基于毕达哥拉斯模糊Frank算子的多属性决策方法
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摘要
针对毕达哥拉斯模糊环境下的多属性决策问题,提出一种基于毕达哥拉斯模糊Frank算子的多属性决策方法。首先将毕达哥拉斯模糊数和Frank算子相结合,给出了基于Frank算子的运算法则;然后提出了毕达哥拉斯模糊Frank算子,包括毕达哥拉斯模糊Frank加权平均算子和毕达哥拉斯模糊Frank加权几何算子,并讨论了这些算子的性质;最后提出了基于毕达哥拉斯模糊Frank算子的多属性决策方法,将该方法应用于绿色供应商的选择中。实例分析表明,运用该方法可以解决实际的多属性决策问题,并可以进一步应用到风险管理、人工智能等领域。
To solve the multi-attribute decision making problems in Pythagorean fuzzy environment,a multi-attribute decision making method based on Pythagorean fuzzy Frank operator was proposed.Firstly,Pythagorean fuzzy number and Frank operator were combined to obtain the operation rule based on Frank operator.Then the Pythagorean fuzzy Frank operator was proposed,including Pythagorean fuzzy Frank weighted average operator and Pythagorean fuzzy Frank weighted geometric operator,and the properties of these operators were discussed.Finally,a multi-attribute decision making method based on Pythagorean fuzzy Frank operator was proposed,which was applied to an example of green supplier selection.The example analysis shows that the proposed method can be used to solve the actual multi-attribute decision making problems,and can be further applied to areas such as risk management and artificial intelligence.
To solve the multi-attribute decision making problems in Pythagorean fuzzy environment,a multi-attribute decision making method based on Pythagorean fuzzy Frank operator was proposed.Firstly,Pythagorean fuzzy number and Frank operator were combined to obtain the operation rule based on Frank operator.Then the Pythagorean fuzzy Frank operator was proposed,including Pythagorean fuzzy Frank weighted average operator and Pythagorean fuzzy Frank weighted geometric operator,and the properties of these operators were discussed.Finally,a multi-attribute decision making method based on Pythagorean fuzzy Frank operator was proposed,which was applied to an example of green supplier selection.The example analysis shows that the proposed method can be used to solve the actual multi-attribute decision making problems,and can be further applied to areas such as risk management and artificial intelligence.
引文
[1]ZADEH L A.Fuzzy sets[J].Information and Control,1965,8(3):338-353.
[2]TURKSEN I B.Interval valued fuzzy sets based on normal forms[J].Fuzzy Sets and Systems,1986,20(2):191-210.
[3]TORRA V,NARUKAWA Y.On hesitant fuzzy sets and decision[C]//Proceedings of the 2009 IEEE International Conference on Fuzzy Systems.Piscataway,NJ:IEEE,2009:1378-1382.
[4]ATANASSOV K T.Intuitionistic fuzzy sets[J].Fuzzy Sets and Systems,1986,20(1):87-96.
[5]ATANASSOV K T,GARGOV g.Interval valued intuitionistic fuzzy sets[J].Fuzzy Sets and Systems,1989,31(3):343-349.
[6]YAGER R R.Pythagorean membership grades in multi-criteria decision making[J].IEEE Transactions on Fuzzy Systems,2014,22(4):958-965.
[7]WEI G,LU M.Pythagorean fuzzy power aggregation operators in multiple attribute decision making[J].International Journal of Intelligent Systems,2018,33(1):169-186.
[8]ZHANG R,WANG J,ZHU X,et al.Some generalized Pythagorean fuzzy Bonferroni mean aggregation operators with their application to multi-attribute group decision-making[J].Complexity,2017,2017(6):1-16.
[9]刘卫锋,杜迎雪,常娟.毕达哥拉斯模糊交叉影响集成算子及其决策应用[J].控制与决策,2017,32(6):1033-1040.(LIU WF,DU Y X,CHANG J.Pythagorean fuzzy interaction aggregation operators and applications in decision making[J].Control&Decision,2017,32(6):1033-1040.
[10]GARG H.A new generalized Pythagorean fuzzy information aggregation using Einstein operations and its application to decision making[J].International Journal of Intelligent Systems,2016,31(9):886-920.
[11]WEI G,LU M,TANG X,et al.Pythagorean hesitant fuzzy Hamacher aggregation operators and their application to multiple attribute decision making[J].International Journal of Intelligent Systems,2018,97(3):24-39.
[12]DESCHRIJVER G.Generalized arithmetic operators and their relationship to T-norms in interval-valued fuzzy set theory[J].Fuzzy Sets and Systems,2009,160(21):3080-3102.
[13]YAGER R R.On some new classes of implication operators and their role in approximate reasoning[J].Information Sciences,2004,167(1/2/3/4):193-216.
[14]QIN J,LIU X,PEDRYCZ W.Frank aggregation operators and their application to hesitant fuzzy multiple attribute decision making[J].Applied Soft Computing,2016,41:428-452.
[15]PENG H-G,WANG J-Q,CHENG P-F.A linguistic intuitionistic multi-criteria decision-making method based on the Frank Heronian mean operator and its application in evaluating coal mine safety[J].International Journal of Machine Learning&Cybernetics,2018,9(6):1053-1068.
[16]ZHANG Z.Interval-valued intuitionistic fuzzy Frank aggregation operators and their applications to multiple attribute group decision making[J].Neural Computing&Applications,2017,28(6):1471-1501.
[17]PENG X,YANG Y.Some results for Pythagorean fuzzy sets[J].International Journal of Intelligent Systems,2015,30(11):1133-1160.
[18]XIA M,XU Z,ZHU B.Some issues on intuitionistic fuzzy aggregation operators based on Archimedean T-conorm and T-norm[J].Knowledge-Based Systems,2012,31:78-88.
[19]WANG W,LIU X.Intuitionistic fuzzy information aggregation using Einstein Operations[J].IEEE Transactions on Fuzzy Systems,2012,20(5):923-938.
[20]DESCHRIJVER G,KERRE E E.Uninorms in L*-fuzzy set theory[J].Fuzzy Sets&Systems,2004,148(2):243-262.
[21]LIU P.Some Hamacher Aggregation operators based on the interval-valued intuitionistic fuzzy numbers and their application to group decision making[J].IEEE Transactions on Fuzzy Systems,2014,22(1):83-97.
[22]KANNAN D,GOVINDAN K,RAJENDRAN S.Fuzzy axiomatic design approach based green supplier selection:a case study from Singapore[J].Journal of Cleaner Production,2015,96:194-208.
[23]KUO R J,WANG Y C,TIEN F C.Integration of artificial neural network and MADA methods for green supplier selection[J].Journal of Cleaner Production,2010,18(12):1161-1170.
[24]罗新星,彭素华.绿色供应链中基于AHP和TOPSIS的供应商评价与选择研究[J].软科学,2011,25(2):53-56.(LUOX X,PENG S H.Research on the vendor evaluation and selection based on the AHP and TOPSIS in green supply chain[J].Soft Science,2011,25(2):53-56.)
[2]TURKSEN I B.Interval valued fuzzy sets based on normal forms[J].Fuzzy Sets and Systems,1986,20(2):191-210.
[3]TORRA V,NARUKAWA Y.On hesitant fuzzy sets and decision[C]//Proceedings of the 2009 IEEE International Conference on Fuzzy Systems.Piscataway,NJ:IEEE,2009:1378-1382.
[4]ATANASSOV K T.Intuitionistic fuzzy sets[J].Fuzzy Sets and Systems,1986,20(1):87-96.
[5]ATANASSOV K T,GARGOV g.Interval valued intuitionistic fuzzy sets[J].Fuzzy Sets and Systems,1989,31(3):343-349.
[6]YAGER R R.Pythagorean membership grades in multi-criteria decision making[J].IEEE Transactions on Fuzzy Systems,2014,22(4):958-965.
[7]WEI G,LU M.Pythagorean fuzzy power aggregation operators in multiple attribute decision making[J].International Journal of Intelligent Systems,2018,33(1):169-186.
[8]ZHANG R,WANG J,ZHU X,et al.Some generalized Pythagorean fuzzy Bonferroni mean aggregation operators with their application to multi-attribute group decision-making[J].Complexity,2017,2017(6):1-16.
[9]刘卫锋,杜迎雪,常娟.毕达哥拉斯模糊交叉影响集成算子及其决策应用[J].控制与决策,2017,32(6):1033-1040.(LIU WF,DU Y X,CHANG J.Pythagorean fuzzy interaction aggregation operators and applications in decision making[J].Control&Decision,2017,32(6):1033-1040.
[10]GARG H.A new generalized Pythagorean fuzzy information aggregation using Einstein operations and its application to decision making[J].International Journal of Intelligent Systems,2016,31(9):886-920.
[11]WEI G,LU M,TANG X,et al.Pythagorean hesitant fuzzy Hamacher aggregation operators and their application to multiple attribute decision making[J].International Journal of Intelligent Systems,2018,97(3):24-39.
[12]DESCHRIJVER G.Generalized arithmetic operators and their relationship to T-norms in interval-valued fuzzy set theory[J].Fuzzy Sets and Systems,2009,160(21):3080-3102.
[13]YAGER R R.On some new classes of implication operators and their role in approximate reasoning[J].Information Sciences,2004,167(1/2/3/4):193-216.
[14]QIN J,LIU X,PEDRYCZ W.Frank aggregation operators and their application to hesitant fuzzy multiple attribute decision making[J].Applied Soft Computing,2016,41:428-452.
[15]PENG H-G,WANG J-Q,CHENG P-F.A linguistic intuitionistic multi-criteria decision-making method based on the Frank Heronian mean operator and its application in evaluating coal mine safety[J].International Journal of Machine Learning&Cybernetics,2018,9(6):1053-1068.
[16]ZHANG Z.Interval-valued intuitionistic fuzzy Frank aggregation operators and their applications to multiple attribute group decision making[J].Neural Computing&Applications,2017,28(6):1471-1501.
[17]PENG X,YANG Y.Some results for Pythagorean fuzzy sets[J].International Journal of Intelligent Systems,2015,30(11):1133-1160.
[18]XIA M,XU Z,ZHU B.Some issues on intuitionistic fuzzy aggregation operators based on Archimedean T-conorm and T-norm[J].Knowledge-Based Systems,2012,31:78-88.
[19]WANG W,LIU X.Intuitionistic fuzzy information aggregation using Einstein Operations[J].IEEE Transactions on Fuzzy Systems,2012,20(5):923-938.
[20]DESCHRIJVER G,KERRE E E.Uninorms in L*-fuzzy set theory[J].Fuzzy Sets&Systems,2004,148(2):243-262.
[21]LIU P.Some Hamacher Aggregation operators based on the interval-valued intuitionistic fuzzy numbers and their application to group decision making[J].IEEE Transactions on Fuzzy Systems,2014,22(1):83-97.
[22]KANNAN D,GOVINDAN K,RAJENDRAN S.Fuzzy axiomatic design approach based green supplier selection:a case study from Singapore[J].Journal of Cleaner Production,2015,96:194-208.
[23]KUO R J,WANG Y C,TIEN F C.Integration of artificial neural network and MADA methods for green supplier selection[J].Journal of Cleaner Production,2010,18(12):1161-1170.
[24]罗新星,彭素华.绿色供应链中基于AHP和TOPSIS的供应商评价与选择研究[J].软科学,2011,25(2):53-56.(LUOX X,PENG S H.Research on the vendor evaluation and selection based on the AHP and TOPSIS in green supply chain[J].Soft Science,2011,25(2):53-56.)