区间直觉正态模糊数的OWGA算子及其在多属性群决策中应用
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摘要
针对准则值为区间直觉正态模糊数(IVINFN)的群决策问题,探讨了区间直觉正态模糊数的运算法则;考虑决策者的乐观程度,定义了区间直觉正态模糊数的得分函数,给出其排序方法;再得到区间直觉正态模糊数的有序加权几何平均(IVINFN-OWGA)算子和连续有序加权几何平均(IVINFN-COWG)算子;最后,建立了基于区间直觉正态模糊数的多属性决策模型,提出了相应的群决策方法,并且通过实例分析验证了该方法的可行性和有效性.
For multi-attribute group decision making problem in which the criteria values are intervalvalued intuitionistic normal fuzzy numbers,the paper defines their operational laws.Considered optimistic degree of decision makers,the score function of interval-valued intuitionistic normal fuzzy number is defined.Based on these,a new approach for raking interval-valued intuitionistic normal fuzzy number is proposed.Moreover,IVINFN ordered weighted geometric averaging(IVINFNOWGA)operator and IVINFN continuous ordered weighted geometric averaging(IVINFN-COWG)operator are presented.Finally,by using these two operators,a model of multi-attribute group decision making is constructed based on interval-valued intuitionistic normal fuzzy numbers.The corresponding method of decision making is also proposed.And an example is given to illustrate the feasibility and effectiveness of this method.
For multi-attribute group decision making problem in which the criteria values are intervalvalued intuitionistic normal fuzzy numbers,the paper defines their operational laws.Considered optimistic degree of decision makers,the score function of interval-valued intuitionistic normal fuzzy number is defined.Based on these,a new approach for raking interval-valued intuitionistic normal fuzzy number is proposed.Moreover,IVINFN ordered weighted geometric averaging(IVINFNOWGA)operator and IVINFN continuous ordered weighted geometric averaging(IVINFN-COWG)operator are presented.Finally,by using these two operators,a model of multi-attribute group decision making is constructed based on interval-valued intuitionistic normal fuzzy numbers.The corresponding method of decision making is also proposed.And an example is given to illustrate the feasibility and effectiveness of this method.
引文
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[4]徐泽水.直觉模糊信息集成理论及应用[M].北京:科学出版社,2008:20-34.
[5]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.
[6]陈华友.区间乘积偏好关系的对数相容度及其性质[J].安徽大学学报:自然科学版,2012,36(1):1-5
[7]Yang M S,Ko C H.On a Class of Fuzzy C-Numbers Clustering Procedures for Fuzzy Data[J].Fuzzy Sets and Systems,1996,84(1):49-60.
[8]许若宁,李楚霖.一类不分明时间序列的回归预测[J].高校应用数学学报:A辑,2001(4):455-461.
[9]王坚强,李康健.基于直觉正态模糊集结算子的多准则决策方法[J].系统工程理论与实践,2013,33(6):1501-1508.
[10]Yager R R.OWA Aggregation over a Continuous Interval Argument with Applications to Decision Making[J].Systems Man and Cybernetics Part B:Cybernetics,IEEE Transactions,2004,34(5):1952-1963.
[11]Yager R R,Xu Z S.The Continuous Ordered Weighted Geometric Operator and its Application to Decision Making[J].Fuzzy Sets and Systems,2006,157(10):1393-1402.
[12]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,2008,30(3):12-16.
[13]倪渊,林健.中层管理者胜任力组合评价模型及实证研究[J].系统工程,2012,30(1):1-7.
[2]Atanassov K T.Intuitionistic fuzzy sets[J].Fuzzy Sets and Systems,1986,20(1):87-96.
[3]Atanassov K,Gargov G.Interval-valued Intuitionistic Fuzzy Sets[J].Fuzzy Sets and Systems,1989,31(3):20-34.
[4]徐泽水.直觉模糊信息集成理论及应用[M].北京:科学出版社,2008:20-34.
[5]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.
[6]陈华友.区间乘积偏好关系的对数相容度及其性质[J].安徽大学学报:自然科学版,2012,36(1):1-5
[7]Yang M S,Ko C H.On a Class of Fuzzy C-Numbers Clustering Procedures for Fuzzy Data[J].Fuzzy Sets and Systems,1996,84(1):49-60.
[8]许若宁,李楚霖.一类不分明时间序列的回归预测[J].高校应用数学学报:A辑,2001(4):455-461.
[9]王坚强,李康健.基于直觉正态模糊集结算子的多准则决策方法[J].系统工程理论与实践,2013,33(6):1501-1508.
[10]Yager R R.OWA Aggregation over a Continuous Interval Argument with Applications to Decision Making[J].Systems Man and Cybernetics Part B:Cybernetics,IEEE Transactions,2004,34(5):1952-1963.
[11]Yager R R,Xu Z S.The Continuous Ordered Weighted Geometric Operator and its Application to Decision Making[J].Fuzzy Sets and Systems,2006,157(10):1393-1402.
[12]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,2008,30(3):12-16.
[13]倪渊,林健.中层管理者胜任力组合评价模型及实证研究[J].系统工程,2012,30(1):1-7.