational Research, 2004, 156(2):445-455.
[15] Roy B. Multicriteria Methodology for Decision Aiding, Kluwer, Dordrecht, The Netherlands, 1996.
[16] Roy B, and Bertier B. La metode ELECTRE II, in:Sixieme Conference Internationale de Rechearche Operationelle, Dublin, 1972.
[17] Gomes L F A M, Lima M M P P TODIM:Basics and application to multi-criteria ranking of projects with environmental impacts[J]. Foundations of Computing and Decision Sciences, 1992,16:113-127.
[18] Lourenzutti R, Krohling R A. A study of TODIM in a intuitionistic fuzzy and random environment[J]. Expert Systems with Applications, 2013, 40(16):6459-6468.
[19] Fan Z P, Zhang X, Chen F D, et al. Extended TODIM method for hybrid multiple attribute decision making problems[J]. Knowledge-Based Systems. 2013, 42(2):40-48.
[20]王坚强,李新娥.基于多值中智集的TODIM方法[J].控制与决策,2015(6):1139-1142.
[21]姜艳萍,梁霞,张业谛.一种属性信息不完全的TODIM决策方法[J].运筹与管理,2015, 24(1):116-121.
[22]王霞,党耀国.基于改进的TODIM方法的区间灰数多属性决策模型[J].控制与决策,2016(2):261-266.
[23] Wei C, Ren Z, Rodríguez R M. A Hesitant Fuzzy Linguistic TODIM Method Based on a Score Function[J]. International Journal of Computational Intelligence Systems, 2015, 8(4):701-712.
[24] Qin Q, Liang F, Li L, et al. A TODIM-based multi-criteria group decision making with triangular intuitionistic fuzzy numbers[J]. Applied Soft Computing, 2017, 55:93-107.
[25] Qin J, Liu X, Pedrycz W. An extended TODIM multi-criteria group decision making method for green supplier selection in interval type-2 fuzzy environment[J]. European Journal of Operational Research, 2016, 258.
[26]孔令艳,谭倩云.犹豫模糊语言TODIM法及其应用[J].统计与决策,2017(5):98-100.
[27]吴良刚,文丽.基于二维二元语义和模糊AHP-TODIM的低碳供应商选择方法[J].运筹与管理,2017,26(3):7-16.
[28] Liu P, Teng F. An extended TODIM method for multiple attribute group decision-making based on 2-dimension uncertain linguistic Variable[J]. Complexity, 2016, 21(5):20-30.
[2] Ramanathan R, Ravindran A R, Mathirajan M. Multi-Criteria Decision Making:An Overview and a Comparative Discussion[M]//Big Data Analytics Using Multiple Criteria Decision-Making Models. 2017.
[3] Xu Z, Wang H. Managing multi-granularity linguistic information in qualitative group decision making:an overview[J]. Granular Computing, 2016, 1(1):21-35.
[4] Xu Z. Uncertain linguistic aggregation operators based approach to multiple attribute group decision making under uncertain linguistic environment[J]. Information Sciences, 2004, 168(1-4):171-184.
[5] Xu Z. Induced uncertain linguistic OWA operators applied to group decision making[J]. Information Fusion, 2006, 7(2):231-238.
[6] GUI-WU WEI. Uncertain Linguistic Hybrid geometric mean operator and its application to group decision making under uncertain linguistic environment[J]. International Journal of Uncertainty,Fuzziness and Knowledge-Based Systems, 2009, 17(02):251-267.
[7] Fan Z P, Liu Y. A method for group decision-making based on multi-granularity uncertain linguistic information[J]. Expert Systems with Applications, 2010, 37(5):4000-4008.
[8] Rodríguez R M, MartíNez L, Herrera F. A group decision making model dealing with comparative linguistic expressions based on hesitant fuzzy linguistic term sets[J]. Information Sciences, 2013,241(12):28-42.
[9]魏翠萍,葛淑娜.犹豫模糊语言幂均算子及其在群决策中的应用[J].系统科学与数学,2016, 36(8):1308-1317.
[10]于倩,候福均.犹豫模糊语言Heronian平均算子在多属性决策中的应用[J].运筹与管理,2016, 25(2):90-97.
[11] Lin M, Xu Z, Zhai Y, et al. Multi-attribute group decision-making under probabilistic uncertain linguistic environment[J]. Journal of the Operational Research Society, 2017(22):1-15.
[12] Peide Liu. Multi-attribute decision-making method research based on interval vague set and TOPSIS method[J]. Ukio Technologinis ir Ekonominis Vystymas, 2009, 15(3):453-463.
[13] Yue Z. Yue Z. An extended TOPSIS for determining weights of decision makers with interval numbers. Knowledge-Based Systems 24, 146-153[J]. Knowledge-Based Systems, 2011, 24(1):146-153.
[14] Opricovic S, Tzeng G H. Compromise solution by MCDM methods:A comparative analysis of VIKOR and TOPSIS[J]. European Journal of Operational Research, 2004, 156(2):445-455.
[15] Roy B. Multicriteria Methodology for Decision Aiding, Kluwer, Dordrecht, The Netherlands, 1996.
[16] Roy B, and Bertier B. La metode ELECTRE II, in:Sixieme Conference Internationale de Rechearche Operationelle, Dublin, 1972.
[17] Gomes L F A M, Lima M M P P TODIM:Basics and application to multi-criteria ranking of projects with environmental impacts[J]. Foundations of Computing and Decision Sciences, 1992,16:113-127.
[18] Lourenzutti R, Krohling R A. A study of TODIM in a intuitionistic fuzzy and random environment[J]. Expert Systems with Applications, 2013, 40(16):6459-6468.
[19] Fan Z P, Zhang X, Chen F D, et al. Extended TODIM method for hybrid multiple attribute decision making problems[J]. Knowledge-Based Systems. 2013, 42(2):40-48.
[20]王坚强,李新娥.基于多值中智集的TODIM方法[J].控制与决策,2015(6):1139-1142.
[21]姜艳萍,梁霞,张业谛.一种属性信息不完全的TODIM决策方法[J].运筹与管理,2015, 24(1):116-121.
[22]王霞,党耀国.基于改进的TODIM方法的区间灰数多属性决策模型[J].控制与决策,2016(2):261-266.
[23] Wei C, Ren Z, Rodríguez R M. A Hesitant Fuzzy Linguistic TODIM Method Based on a Score Function[J]. International Journal of Computational Intelligence Systems, 2015, 8(4):701-712.
[24] Qin Q, Liang F, Li L, et al. A TODIM-based multi-criteria group decision making with triangular intuitionistic fuzzy numbers[J]. Applied Soft Computing, 2017, 55:93-107.
[25] Qin J, Liu X, Pedrycz W. An extended TODIM multi-criteria group decision making method for green supplier selection in interval type-2 fuzzy environment[J]. European Journal of Operational Research, 2016, 258.
[26]孔令艳,谭倩云.犹豫模糊语言TODIM法及其应用[J].统计与决策,2017(5):98-100.
[27]吴良刚,文丽.基于二维二元语义和模糊AHP-TODIM的低碳供应商选择方法[J].运筹与管理,2017,26(3):7-16.
[28] Liu P, Teng F. An extended TODIM method for multiple attribute group decision-making based on 2-dimension uncertain linguistic Variable[J]. Complexity, 2016, 21(5):20-30.