基于直觉梯形模糊数的多属性决策方法
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摘要
现实决策中,由于社会经济环境的日益复杂性和不确定性,人们对事物的认识过程中,往往存在不同程度的犹豫或表现出一定程度的知识缺乏,从而使得认知的结果表现为肯定、否定或介于肯定和否定之间的犹豫性这三个方面,如在各种选举事件中,除了支持与反对两方面,常常有弃权的情况发生。由于直觉模糊集在模糊集的基础上增加了一个新的参数——非隶属度,能更加细腻地描述和刻画客观世界的模糊本质,在模糊多属性决策和群决策领域中有广泛的应用。文章对属性值为直觉梯形模糊数,从属性权重是否已知的方面入手,讨论了直觉梯形模糊数多属性决策的方法。
系统介绍了直觉梯形模糊数的基本运算法则及其相关集成算子。并给出直觉梯形模糊数的倒数运算,提出了新的调和平均集成算子,给出了直觉梯形模糊数的均值、得分函数、精确度函数及距离函数。
针对属性权重已知且分别以确定的实数或直觉梯形模糊数给出,且属性值为直觉梯形模糊数的多属性决策问题,分别提出基于调和平均算子和得分函数下的决策模型及算法,并给出相应的算例。
针对属性权重信息不完全,属性值为直觉梯形模糊数的多属性决策问题,分别提出基于得分函数和距离函数下的多属性决策方法,并给出相应的算例。
针对属性权重信息完全未知,属性值为直觉梯形模糊数,且对方案有无偏好多属性决策问题,分别提出了基于离差最大化和偏差最小化的决策模型及算法来确定权重信息,并利用调和平均算子进行多属性决策,且给出相应的算例。
In the real decision-making, due to the increasing complexity and uncertainty of the social economic environment, there is affirmation, negation and hesitation in the cognitive results. As in all election events, in addition to support and against, often occur about the abstention. Because of intuitionistic fuzzy sets based on fuzzy set by adding a new parameter--non membership, the fuzzy nature can be more delicate description and characterization of the objective world. The intuitionistic fuzzy sets are widely used in the fuzzy multiple attribute decision-making and group decision-making in the field. In this paper, whether the attribute weights are known. We discuss the method of intuitionistic trapezoidal fuzzy multiple attribute decision making.
This paper introduces the basic algorithms and related integrated operator of intuitionistic trapezoidal fuzzy numbers, discusses the intuitionistic trapezoidal fuzzy number reciprocal operation, and gives a new integrated operator of the harmonic averaging operator. Finally, the mean score function and accuracy function distance functions are given about the intuitionistic trapezoidal fuzzy number.
For multiple attribute decision making problems, in which the information on attribute weights are known, and the attribute value are intuitionistic trapezoidal fuzzy numbers. Respectively we put forward decision-making model and algorithm of harmonic averaging operator based on the score function. Finally, we give the corresponding examples.
With incomplete known of information about attribute weights in multiple attribute decision making problems for attribute values is intuitionistic trapezoidal fuzzy number. The alternative is ranked base on the score function and distance function and we give the corresponding examples.
For unknown attribute weights, attribute values are intuitionistic trapezoidal fuzzy number. And the scheme is biased or unbiased multi-attribute decision making problems. We are presented to determine the weight deviation decision model and algorithm based on maximum and minimum deviation. The alternative is ranked by harmonic averaging operators. Finally, the corresponding example is given.
系统介绍了直觉梯形模糊数的基本运算法则及其相关集成算子。并给出直觉梯形模糊数的倒数运算,提出了新的调和平均集成算子,给出了直觉梯形模糊数的均值、得分函数、精确度函数及距离函数。
针对属性权重已知且分别以确定的实数或直觉梯形模糊数给出,且属性值为直觉梯形模糊数的多属性决策问题,分别提出基于调和平均算子和得分函数下的决策模型及算法,并给出相应的算例。
针对属性权重信息不完全,属性值为直觉梯形模糊数的多属性决策问题,分别提出基于得分函数和距离函数下的多属性决策方法,并给出相应的算例。
针对属性权重信息完全未知,属性值为直觉梯形模糊数,且对方案有无偏好多属性决策问题,分别提出了基于离差最大化和偏差最小化的决策模型及算法来确定权重信息,并利用调和平均算子进行多属性决策,且给出相应的算例。
In the real decision-making, due to the increasing complexity and uncertainty of the social economic environment, there is affirmation, negation and hesitation in the cognitive results. As in all election events, in addition to support and against, often occur about the abstention. Because of intuitionistic fuzzy sets based on fuzzy set by adding a new parameter--non membership, the fuzzy nature can be more delicate description and characterization of the objective world. The intuitionistic fuzzy sets are widely used in the fuzzy multiple attribute decision-making and group decision-making in the field. In this paper, whether the attribute weights are known. We discuss the method of intuitionistic trapezoidal fuzzy multiple attribute decision making.
This paper introduces the basic algorithms and related integrated operator of intuitionistic trapezoidal fuzzy numbers, discusses the intuitionistic trapezoidal fuzzy number reciprocal operation, and gives a new integrated operator of the harmonic averaging operator. Finally, the mean score function and accuracy function distance functions are given about the intuitionistic trapezoidal fuzzy number.
For multiple attribute decision making problems, in which the information on attribute weights are known, and the attribute value are intuitionistic trapezoidal fuzzy numbers. Respectively we put forward decision-making model and algorithm of harmonic averaging operator based on the score function. Finally, we give the corresponding examples.
With incomplete known of information about attribute weights in multiple attribute decision making problems for attribute values is intuitionistic trapezoidal fuzzy number. The alternative is ranked base on the score function and distance function and we give the corresponding examples.
For unknown attribute weights, attribute values are intuitionistic trapezoidal fuzzy number. And the scheme is biased or unbiased multi-attribute decision making problems. We are presented to determine the weight deviation decision model and algorithm based on maximum and minimum deviation. The alternative is ranked by harmonic averaging operators. Finally, the corresponding example is given.
引文
[1]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.
[2]王应明,傅国伟.运用无限方案多目标决策方法进行有限方案多目标决策[J].控制与决策,1993,8(1)：25-29.
[3]王绪柱,单静.模糊量排序综述[J].模糊系统与数学,2002,16(4)：28-34.
[4]王坚强.模糊多准则决策方法研究综述[J].控制与决策,2008,23(6)：601-612.
[5]万树平.直觉模糊多属性决策方法综述[J].控制与决策,2010,25(11)：1601-1606.
[6]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,2008,23(10)：1145-1148.
[7]Wang Jianqing, Zhang Zhong. Aggregation operators on intuitionistic trapezoidal fuzzy number and its application to multicriteria decision making problems [J]. Journal of systems Engineering and Electronics,2009,20(2):321-326.
[8]Wei Guiwu. Some Arithmetic Aggregation Operators with Intuitionistic Trapezoidal Fuzzy Numbers and their Application to Group Decision Makings [J]. Journal of computer,2010,5(3):345-351.
[9]万树平,董九英.多属性群决策的直觉梯形模糊数法[J].控制与决策,2010,25(5)：773-776.
[10]张市芳,刘三阳,翟任何.直觉梯形模糊数MADM问题的灰色关联分析法[J].计算机科学,2010,37(11)：214-216.
[11]万树平.基于区间直觉梯形模糊数的多属性决策方法[J].控制与决策,2011,26(6)：857-866.
[12]高岩,周德群,章玲.基于直觉梯形模糊数的关联变权多属性决策方法[J].系统工程,2011,29(5)：102-107.
[13]Jian Wu, Qing-wei Cao. Same Families Of Geometric Aggregation Operators with Intuitionistic Trapezoidal Fuzzy Numbers [J]. Applied Mathematical Modeling,2012,5 (3):1-10.
[14]王莹,张市芳,谢世强.直觉梯形模糊几何集成算子及其在群决策中的应用[J].价值工程,2012,01(1)：159-161.
[15]ATANASSOV K T. Intuitionistic fuzzy sets[J]. Fuzzy sets and Systems,1986,20(1): 87-96.
[16]ATANASSOV K T. More on intuitionistic fuzzy sets[J]. Fuzzy sets and Systems,1989," 33:37-46.
[17]ATANASSOV K T. New operations defined over the intuitionistic fuzzy sets[J]. Fuzzy sets and Systems,1994,61:137-142.
[18]ATANASSOV K T. Remarks on the intuitionistic fuzzy sets[J]. Fuzzy sets and Systems, 1995,75:401-402.
[19]王中兴,谢海斌.一种基于优势度的直觉梯形模糊数排序方法[J].统计与决策,2011,18(342)：27-30.
[20]Abbasbandy S, Amirfakhrian. The Nearest Trapezoidal Form of a Generaliazed Left Right Fuzzy Number [J]. International Journal of Approximate Reasoning,2006(43):166-178.
[21]Carlsson C, Fuller R. On Possibilistic Mean Value and Variance of Fuzzy Numbers[J]. Fuzzy Sets and Systerms,2001,122:315-326.
[22]Li D F. A Ratio Ranking Method of Triangular Intuitionistic Fuzzy Numbers and. Its Application to MADM Problems [J]. Computers and Mathematics with Applications. 2010,7(3):1557-1570.
[23]Xu Z S. An overview of methods for methods for determining OWA weights [J].Inter-national Journal of Intelligent Systems,2005,20:843-865.
[24]Xu Z S.Yager R R. Some geometric aggregation operators based on intuitionistic fuzzy sets [J]. International Journal of General Systems,2006,35:417-433.
[25]Xu Z S. Intuitionistic fuzzy aggregation operators[J]. IEEE Transactions on Fuzzy Systems,2007,15:1179-1187
[26]王坚强,张忠.基于直觉梯形模糊数的信息不完全的多准则决策方法[J].控制与决策,2009,24(2)：226-230.
[27]孙丽娟,刑小军,周德群.熵值赋权法的改进[J].统计与决策,2010,21(321)：153-154.
[28]郭显光.熵值法及其综合评价中的应用[J].财贸研究,1994,6：56-60.
[29]卫贵武.基于模糊信息的多属性决策理论与方法[M].北京：中国经济出版社,2010.
[30]王应明.多指标决策与评价的新方法-投影法[J].系统工程和电子技术,1999.21(3)：1-4.
[31]张伟竞,黄天民,陈尚云.基于直觉梯形模糊数的多属性决策方法[J].西南民族大学学报,2012,38(4)：545-549.
[32]王煜,徐泽水.OWA算子赋权新方法[J].数学实践与认识,2008,38(3)：51-60.
[33]Jun Ye. Expected value method for intuitionistic trapezoidal fuzzy multicriteria decision making problems[J]. Expert Systems with Applications,2011,38:11730-11734.
[34]Lee K S, Park K S, Eum Y S. Extend methods for identifying dominance and potential optimality in multicriteria analysis with imprecise information[J]. European Journal of Operational Research,2001,134(4):557-563.
[35]Kim S H, Han C H. An interactive procedure for multiple attribute group decision making procedure with incomplete information[J]. Computer & Operational Research, 1999,26(8):755-772.
[36]李井翠,黄敢基,邵翠丽.一种直觉梯形模糊数的排序方法及其多准则决策中的应用[J].广西科学,2011,18(2)：113-116.
[37]李因果,李新春.综合评价模型权重确定方法研究[J].辽东学院学报,2007,9(2)：92-97.
[38]刘宏.综合评价中指标权重确定方法研究[J].河北工业大学学报,1996,25(4)：75-79.
[39]Supriya K D, Ranjit B, Akhil R R. Some operations on intuitionistic fuzzy sets [J]. Fuzzy Sets and Systems,2000,114:477-484.
[40]王应明.运用离差最大化方法进行多指标决策与排序[J].系统工程与电子技术,1998,20(7)：24-26.
[41]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.
[42]Bustince H, Burillo P. Vague sets are ntuitionistic fuzzy sets [J]. Fuzzy Sets and Systems,1996,79:403-405.
[43]Li D F. Multiattribute decision making models and methods using intuitionistic fuzzy sets. [J]. Computer System Sci,2005,70:73-85.
[44]Wang J Q. Multi criteria interval intuitionistic fuzzy decision-making approach with incomplete certain information[J]. Control and Decision,2006(11):1253-1256.
[45]Xu Z S. Methods for aggregating interval-valued intuitionistic fuzzy information and their application to decision making[J]. Control and Decision,2007,22(2):215-219.
[46]Shu M H, Cheng C H, Chang J R. Using intuitionistic fuzzy sets for fault-tree analysis on printed circuit board assembly[J]. Microelectronics Reliability,2006(46):2139-2148.
[47]Wang J Q. Survey on fuzzy multi-criteria decision making approach[J]. Control and Decision,2008(2):152-157.
[48]Xu Z S, Da Q L. Possibility degree method for ranking interval numbers and its application[J]. Journal of Systems Engineering,2003(18):67-70.
[49]Hwang C L, Yoon K. Multiple Attribute Decision Making and Applications[M]. New York:SpringerVerlag,1981.
[50]Hwang C L, Lin M J. Group Decision Making under Multiple Criteria:Methods and Applications[M]. Berlin:Springer,1987.
[51]王应明,傅国伟.运用无限方案多目标决策方法进行有限方案多目标决策[J].控制与决策,1993,8(1)：25-29.
[52]李美娟,陈国宏,陈衍泰.综合评价中指标标准化方法研究[J].中国管理科学,2004,12(s1)：45-47.
[2]王应明,傅国伟.运用无限方案多目标决策方法进行有限方案多目标决策[J].控制与决策,1993,8(1)：25-29.
[3]王绪柱,单静.模糊量排序综述[J].模糊系统与数学,2002,16(4)：28-34.
[4]王坚强.模糊多准则决策方法研究综述[J].控制与决策,2008,23(6)：601-612.
[5]万树平.直觉模糊多属性决策方法综述[J].控制与决策,2010,25(11)：1601-1606.
[6]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,2008,23(10)：1145-1148.
[7]Wang Jianqing, Zhang Zhong. Aggregation operators on intuitionistic trapezoidal fuzzy number and its application to multicriteria decision making problems [J]. Journal of systems Engineering and Electronics,2009,20(2):321-326.
[8]Wei Guiwu. Some Arithmetic Aggregation Operators with Intuitionistic Trapezoidal Fuzzy Numbers and their Application to Group Decision Makings [J]. Journal of computer,2010,5(3):345-351.
[9]万树平,董九英.多属性群决策的直觉梯形模糊数法[J].控制与决策,2010,25(5)：773-776.
[10]张市芳,刘三阳,翟任何.直觉梯形模糊数MADM问题的灰色关联分析法[J].计算机科学,2010,37(11)：214-216.
[11]万树平.基于区间直觉梯形模糊数的多属性决策方法[J].控制与决策,2011,26(6)：857-866.
[12]高岩,周德群,章玲.基于直觉梯形模糊数的关联变权多属性决策方法[J].系统工程,2011,29(5)：102-107.
[13]Jian Wu, Qing-wei Cao. Same Families Of Geometric Aggregation Operators with Intuitionistic Trapezoidal Fuzzy Numbers [J]. Applied Mathematical Modeling,2012,5 (3):1-10.
[14]王莹,张市芳,谢世强.直觉梯形模糊几何集成算子及其在群决策中的应用[J].价值工程,2012,01(1)：159-161.
[15]ATANASSOV K T. Intuitionistic fuzzy sets[J]. Fuzzy sets and Systems,1986,20(1): 87-96.
[16]ATANASSOV K T. More on intuitionistic fuzzy sets[J]. Fuzzy sets and Systems,1989," 33:37-46.
[17]ATANASSOV K T. New operations defined over the intuitionistic fuzzy sets[J]. Fuzzy sets and Systems,1994,61:137-142.
[18]ATANASSOV K T. Remarks on the intuitionistic fuzzy sets[J]. Fuzzy sets and Systems, 1995,75:401-402.
[19]王中兴,谢海斌.一种基于优势度的直觉梯形模糊数排序方法[J].统计与决策,2011,18(342)：27-30.
[20]Abbasbandy S, Amirfakhrian. The Nearest Trapezoidal Form of a Generaliazed Left Right Fuzzy Number [J]. International Journal of Approximate Reasoning,2006(43):166-178.
[21]Carlsson C, Fuller R. On Possibilistic Mean Value and Variance of Fuzzy Numbers[J]. Fuzzy Sets and Systerms,2001,122:315-326.
[22]Li D F. A Ratio Ranking Method of Triangular Intuitionistic Fuzzy Numbers and. Its Application to MADM Problems [J]. Computers and Mathematics with Applications. 2010,7(3):1557-1570.
[23]Xu Z S. An overview of methods for methods for determining OWA weights [J].Inter-national Journal of Intelligent Systems,2005,20:843-865.
[24]Xu Z S.Yager R R. Some geometric aggregation operators based on intuitionistic fuzzy sets [J]. International Journal of General Systems,2006,35:417-433.
[25]Xu Z S. Intuitionistic fuzzy aggregation operators[J]. IEEE Transactions on Fuzzy Systems,2007,15:1179-1187
[26]王坚强,张忠.基于直觉梯形模糊数的信息不完全的多准则决策方法[J].控制与决策,2009,24(2)：226-230.
[27]孙丽娟,刑小军,周德群.熵值赋权法的改进[J].统计与决策,2010,21(321)：153-154.
[28]郭显光.熵值法及其综合评价中的应用[J].财贸研究,1994,6：56-60.
[29]卫贵武.基于模糊信息的多属性决策理论与方法[M].北京：中国经济出版社,2010.
[30]王应明.多指标决策与评价的新方法-投影法[J].系统工程和电子技术,1999.21(3)：1-4.
[31]张伟竞,黄天民,陈尚云.基于直觉梯形模糊数的多属性决策方法[J].西南民族大学学报,2012,38(4)：545-549.
[32]王煜,徐泽水.OWA算子赋权新方法[J].数学实践与认识,2008,38(3)：51-60.
[33]Jun Ye. Expected value method for intuitionistic trapezoidal fuzzy multicriteria decision making problems[J]. Expert Systems with Applications,2011,38:11730-11734.
[34]Lee K S, Park K S, Eum Y S. Extend methods for identifying dominance and potential optimality in multicriteria analysis with imprecise information[J]. European Journal of Operational Research,2001,134(4):557-563.
[35]Kim S H, Han C H. An interactive procedure for multiple attribute group decision making procedure with incomplete information[J]. Computer & Operational Research, 1999,26(8):755-772.
[36]李井翠,黄敢基,邵翠丽.一种直觉梯形模糊数的排序方法及其多准则决策中的应用[J].广西科学,2011,18(2)：113-116.
[37]李因果,李新春.综合评价模型权重确定方法研究[J].辽东学院学报,2007,9(2)：92-97.
[38]刘宏.综合评价中指标权重确定方法研究[J].河北工业大学学报,1996,25(4)：75-79.
[39]Supriya K D, Ranjit B, Akhil R R. Some operations on intuitionistic fuzzy sets [J]. Fuzzy Sets and Systems,2000,114:477-484.
[40]王应明.运用离差最大化方法进行多指标决策与排序[J].系统工程与电子技术,1998,20(7)：24-26.
[41]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.
[42]Bustince H, Burillo P. Vague sets are ntuitionistic fuzzy sets [J]. Fuzzy Sets and Systems,1996,79:403-405.
[43]Li D F. Multiattribute decision making models and methods using intuitionistic fuzzy sets. [J]. Computer System Sci,2005,70:73-85.
[44]Wang J Q. Multi criteria interval intuitionistic fuzzy decision-making approach with incomplete certain information[J]. Control and Decision,2006(11):1253-1256.
[45]Xu Z S. Methods for aggregating interval-valued intuitionistic fuzzy information and their application to decision making[J]. Control and Decision,2007,22(2):215-219.
[46]Shu M H, Cheng C H, Chang J R. Using intuitionistic fuzzy sets for fault-tree analysis on printed circuit board assembly[J]. Microelectronics Reliability,2006(46):2139-2148.
[47]Wang J Q. Survey on fuzzy multi-criteria decision making approach[J]. Control and Decision,2008(2):152-157.
[48]Xu Z S, Da Q L. Possibility degree method for ranking interval numbers and its application[J]. Journal of Systems Engineering,2003(18):67-70.
[49]Hwang C L, Yoon K. Multiple Attribute Decision Making and Applications[M]. New York:SpringerVerlag,1981.
[50]Hwang C L, Lin M J. Group Decision Making under Multiple Criteria:Methods and Applications[M]. Berlin:Springer,1987.
[51]王应明,傅国伟.运用无限方案多目标决策方法进行有限方案多目标决策[J].控制与决策,1993,8(1)：25-29.
[52]李美娟,陈国宏,陈衍泰.综合评价中指标标准化方法研究[J].中国管理科学,2004,12(s1)：45-47.