毕达哥拉斯不确定语言Maclaurin对称集成算子及其在多属性决策中的应用
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摘要
毕达哥拉斯不确定语言变量是直觉不确定语言变量的拓展和一般化.针对毕达哥拉斯不确定语言变量的集成问题,首先结合语言刻度函数,提出新的毕达哥拉斯不确定语言变量运算法则和排序方法,克服已有运算存在的缺少封闭性和灵活性的不足.进而,提出了捕获多元关联关系的毕达哥拉斯不确定语言Maclaurin对称集成算子(PULMSM)及其加权形式(PULWMSM),并探讨其优良性质和特例.最后,提出一种基于PULWMSM的毕达哥拉斯不确定语言多属性决策方法,并通过实例来分析其合理性和有效性.
Pythagorean uncertain linguistic variables are the extension and generalization of intuitionistic uncertain linguistic variables.In order to aggregate Pythagorean uncertain linguistic variables,some new operational laws and comparison method of the Pythagorean uncertain linguistic variables are proposed by combining with linguistic scale function,which overcomes the shortcomings of closeness and flexibility in existing operations.Furthermore,the Pythagorean uncertain linguistic Maclaurin symmetric mean operator(PULMSM)and its weighted form(PULWMSM)are proposed to aggregate Pythagorean uncertain linguistic variables,which can model the interrelationship among multi-inputs.Meanwhile,some of desirable properties and special cases are discussed.Finally,a Pythagorean uncertain linguistic multi-attribute decision making method is proposed based on the proposed PULMSM operator,then an illustrative example is conducted to show the rationality and effectiveness.
Pythagorean uncertain linguistic variables are the extension and generalization of intuitionistic uncertain linguistic variables.In order to aggregate Pythagorean uncertain linguistic variables,some new operational laws and comparison method of the Pythagorean uncertain linguistic variables are proposed by combining with linguistic scale function,which overcomes the shortcomings of closeness and flexibility in existing operations.Furthermore,the Pythagorean uncertain linguistic Maclaurin symmetric mean operator(PULMSM)and its weighted form(PULWMSM)are proposed to aggregate Pythagorean uncertain linguistic variables,which can model the interrelationship among multi-inputs.Meanwhile,some of desirable properties and special cases are discussed.Finally,a Pythagorean uncertain linguistic multi-attribute decision making method is proposed based on the proposed PULMSM operator,then an illustrative example is conducted to show the rationality and effectiveness.
引文
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[3]刘培德,张新.直觉不确定语言集成算子及在群决策中的应用[J].系统工程理论与实践,2012,32(12):2704-2711.
[4]Xu Z,Yager R R,Some geometric aggregation operators based on intuitionistic fuzzy sets[J].nternational journal of general systems,2006,35(4):417-433.
[5]Yager R R.Pythagorean membership grades in multicriteria decision making[J].IEEE Transactions on Fuzzy Systems,2014,22(4):958-965.
[6]刘政敏,刘培德,刘位龙.基于Pythagorean不确定语言的扩展VIKOR多属性群决策方法[J].控制与决策,2017,32(12):2145-2152.
[7]王坚强,李寒波.基于直觉语言集结算子的多准则决策方法[J].控制与决策,2010,25(10):1571-1574.
[8]Xu Z S.Uncertain linguistic aggregation operators based approach to multiple attribute group decision making under uncertain linguistic environment[J].Information Sciences,2004,168(1):171-184.
[9]Lu M,Wei G W.Pythagorean uncertain linguistic aggregation operators for multiple attribute decision making[J].International Journal of Knowledge-based and Intelligent Engineering Systems,2017,21(3):165-179.
[10]Liu Z,Liu P,Liu W,et al.Pythagorean uncertain linguistic partitioned Bonferroni mean operators and their application in multi-attribute decision making[J].Journal of Intelligent&Fuzzy Systems,2017,32(3):2779-2790.
[11]Wang J,Wu J,Wang J,et al.Interval-valued hesitant fuzzy linguistic sets and their applications in multi-criteria decision-making problems[J].Information Sciences,2014,288:55-72.
[12]Zhang X,Xu Z.Extension of TOPSIS to multiple criteria decision making with Pythagorean fuzzy sets[J].International Journal of Intelligent Systems,2014,29(12):1061-1078.
[13]Xu Z.A method based on linguistic aggregation operators for group decision making with linguistic preference relations[J].Information sciences,2004,166(1-4):19-30.
[14]Maclaurin C.A second letter to Martin Folkes Esq concerning the roots of equations,with the demonstartion of other rules in algebra[J],Phil.Transactions,1970(36):59-96.
[15]Yager R R.On generalized Bonferroni mean operators for multi-criteria aggregation[J].International Journal of Approximate Reasoning,2009,50(8):1279-1286.
[16]Beliakov G,Pradera A,Calvo T.Aggregation Functions:A Guide for Practitioners[M].Heidelberg:Springer,2007.
[2]Atanassov K[T],Gargov G.Interval valued intuitionistic fuzzy sets[J].Fuzzy sets and systems,1989,31(3):343-349.
[3]刘培德,张新.直觉不确定语言集成算子及在群决策中的应用[J].系统工程理论与实践,2012,32(12):2704-2711.
[4]Xu Z,Yager R R,Some geometric aggregation operators based on intuitionistic fuzzy sets[J].nternational journal of general systems,2006,35(4):417-433.
[5]Yager R R.Pythagorean membership grades in multicriteria decision making[J].IEEE Transactions on Fuzzy Systems,2014,22(4):958-965.
[6]刘政敏,刘培德,刘位龙.基于Pythagorean不确定语言的扩展VIKOR多属性群决策方法[J].控制与决策,2017,32(12):2145-2152.
[7]王坚强,李寒波.基于直觉语言集结算子的多准则决策方法[J].控制与决策,2010,25(10):1571-1574.
[8]Xu Z S.Uncertain linguistic aggregation operators based approach to multiple attribute group decision making under uncertain linguistic environment[J].Information Sciences,2004,168(1):171-184.
[9]Lu M,Wei G W.Pythagorean uncertain linguistic aggregation operators for multiple attribute decision making[J].International Journal of Knowledge-based and Intelligent Engineering Systems,2017,21(3):165-179.
[10]Liu Z,Liu P,Liu W,et al.Pythagorean uncertain linguistic partitioned Bonferroni mean operators and their application in multi-attribute decision making[J].Journal of Intelligent&Fuzzy Systems,2017,32(3):2779-2790.
[11]Wang J,Wu J,Wang J,et al.Interval-valued hesitant fuzzy linguistic sets and their applications in multi-criteria decision-making problems[J].Information Sciences,2014,288:55-72.
[12]Zhang X,Xu Z.Extension of TOPSIS to multiple criteria decision making with Pythagorean fuzzy sets[J].International Journal of Intelligent Systems,2014,29(12):1061-1078.
[13]Xu Z.A method based on linguistic aggregation operators for group decision making with linguistic preference relations[J].Information sciences,2004,166(1-4):19-30.
[14]Maclaurin C.A second letter to Martin Folkes Esq concerning the roots of equations,with the demonstartion of other rules in algebra[J],Phil.Transactions,1970(36):59-96.
[15]Yager R R.On generalized Bonferroni mean operators for multi-criteria aggregation[J].International Journal of Approximate Reasoning,2009,50(8):1279-1286.
[16]Beliakov G,Pradera A,Calvo T.Aggregation Functions:A Guide for Practitioners[M].Heidelberg:Springer,2007.