直觉模糊多属性决策问题的决策方法研究
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摘要
本文用理论与实验的方法研究基于直觉模糊集和区间直觉模糊集的多属性决策,建立了几种不同决策环境下的多属性决策模型,对直觉模糊多属性决策方法进行了探讨。
针对属性权重已知的区间直觉模糊多属性决策,基于直觉模糊集思想与集对分析思想兼容性的考虑,将区间直觉模糊决策矩阵转化为联系度矩阵,算出各方案的综合联系度,由模糊集对势给出方案排序式,再结合区间数排序方法最终实现方案排序,最后利用算例说明该方法的可行性。
多属性决策问题的许多求解方法,一般都与属性权重有着密切的关系,因为权重的合理性直接影响着多属性决策排序的准确性,所以在多属性决策中,权重问题的研究占据有重要地位。
针对属性权重完全未知的直觉模糊多属性决策,先从局部考虑,建立一个目标规划模型来获得单个方案的最优权重,再从全局考虑,基于投影法提出了一种非线性的二次规划模型,获得系统最优权重；对于属性权重完全未知且属性值为区间直觉模糊数的多属性决策问题,提出了区间直觉模糊熵权的确定方法；针对决策者的偏好信息和决策矩阵元素均为区间直觉模糊数的多属性决策问题,通过求解主观偏好与客观偏好的总绝对偏差最小,同时各方案综合属性值差距最大的双目标规划模型,得到属性的最优权重向量。求得属性权重后可算出方案综合属性值,通过比较得分函数值和精确函数值实现方案排序或择优。
This paper studies multil-attribute decision-making problems based on intuitionist fuzzy sets and interval-valued intuitionist fuzzy sets. Several multi-attribute decision models were established under the different decision-making environment. This paper mainly discussed the methods of intuitionist fuzzy multil-attribute decision-making problems.
Studies a kind of multi-attribute decision-making problem in which the attributes weights are given as real numbers and the attribute values are described by interval-valued intuitionist fuzzy numbers. First based on the compatibility between the set pair analysis theory and intuitionist fuzzy set theory, the interval-valued intuitionist fuzzy decision matrix is transformed into the relation degree matrix. Second obtained the synthesize relation degree. Get an interval numbers form raking by a raking formula, and then raking alternatives by interval numbers raking. Finally, an example is used to illustrate the feasibiling and practicability of the proposed approach.
Many multi-attributes decision-making problems solving methods were associated to attribute weights. Because reasonable weight direct influence the accuracy of multi-attribute decision making. Therefore, in multi-attribute decision making, weight studies occupy an important position.
When the multi-attribute decision-making problems in which the information about the attribute weights are unknown completely and the attribute values are described by intuitionist fuzzy numbers. Firstly, a linear objective programming model for determine the ideal attribute weights of single program is proposed by considering in local. Secondly, a quadratic programming model is set up based on the projection method. Then the optimal weights were gated. When the multi-attribute decision-making problem in which the information about the attribute weights are unknown completely and the attribute values are described by interval-valued intuitionist fuzzy numbers, a new method is proposed to determine entropy weights of interval-valued intuitionist fuzzy number. When the multi-attribute decision-making problem in which the preference information on alternatives and the attribute values are described by interval-valued intuitionist fuzzy numbers. After solving the two objects programming of minimizing the total absolute deviation between the subjective and objective preference and maximizing the ranges of the comprehensive attribute values of alternative, the weights of the attributes were obtained objectively. According to the comprehensive attribute values, the alternatives were ranked by using score function.
针对属性权重已知的区间直觉模糊多属性决策,基于直觉模糊集思想与集对分析思想兼容性的考虑,将区间直觉模糊决策矩阵转化为联系度矩阵,算出各方案的综合联系度,由模糊集对势给出方案排序式,再结合区间数排序方法最终实现方案排序,最后利用算例说明该方法的可行性。
多属性决策问题的许多求解方法,一般都与属性权重有着密切的关系,因为权重的合理性直接影响着多属性决策排序的准确性,所以在多属性决策中,权重问题的研究占据有重要地位。
针对属性权重完全未知的直觉模糊多属性决策,先从局部考虑,建立一个目标规划模型来获得单个方案的最优权重,再从全局考虑,基于投影法提出了一种非线性的二次规划模型,获得系统最优权重；对于属性权重完全未知且属性值为区间直觉模糊数的多属性决策问题,提出了区间直觉模糊熵权的确定方法；针对决策者的偏好信息和决策矩阵元素均为区间直觉模糊数的多属性决策问题,通过求解主观偏好与客观偏好的总绝对偏差最小,同时各方案综合属性值差距最大的双目标规划模型,得到属性的最优权重向量。求得属性权重后可算出方案综合属性值,通过比较得分函数值和精确函数值实现方案排序或择优。
This paper studies multil-attribute decision-making problems based on intuitionist fuzzy sets and interval-valued intuitionist fuzzy sets. Several multi-attribute decision models were established under the different decision-making environment. This paper mainly discussed the methods of intuitionist fuzzy multil-attribute decision-making problems.
Studies a kind of multi-attribute decision-making problem in which the attributes weights are given as real numbers and the attribute values are described by interval-valued intuitionist fuzzy numbers. First based on the compatibility between the set pair analysis theory and intuitionist fuzzy set theory, the interval-valued intuitionist fuzzy decision matrix is transformed into the relation degree matrix. Second obtained the synthesize relation degree. Get an interval numbers form raking by a raking formula, and then raking alternatives by interval numbers raking. Finally, an example is used to illustrate the feasibiling and practicability of the proposed approach.
Many multi-attributes decision-making problems solving methods were associated to attribute weights. Because reasonable weight direct influence the accuracy of multi-attribute decision making. Therefore, in multi-attribute decision making, weight studies occupy an important position.
When the multi-attribute decision-making problems in which the information about the attribute weights are unknown completely and the attribute values are described by intuitionist fuzzy numbers. Firstly, a linear objective programming model for determine the ideal attribute weights of single program is proposed by considering in local. Secondly, a quadratic programming model is set up based on the projection method. Then the optimal weights were gated. When the multi-attribute decision-making problem in which the information about the attribute weights are unknown completely and the attribute values are described by interval-valued intuitionist fuzzy numbers, a new method is proposed to determine entropy weights of interval-valued intuitionist fuzzy number. When the multi-attribute decision-making problem in which the preference information on alternatives and the attribute values are described by interval-valued intuitionist fuzzy numbers. After solving the two objects programming of minimizing the total absolute deviation between the subjective and objective preference and maximizing the ranges of the comprehensive attribute values of alternative, the weights of the attributes were obtained objectively. According to the comprehensive attribute values, the alternatives were ranked by using score function.
引文
[1]Atanassov, K. T. Intuitionistic Fuzzy-Sets. [J]. Fuzzy Sets and Systems 1986,20(1):87-96.
[2]Chen, S. M. and J. M. Tan. Handling Multicriteria Fuzzy Decision-Making Problems Based on Vague Set-Theory [J]. Fuzzy Sets and Systems.1994.67(2):163-172.
[3]Gau, W. L. and D. J. Buehrer. Vague Sets. [J]. IEEE Transactions on Systems Man and Cybernetics. 1993.23(2):610-614.
[4]Bustince, H. and P. Burillo. Vague sets are intuitionistic fuzzy sets [J]. Fuzzy Sets and Systems 1996. 79(3):403-405.
[5]Hong, D. H. and C. H. Choi. Multicriteria fuzzy decision-making problems based on vague set theory [J]. Fuzzy Sets and Systems.2000.114(1):103-113.
[6]Atanassov, K., G. Pasi, et al. Intuitionistic fuzzy interpretations of multi-criteria multi-person and multi-measurement tool decision making [J]. International Journal of Systems Science.2005.36(14): 859-868.
[7]Li. D. F. Multiattribute decision making models and methods using intuitionistic fuzzy sets. [J].Journal of Computer and System Sciences.2005.70(1):73-85.
[8]Xu, Z. S. and R. R. Yager. Some geometric aggregation operators based on intuitionistic fuzzy sets [J].International Journal of General Systems.2006.35(4):417-433.
[9]Pankowska, A. and M. Wygralak. General IF-sets with triangular norms and their applications to group decision making [J]. Information Sciences.2006.176(18):2713-2754.
[10]Atanassov, K. and G. Gargov. Interval Valued Intuitionistic Fuzzy-Sets. [J]. Fuzzy Sets and Systems. 1989.31(3):343-349.
[11]Herrera, F., L. Martinez, et al. Managing non-homogeneous information in group decision [J].European Journal of Operational Research.2005.166(1):115-132.
[12]Xu, Z. S. A survey of preference relations [J]. International Journal of General Systems.2007.36(2): 179-203.
[13]李鹏,魏翠萍.直觉模糊多属性决策新方法[J],计算机工程与应用,2009,45(1)：59-60.
[14]戴跃强,徐泽水,达庆利.基于不同直觉偏好结构的多属性决策方法[J].东南大学学报,2007,37(4)：706-710.
[15]Atanassov. K. T. Operators over Interval Valued Intuitionistic Fuzzy-Sets. [J]. Fuzzy Sets and Systems. 1994.64(2):159-174.
[16]Bustince. H. and P. Burillo. Correlation of Interval-Valued Intuitionistic Fuzzy-Sets. [J]. Fuzzy Sets and Systems.1995.74(2):237-244.
[17]Hong. D. H.A note on correlation of interval-valued intuitionistic fuzzy sets. [J]. Fuzzy Sets and Systems.1998.95(1):113-117.
[18]Mondal. T. K. and S. K. Samanta. Topology of interval-valued intuitionistic fuzzy sets. [J]. Fuzzy Sets and Systems.2001.119(3):483-494.
[19]Deschrijver, G. and E. E. Kerre. On the relationship between some extensions of fuzzy set theory. [J]. Fuzzy Sets and Systems.2003.133(2):227-235.
[20]卫贵武.对方案有偏好的区间直觉模糊多属性决策方法[J].系统工程与电子技术,2009.1：116-120.
[21]卫贵武.权重信息不完全的区间直觉模糊数多属性决策方法[J].管理学报,2008.3：208-211.
[22]Xu, Z. S. Models for multiple attribute decision making with intuitionistic fuzzy information. [J]. International Journal of Uncertainty Fuzziness and Knowledge-Based Systems.2007.15(3): 285-297.
[23]Liu. H. W. and G. J. Wang. Multi-criteria decision-making methods based on intuitionistic fuzzy sets. [J]. European Journal of Operational Research.2007.179(1):220-233.
[24]Lin, L.. X. H. Yuan, et al. Multicriteria fuzzy decision-making methods based on intuitionistic fuzzy sets. [J]. Journal of Computer and System Sciences.2007.73(1):84-88.
[25]郝颖娟,李继乾.基于方案偏好关系的直觉模糊多属性MADM方法[J].济南大学学报,2008,22(4)：316-319.
[26]徐泽水.直觉模糊信息集成理论及应用[M].北京：科学出版社,2008.
[27]周宏安,梁晓龙等.部分权重信息下基于两阶段优化的多属性决策方法[J].空军工程大学学报,2006,7(5)：85-87.
[28]周宏安,刘三阳.基于两阶段优化的多属性决策法及其解得理论证明[J].系统工程与电子技术,2005,27(8)：1425-1427.
[29]Hung, W. L. and J. W. Wu. Correlation of intuitionistic fuzzy sets by centroid method. [J]. Information Sciences.2002.144(1-4):219-225.
[30]胡辉,徐泽水。基于TOPSIS的区间直觉模糊多属性决策方法[J].模糊系统与数学,2007.21(5)108-112.
[31]赵克勤.集对分析及其应用[M].杭州：浙江科学技术出版社,2000.
[32]徐泽水.区间直觉模糊信息的集成方法及其在决策中的应用[J].控制与决策.2007,22(2)：215-219.
[33]黄树林等。模糊化的联系数及其应用初探[J].模糊集理论与应用(论文集)。1998,保定：河北大学出版社.
[34]张肃.基于集对分析和直觉模糊集的语言型多属性决策方法[J].科技导报,2008,26(12)
[35]郭春香,郭耀煌。具有区间数的多目标格序决策方法研究[J].预测.2004.5：71-73.
[36]郭效芝.模糊不确定性度量的探讨及扩展[D].西北大学硕士学位论文.2004：48-50.
[37]俞峰,杨成梧.直觉区间值模糊集的熵,距离测度和相似度[J].计算机科学,2008.35：199-205.
[38]Hwang C L, Yoon K. Multiple attribute decision making and application [M].New York:Springer-verlag.1981.
[39]夏梅梅,李鹏,宋现高。一种区间直觉模糊信息集成的新方法[J].泰山学院学报,2008.512-15.
[40]万树平。基于拉开差距的模糊多属性决策方法[J].统计与决策,2008.20.
[41]李雪梅,李学伟。交通运输项目决策中综合评价方法及应用[J].交通运输系统与信息,2004.8：55-59.
[42]赵成元,李继乾,张智刚.基于区间直觉模糊集的多准则模糊决策方法[J].济南大学学报.2008,33：16-319.
[43]汤少梁,巩在武.直觉模糊评价矩阵群决策[J].系统工程.2007,6：79-83.
[44]王坚强.信息不完全确定的多准则区间直觉模糊决策方法[J].控制与决策.2006,11：1253-1256.
[45]巩在武,刘思峰.直觉模糊判断矩阵群决策中的逆判问题[J].系统管理学报.2007,10：497-501.
[46]汪新凡.模糊数直觉模糊几何集成算子及其在决策中的应用[J].控制与决策.2008.6：607-612.
[47]王坚强,张忠.基于直觉模糊数的信息不完全的多准则规划方法[J].控制与决策.2008,10：1145-1152.
[48]王坚强.模糊多准则决策方法研究综述[J].控制与决策.2008,6：601-605.
[49]陈东锋,胥林,龙戈农.两种改进的直觉模糊多属性决策方法[J].空军工程大学学报.2008,4：76-79.
[50]高岩,周德群,刘晨琛.直觉模糊信息下的多属性决策组合赋权新方法[J].统计与决策.2009,6：151-152..
[2]Chen, S. M. and J. M. Tan. Handling Multicriteria Fuzzy Decision-Making Problems Based on Vague Set-Theory [J]. Fuzzy Sets and Systems.1994.67(2):163-172.
[3]Gau, W. L. and D. J. Buehrer. Vague Sets. [J]. IEEE Transactions on Systems Man and Cybernetics. 1993.23(2):610-614.
[4]Bustince, H. and P. Burillo. Vague sets are intuitionistic fuzzy sets [J]. Fuzzy Sets and Systems 1996. 79(3):403-405.
[5]Hong, D. H. and C. H. Choi. Multicriteria fuzzy decision-making problems based on vague set theory [J]. Fuzzy Sets and Systems.2000.114(1):103-113.
[6]Atanassov, K., G. Pasi, et al. Intuitionistic fuzzy interpretations of multi-criteria multi-person and multi-measurement tool decision making [J]. International Journal of Systems Science.2005.36(14): 859-868.
[7]Li. D. F. Multiattribute decision making models and methods using intuitionistic fuzzy sets. [J].Journal of Computer and System Sciences.2005.70(1):73-85.
[8]Xu, Z. S. and R. R. Yager. Some geometric aggregation operators based on intuitionistic fuzzy sets [J].International Journal of General Systems.2006.35(4):417-433.
[9]Pankowska, A. and M. Wygralak. General IF-sets with triangular norms and their applications to group decision making [J]. Information Sciences.2006.176(18):2713-2754.
[10]Atanassov, K. and G. Gargov. Interval Valued Intuitionistic Fuzzy-Sets. [J]. Fuzzy Sets and Systems. 1989.31(3):343-349.
[11]Herrera, F., L. Martinez, et al. Managing non-homogeneous information in group decision [J].European Journal of Operational Research.2005.166(1):115-132.
[12]Xu, Z. S. A survey of preference relations [J]. International Journal of General Systems.2007.36(2): 179-203.
[13]李鹏,魏翠萍.直觉模糊多属性决策新方法[J],计算机工程与应用,2009,45(1)：59-60.
[14]戴跃强,徐泽水,达庆利.基于不同直觉偏好结构的多属性决策方法[J].东南大学学报,2007,37(4)：706-710.
[15]Atanassov. K. T. Operators over Interval Valued Intuitionistic Fuzzy-Sets. [J]. Fuzzy Sets and Systems. 1994.64(2):159-174.
[16]Bustince. H. and P. Burillo. Correlation of Interval-Valued Intuitionistic Fuzzy-Sets. [J]. Fuzzy Sets and Systems.1995.74(2):237-244.
[17]Hong. D. H.A note on correlation of interval-valued intuitionistic fuzzy sets. [J]. Fuzzy Sets and Systems.1998.95(1):113-117.
[18]Mondal. T. K. and S. K. Samanta. Topology of interval-valued intuitionistic fuzzy sets. [J]. Fuzzy Sets and Systems.2001.119(3):483-494.
[19]Deschrijver, G. and E. E. Kerre. On the relationship between some extensions of fuzzy set theory. [J]. Fuzzy Sets and Systems.2003.133(2):227-235.
[20]卫贵武.对方案有偏好的区间直觉模糊多属性决策方法[J].系统工程与电子技术,2009.1：116-120.
[21]卫贵武.权重信息不完全的区间直觉模糊数多属性决策方法[J].管理学报,2008.3：208-211.
[22]Xu, Z. S. Models for multiple attribute decision making with intuitionistic fuzzy information. [J]. International Journal of Uncertainty Fuzziness and Knowledge-Based Systems.2007.15(3): 285-297.
[23]Liu. H. W. and G. J. Wang. Multi-criteria decision-making methods based on intuitionistic fuzzy sets. [J]. European Journal of Operational Research.2007.179(1):220-233.
[24]Lin, L.. X. H. Yuan, et al. Multicriteria fuzzy decision-making methods based on intuitionistic fuzzy sets. [J]. Journal of Computer and System Sciences.2007.73(1):84-88.
[25]郝颖娟,李继乾.基于方案偏好关系的直觉模糊多属性MADM方法[J].济南大学学报,2008,22(4)：316-319.
[26]徐泽水.直觉模糊信息集成理论及应用[M].北京：科学出版社,2008.
[27]周宏安,梁晓龙等.部分权重信息下基于两阶段优化的多属性决策方法[J].空军工程大学学报,2006,7(5)：85-87.
[28]周宏安,刘三阳.基于两阶段优化的多属性决策法及其解得理论证明[J].系统工程与电子技术,2005,27(8)：1425-1427.
[29]Hung, W. L. and J. W. Wu. Correlation of intuitionistic fuzzy sets by centroid method. [J]. Information Sciences.2002.144(1-4):219-225.
[30]胡辉,徐泽水。基于TOPSIS的区间直觉模糊多属性决策方法[J].模糊系统与数学,2007.21(5)108-112.
[31]赵克勤.集对分析及其应用[M].杭州：浙江科学技术出版社,2000.
[32]徐泽水.区间直觉模糊信息的集成方法及其在决策中的应用[J].控制与决策.2007,22(2)：215-219.
[33]黄树林等。模糊化的联系数及其应用初探[J].模糊集理论与应用(论文集)。1998,保定：河北大学出版社.
[34]张肃.基于集对分析和直觉模糊集的语言型多属性决策方法[J].科技导报,2008,26(12)
[35]郭春香,郭耀煌。具有区间数的多目标格序决策方法研究[J].预测.2004.5：71-73.
[36]郭效芝.模糊不确定性度量的探讨及扩展[D].西北大学硕士学位论文.2004：48-50.
[37]俞峰,杨成梧.直觉区间值模糊集的熵,距离测度和相似度[J].计算机科学,2008.35：199-205.
[38]Hwang C L, Yoon K. Multiple attribute decision making and application [M].New York:Springer-verlag.1981.
[39]夏梅梅,李鹏,宋现高。一种区间直觉模糊信息集成的新方法[J].泰山学院学报,2008.512-15.
[40]万树平。基于拉开差距的模糊多属性决策方法[J].统计与决策,2008.20.
[41]李雪梅,李学伟。交通运输项目决策中综合评价方法及应用[J].交通运输系统与信息,2004.8：55-59.
[42]赵成元,李继乾,张智刚.基于区间直觉模糊集的多准则模糊决策方法[J].济南大学学报.2008,33：16-319.
[43]汤少梁,巩在武.直觉模糊评价矩阵群决策[J].系统工程.2007,6：79-83.
[44]王坚强.信息不完全确定的多准则区间直觉模糊决策方法[J].控制与决策.2006,11：1253-1256.
[45]巩在武,刘思峰.直觉模糊判断矩阵群决策中的逆判问题[J].系统管理学报.2007,10：497-501.
[46]汪新凡.模糊数直觉模糊几何集成算子及其在决策中的应用[J].控制与决策.2008.6：607-612.
[47]王坚强,张忠.基于直觉模糊数的信息不完全的多准则规划方法[J].控制与决策.2008,10：1145-1152.
[48]王坚强.模糊多准则决策方法研究综述[J].控制与决策.2008,6：601-605.
[49]陈东锋,胥林,龙戈农.两种改进的直觉模糊多属性决策方法[J].空军工程大学学报.2008,4：76-79.
[50]高岩,周德群,刘晨琛.直觉模糊信息下的多属性决策组合赋权新方法[J].统计与决策.2009,6：151-152..