基于三角Pythagorean模糊集的多准则决策方法
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摘要
Pythagorean模糊集在直觉模糊集的基础上扩大了适用范围,三角模糊数在决策过程中可以保留决策者较多的不确定信息.鉴于此,首先提出三角Pythagorean模糊集的定义及其欧氏距离表示;然后定义三角Pythagorean模糊加权平均(TPFWA)算子、广义三角Pythagorean模糊加权平均(GTPFWA)算子、三角Pythagorean模糊加权几何(TPFWG)算子和广义三角Pythagorean模糊加权几何(GTPFWG)算子,并对算子所满足的幂等性、有界性和单调性予以证明;最后通过一个医药代表选择的多准则决策问题和灵敏度分析验证所提出算子的合理性和有效性.
Pythagorean fuzzy sets expand the range of application based on intuitionistic fuzzy sets, triangular fuzzy number reserves more uncertain information in the decision making process. Firstly, a triangular Pythagorean fuzzy set and Euclidean distance are defined. Then, triangular Pythagorean fuzzy weighted averaging(TPFWA), generalized triangular Pythagorean fuzzy weighted averaging(GTPFWA), triangular Pythagorean fuzzy weighted geometric(TPFWG) and generalized triangular Pythagorean fuzzy weighted geometric(GTPFWG) operators are defined, and correlative idempotency, boundedness and monotonity are proved. Finally the reasonableness and validity are verified by a multicriteria decision making about medical representative selection and sensitivity analysis.
Pythagorean fuzzy sets expand the range of application based on intuitionistic fuzzy sets, triangular fuzzy number reserves more uncertain information in the decision making process. Firstly, a triangular Pythagorean fuzzy set and Euclidean distance are defined. Then, triangular Pythagorean fuzzy weighted averaging(TPFWA), generalized triangular Pythagorean fuzzy weighted averaging(GTPFWA), triangular Pythagorean fuzzy weighted geometric(TPFWG) and generalized triangular Pythagorean fuzzy weighted geometric(GTPFWG) operators are defined, and correlative idempotency, boundedness and monotonity are proved. Finally the reasonableness and validity are verified by a multicriteria decision making about medical representative selection and sensitivity analysis.
引文
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[28]Biswas P,Pramanik S,Giri B C.Aggregation of triangular fuzzy neutrosophic set information and its application to multi-attribute decision making[J].Neutrosophic Sets and Systems,2016,12:20-40.
[2]Atanassov K T.Intuitionistic fuzzy sets[J].Fuzzy Sets&Systems,1986,20(1):87-96.
[3]Torra V.Hesitant fuzzy sets[J].Int J of Intelligent Systems,2010,25(6):529-539.
[4]Yager R R.Pythagorean membership grades in multicriteria decision making[J].IEEE Trans on Fuzzy Systems,2014,22(4):958-965.
[5]Yager R R,Abbasov A M.Pythagorean membership grades,complex numbers,and decision making[J].Int J of Intelligent Systems,2013,28(5):436-452.
[6]Zhang X,Xu Z.Extension of TOPSIS to multiple criteria decision making with pythagorean fuzzy sets[J].Int J of Intelligent Systems,2014,29(15):1061-1078.
[7]Garg H.A novel accuracy function under interval-valued Pythagorean fuzzy environment for solving multicriteria decision making problem[J].J of Intelligent&Fuzzy Systems,2016,31(1):529-540.
[8]Garg H.A novel correlation coefficients between pythagorean fuzzy sets and its applications to decisionmaking processes[J].Int J of Intelligent Systems,2016,31(12):1234-1252.
[9]Ren P,Xu Z,Gou X.Pythagorean fuzzy TODIMapproach to multi-criteria decision making[J].Applied Soft Computing,2016,42:246-259.
[10]刘卫锋,常娟,何霞.广义毕达哥拉斯模糊集成算子及其决策应用[J].控制与决策,2016,31(12):2280-2286.(Liu W F,Chang J,He X.Generalized Pythagorean fuzzy aggregation operators and applications in decision making[J].Control and Decision,2016,31(12):2280-2286.)
[11]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 W F,Du Y X,Chang J.Pythagorean fuzzy interaction aggregation operators and applications in decision making[J].Control and Decision,2017,32(6):1033-1040.)
[12]Zhang X.A novel approach based on similarity measure for pythagorean fuzzy multiple criteria group decision making[J].Int J of Intelligent Systems,2016,31(6):593-611.
[13]Rajkuma A,Devadoss A V.A study on miracles through the holy bible using new triangular neutrosophic cognitive maps(TrNCMs)[J].Int J of Computer Application,2014,4(4):152-160.
[14]Sujit Kumar De,Ismat Beg.Triangular dense fuzzy neutrosophic sets[J].Neutrosophic Sets and Systems,2016,13:24-37.
[15]Esmailzadeh M,Esmailzadeh M.New distance between triangular intuitionistic fuzzy numbers[J].Advances in Computational Mathematics&Its Applications,2013,2(3):310-314.
[16]Nan Jiangxia,Li Dengfeng,Zhang Maojun.Alexicographic method for matrix games with payoffs of triangular intuitionistic fuzzy numbers[J].Int Jof Computational Intelligence Systems,2010,3(3):280-289.
[17]Li D F.A ratio ranking method of triangular intuitionistic fuzzy numbers and its application to MADM problems[J].Computers&Mathematics with Applications,2010,60(6):1557-1570.
[18]Li Dengfeng,Nan Jiangxia,Zhang Maojun.A ranking method of triangular intuitionistic fuzzy numbers and application to decision making[J].Int J of Computational Intelligence Systems,2010,3(5):522-530.
[19]Dubois D,Foulloy L,Mauris G,et al.Probability-possibility transformations,triangular fuzzy sets,and probabilistic inequalities[J].Reliable Computing,2004,10(4):273-297.
[20]Meng F,Lin J,Tan C,et al.A new multiplicative consistency based method for decision making with triangular fuzzy reciprocal preference relations[J].Fuzzy Sets&Systems,2016,315:1-25.
[21]Zamri N,Abdullah L,Hitam M S,et al.A novel hybrid fuzzy weighted average for MCDM with interval,triangular type-2 fuzzy sets[J].Wseas Trans on Systems,2013,12(4):212-228.
[22]Yong S Y,Sang U,Jin W Park.The generalized triangular fuzzy sets[J].J of the Chungcheong Mathematical Society,2009,22(2):161-170.
[23]Wang J Q,Nie R,Zhang H Y,et al.New operators on triangular intuitionistic fuzzy numbers and their applications in system fault analysis[J].Information Sciences,2013,251(12):79-95.
[24]Sankar P,Mondal S,Roy T K.Non-linear arithmetic operation on generalized triangular intuitionistic fuzzy numbers[J].Notes on Intuitionistic Fuzzy Sets,2014,20:9-19.
[25]Yu D.Triangular hesitant fuzzy set and its application to teaching quality evaluation[J].J of Information&Computational Science,2013,10(7):1925-1934.
[26]Yu D.Prioritized information fusion method for triangular intuitionistic fuzzy set and its application to teaching quality evaluation[J].Int J of Intelligent Systems,2013,28(5):411-435.
[27]Zhang X,Liu Peide.Method for aggregating triangular fuzzy intuitionistic fuzzy information and its application to decision making[J].Ukio Technologinis Ir Ekonominis Vystymas,2010,16(2):280-290.
[28]Biswas P,Pramanik S,Giri B C.Aggregation of triangular fuzzy neutrosophic set information and its application to multi-attribute decision making[J].Neutrosophic Sets and Systems,2016,12:20-40.