区间二元语义信息的C-OWGD算子在多属性群决策中的应用
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摘要
基于C-OWGD算子定义了一种新的区间二元语义距离,再将其和语言环境下的有序加权距离(OWD)算子相结合,提出了基于区间二元语义C-OWGD算子距离的有序加权距离(ITC-OWGD)算子,并探讨了该算子的一些性质和特例。最后,给出了基于ITC-OWGD算子的区间二元语义多属性群决策方法。该方法在决策者权重、属性权重信息皆未知的条件下,给出了求解决策者权重和属性权重的公式,从而获得相应的权重。
A group decision making method based on interval-valued 2-tuple linguistic information and distance measure is developed. Firstly,a new interval-valued 2-tuple linguistic distance measure based on the C-OWG operator is defined. Secondly,the interval-valued 2-tuple linguistic continuous ordered weighted geometric distance( ITC-OWGD) operator is proposed,which combines the new distance measure with the ordered weighted distance( OWD) operator under linguistic environment.Simultaneously,some desired properties and different special cases of the ITC-OWGD operator are also investigated. Furthermore,a method of MAGDM under interval-valued 2-tuple linguistic environment is proposed based on ITC-OWGD operator. The merits are in two respects: 1) the proposed method can be used to deal with the situations,where decision makers ' weights and attributes 'weights are completely unknown; 2) two simple and exact formulas are used to determine the weighting vector of decision makers and the weighting vector of attributes.
A group decision making method based on interval-valued 2-tuple linguistic information and distance measure is developed. Firstly,a new interval-valued 2-tuple linguistic distance measure based on the C-OWG operator is defined. Secondly,the interval-valued 2-tuple linguistic continuous ordered weighted geometric distance( ITC-OWGD) operator is proposed,which combines the new distance measure with the ordered weighted distance( OWD) operator under linguistic environment.Simultaneously,some desired properties and different special cases of the ITC-OWGD operator are also investigated. Furthermore,a method of MAGDM under interval-valued 2-tuple linguistic environment is proposed based on ITC-OWGD operator. The merits are in two respects: 1) the proposed method can be used to deal with the situations,where decision makers ' weights and attributes 'weights are completely unknown; 2) two simple and exact formulas are used to determine the weighting vector of decision makers and the weighting vector of attributes.
引文
[1]Yager R R.On Ordered Weighted Averaging Aggregation operators in multi-criteria decision making[J].IEEE Transactions on Systems,Man and Cybernetics,B,1988,18:183-190.
[2]Chiclana F,Herrera F,Herrera-Viedma E.The Ordered Weighted Geometric Operator:Properties and Applications[C].Proceeding 8th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems,Madrid,2000:985-991.
[3]陈华友,刘春林,盛昭瀚.IOWHA算子及其在组合预测中的应用[J].中国管理科学,2004,12(5):35-40.
[4]Yager R R.OWA Aggregation over a Continuous Interval Argument With Applications to Decision Making[J].IEEE Transactions on Systems,Man and Cybernetics,B,2004,34:1952-1963.
[5]Yager R.R.Generalized OWA aggregation operators[J].Fuzzy Optimization and Decision Making,2004,3:93-107.
[6]张洪美,徐泽水.基于不确定语言信息的C-OWA和C-OWG算子及其应用[J].解放军理工大学学报(自然科学版),2005,6(6):604-608.
[7]Xu Y J,MerigóJ M,Wang H M.Linguistic Power Aggregation Operators and Their Application to Multiple Attribute Group Decision Making[J].Applied Mathematical Modelling,2012,36:5427-5444.
[8]Wei G W,Zhao X F,Lin R,Wang H J.Uncertain Linguistic Bonferroni Mean Operators and Their Application to Multiple Attribute Decision Making[J].Applied Mathematical Modelling,2013,37(7):5277-5285.
[9]Zhang H M.Some Interval-Valued 2-Tuple Linguistic Aggregation Operators and Application in Multiattribute Group Decision Making[J].Applied Mathematical Modelling,2013,37:4269-4282.
[10]Xu Z S,Chen J.Ordered Weighted Distance Measure[J].Journal of Systems Science and Systems Engineering,2008,17:432-445.
[11]MerigóJ M,Casanovas M.Decision Making with Distance Measures and Linguistic Aggregation Operators[J].International Journal of Fuzzy Systems,2010,2:190-198.
[12]Zeng S Z,Bale6entis T,Zhang CH.A Method Based on OWA Operator and Distance Measure for Multiple Attribute Decision Making with 2-tuple Linguistic Information[J].Informatica,2012,23:665-681.
[13]Zhou L G,Wu J X,Chen H Y.Linguistic Continuous Ordered Weighted Distance Measure and Its Application to Multiple Attributes Group Decision Making[J].Applied Soft Computing,2014,25:266-276.
[14]Herrera F,Martinez L.A 2-tuple fuzzy Linguistic Representation Model for Computing with Words[J].IEEE Transactions on Fuzzy Systems,2000,8(6):746-752.
[15]Herrera F,Martinez L.A Model Based on Linguistic 2-tuples for Dealing with Multi-granular Hierarchical Linguistic Contexts in Multi-expert Decision-making[J].IEEE Transactions on Systems,Man and Cybernetics,B,2001,31(2):227-234.
[16]Chen C T,Tai W S.Measuring the Intellectual Capital Performance Based on 2-tuple Fuzzy Linguistic Information[C].Proceedings of the 10th Annual Meeting of Asia Pacific Region of Decision Sciences Institute,Taiwan,2005.
[17]Zhang H M.The Multiattribute Group Decision Making Method Based on Aggregation Operators with Interval-valued 2-tuple Linguistic Information[J].Mathematical and Computer Modelling,2012,56:27-35.
[18]Yager R R,Xu Z S.The Continuous Ordered Weighted Geometric Operator and Its Application to Decision Making[J].Fuzzy sets and systems,2006,157:1393-1402.
[19]Fodor J,Marichal J L,Roubens M.Characterization of the Ordered Weighted Averaging Operators[J].IEEE Transactions on Fuzzy Systems,1995,3:236-240.
[20]Xu Z.S.Dependent Uncertain Ordered Weighted Aggregation Operators[J].Information Fusion,2008,9:310-316.
[21]Wei G.W.Some Generalized Aggregating Operators With Linguistic Information And Their Application To Multiple Attribute Group Decision Making[J].Computers&Industrial Engineering,2011,61:32-38.
[2]Chiclana F,Herrera F,Herrera-Viedma E.The Ordered Weighted Geometric Operator:Properties and Applications[C].Proceeding 8th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems,Madrid,2000:985-991.
[3]陈华友,刘春林,盛昭瀚.IOWHA算子及其在组合预测中的应用[J].中国管理科学,2004,12(5):35-40.
[4]Yager R R.OWA Aggregation over a Continuous Interval Argument With Applications to Decision Making[J].IEEE Transactions on Systems,Man and Cybernetics,B,2004,34:1952-1963.
[5]Yager R.R.Generalized OWA aggregation operators[J].Fuzzy Optimization and Decision Making,2004,3:93-107.
[6]张洪美,徐泽水.基于不确定语言信息的C-OWA和C-OWG算子及其应用[J].解放军理工大学学报(自然科学版),2005,6(6):604-608.
[7]Xu Y J,MerigóJ M,Wang H M.Linguistic Power Aggregation Operators and Their Application to Multiple Attribute Group Decision Making[J].Applied Mathematical Modelling,2012,36:5427-5444.
[8]Wei G W,Zhao X F,Lin R,Wang H J.Uncertain Linguistic Bonferroni Mean Operators and Their Application to Multiple Attribute Decision Making[J].Applied Mathematical Modelling,2013,37(7):5277-5285.
[9]Zhang H M.Some Interval-Valued 2-Tuple Linguistic Aggregation Operators and Application in Multiattribute Group Decision Making[J].Applied Mathematical Modelling,2013,37:4269-4282.
[10]Xu Z S,Chen J.Ordered Weighted Distance Measure[J].Journal of Systems Science and Systems Engineering,2008,17:432-445.
[11]MerigóJ M,Casanovas M.Decision Making with Distance Measures and Linguistic Aggregation Operators[J].International Journal of Fuzzy Systems,2010,2:190-198.
[12]Zeng S Z,Bale6entis T,Zhang CH.A Method Based on OWA Operator and Distance Measure for Multiple Attribute Decision Making with 2-tuple Linguistic Information[J].Informatica,2012,23:665-681.
[13]Zhou L G,Wu J X,Chen H Y.Linguistic Continuous Ordered Weighted Distance Measure and Its Application to Multiple Attributes Group Decision Making[J].Applied Soft Computing,2014,25:266-276.
[14]Herrera F,Martinez L.A 2-tuple fuzzy Linguistic Representation Model for Computing with Words[J].IEEE Transactions on Fuzzy Systems,2000,8(6):746-752.
[15]Herrera F,Martinez L.A Model Based on Linguistic 2-tuples for Dealing with Multi-granular Hierarchical Linguistic Contexts in Multi-expert Decision-making[J].IEEE Transactions on Systems,Man and Cybernetics,B,2001,31(2):227-234.
[16]Chen C T,Tai W S.Measuring the Intellectual Capital Performance Based on 2-tuple Fuzzy Linguistic Information[C].Proceedings of the 10th Annual Meeting of Asia Pacific Region of Decision Sciences Institute,Taiwan,2005.
[17]Zhang H M.The Multiattribute Group Decision Making Method Based on Aggregation Operators with Interval-valued 2-tuple Linguistic Information[J].Mathematical and Computer Modelling,2012,56:27-35.
[18]Yager R R,Xu Z S.The Continuous Ordered Weighted Geometric Operator and Its Application to Decision Making[J].Fuzzy sets and systems,2006,157:1393-1402.
[19]Fodor J,Marichal J L,Roubens M.Characterization of the Ordered Weighted Averaging Operators[J].IEEE Transactions on Fuzzy Systems,1995,3:236-240.
[20]Xu Z.S.Dependent Uncertain Ordered Weighted Aggregation Operators[J].Information Fusion,2008,9:310-316.
[21]Wei G.W.Some Generalized Aggregating Operators With Linguistic Information And Their Application To Multiple Attribute Group Decision Making[J].Computers&Industrial Engineering,2011,61:32-38.