In this paper, we extend the Bonferroni mean (BM) operator, generalized Bonferroni mean (GBM), and dual generalized Bonferroni mean (DGBM) operator with interval-valued 2-tuple linguistic Pythagorean fuzzy numbers (IV2TLPFNs) to propose interval-valued 2-tuple linguistic Pythagorean fuzzy weighted Bonferroni mean (IV2TLPFWBM) operator, interval-valued 2-tuple linguistic Pythagorean fuzzy weighted geometric Bonferroni mean (IV2TLPFWGBM) operator, generalized interval-valued 2-tuple linguistic Pythagorean fuzzy weighted Bonferroni mean (GIV2TLPFWBM) operator, generalized interval-valued 2-tuple linguistic Pythagorean fuzzy weighted geometric Bonferroni mean (GIV2TLPFWGBM) operator, dual generalized interval-valued 2-tuple linguistic Pythagorean fuzzy weighted Bonferroni mean (DGIV2TLPFWBM) operator, dual generalized interval-valued 2-tuple linguistic Pythagorean fuzzy weighted geometric Bonferroni mean (DGIV2TLPFWGBM) operator. Then the MADM methods are proposed with these operators. In the end, we utilize an applicable example for green supplier selection in green supply chain management to prove the proposed methods.
YagerR.R., Pythagorean fuzzy subsets, In: Proceeding of The Joint IFSA World Congress and NAFIPS Annual Meeting, Edmonton, Canada, 2013, pp. 57–61.
2.
YagerR.R., Pythagorean membership grades in multicriteria decision making, IEEE Trans Fuzzy Syst22 (2014), 958–965.
3.
PengX. and YangY., Some results for Pythagorean Fuzzy Sets, International Journal of Intelligent systems30 (2015), 1133–1160.
4.
BeliakovG. and JamesS., Averaging aggregation functions for preferences expressed as Pythagorean membership grades and fuzzy orthopairs, FUZZ-IEEE (2014), 298–305.
5.
PengX.D. and YangY., Some results for Pythagorean fuzzy sets, Int J Intell Syst30(11) (2015), 1133–1160.
6.
WeiG.W. et al., Dual hesitant Pythagorean fuzzy hamy mean operators in multiple attribute decision making, IEEE Access7(1) (2019), 86697–86716.
7.
LuJ.P. et al., Bidirectional project method for dual hesitant Pythagorean fuzzy multiple attribute decision-making and their application to performance assessment of new rural construction, International Journal of Intelligent Systems34(8) (2019), 1920–1934.
8.
TangX.Y. and WeiG.W., Dual hesitant Pythagorean fuzzy Bonferroni mean operators in multi-attribute decision making, Archives of Control Sciences29(2) (2019), 339–386.
9.
GouX.J.XuZ.S. and RenP.J., The properties of continuous Pythagorean fuzzy information, Int J Intell Syst31(5) (2016), 401–424.
10.
TangX.Y.WeiG.W. and GaoH., Models for multiple attribute decision making with interval-valued Pythagorean fuzzy muirhead mean operators and their application to green suppliers selection, Informatica30(1) (2019), 153–186.
11.
TangX.Y. and WeiG.W., Multiple attribute decision-making with dual hesitant Pythagorean fuzzy information, Cognitive Computation11(2) (2019), 193–211.
12.
TangX.Y.WeiG.W. and GaoH., Pythagorean fuzzy muirhead mean operators in multiple attribute decision making for evaluating of emerging technology commercialization, Economic Research-Ekonomska Istraživanja32(1) (2019), 1667–1696.
13.
ZhangX.L. and XuZ.S., Extension of TOPSIS to multiple criteria decision making with Pythagorean fuzzy sets, Int J Intell Syst29 (2014), 1061–1078.
14.
YangY. et al., A note on extension of topsis to multiple criteria decision making with Pythagorean fuzzy sets, Int J Intell Syst31(1) (2016), 68–72.
15.
LiangD.C. and XuZ.S., The new extension of TOPSIS method for multiple criteria decision making with hesitant Pythagorean fuzzy sets, Appl Soft Comput60 (2017), 167–179.
16.
LiangD.C. et al., Method for three-way decisions using ideal TOPSIS solutions at Pythagorean fuzzy information, Inf Sci435 (2018), 282–295.
17.
KhanM.S.A. et al., Extension of TOPSIS method base on Choquet integral under interval-valued Pythagorean fuzzy environment, Journal of Intelligent and Fuzzy Systems34(1) (2018), 267–282.
18.
OnarS.Ç.ÖztaysiB. and KahramanC., Multicriteria evaluation of cloud service providers using Pythagorean fuzzy TOPSIS, Multiple-Valued Logic and Soft Computing30(2–3) (2018), 263–283.
19.
RenP.J.XuZ.S. and GouX.J., Pythagorean fuzzy TODIM approach to multi-criteria decision making, Appl Soft Comput42 (2016), 246–259.
20.
ZhangX.L., Multicriteria Pythagorean fuzzy decision analysis: A hierarchical QUALIFLEX approach with the closeness index-based ranking methods, Inf Sci330 (2016), 104–124.
21.
ChenT.Y., Remoteness index-based Pythagorean fuzzy VIKOR methods with a generalized distance measure for multiple criteria decision analysis, Information Fusion41 (2018), 129–150.
22.
PengX.D. and DaiJ.G., Approaches to Pythagorean fuzzy stochastic multi-criteria decision making based on prospect theory and regret theory with new distance measure and score function, Int J Intell Syst32(11) (2017), 1187–1214.
23.
XueW.T. et al., Pythagorean fuzzy LINMAP method based on the entropy theory for railway project investment decision making, Int J Intell Syst33(1) (2018), 93–125.
24.
WanS.P.JinZ. and DongJ.Y., Pythagorean fuzzy mathematical programming method for multi-attribute group decision making with Pythagorean fuzzy truth degrees, Knowl Inf Syst55(2) (2018), 437–466.
25.
GargH., A linear programming method based on an improved score function for interval-valued Pythagorean fuzzy numbers and its application to decision-making, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems26(1) (2018), 67–80.
26.
LiangD.C.XuZ.S. and DarkoA.P., Projection model for fusing the information of Pythagorean fuzzy multicriteria group decision making based on geometric bonferroni mean, Int J Intell Syst32(9) (2017), 966–987.
27.
PengX.D. and YangY., Pythagorean fuzzy choquet integral based MABAC Method for multiple attribute group decision making, Int J Intell Syst31(10) (2016), 989–1020.
28.
PengX.D.YuanH.Y. and YangY., Pythagorean fuzzy information measures and their applications, Int J Intell Syst32(10) (2017), 991–1029.
29.
PengX.D. and DaiJ.G., Approaches to Pythagorean fuzzy stochastic multi-criteria decision making based on prospect theory and regret theory with new distance measure and score function, Int J Intell Syst32(11) (2017), 1187–1214.
30.
QinY.LiuY. and HongZ.Y., Multicriteria decision making method based on generalized Pythagorean fuzzy ordered weighted distance measures, Journal of Intelligent and Fuzzy Systems33(6) (2017), 3665–3675.
31.
WeiG.W. and WeiY., Similarity measures of Pythagorean fuzzy sets based on the cosine function and their applications, International Journal of Intelligent Systems33(3) (2018), 634–652.
32.
WangJ.GaoH. and WeiG.W., The generalized Dice similarity measures for Pythagorean fuzzy multiple attribute group decision making, International Journal of Intelligent Systems34(6) (2019), 1158–1183.
33.
ZhangX.L., A novel approach based on similarity measure for Pythagorean fuzzy multiple criteria group decision making, International Journal of Intelligent Systems31(6) (2016), 593–611.
34.
GargH., A novel correlation coefficients between Pythagorean fuzzy sets and its applications to decision-making processes, International Journal of Intelligent Systems31(12) (2016), 1234–1252.
35.
MaZ.M. and XuZ.S., Symmetric Pythagorean fuzzy weighted geometric/averaging operators and their application in multicriteria decision-making problems, International Journal of Intelligent Systems31(12) (2016), 1198–1219.
36.
PengX.D. and YangY., Fundamental properties of interval-valued Pythagorean fuzzy aggregation operators, Int J Intell Syst31(5) (2016), 444–487.
37.
PengX.D. and YuanH.Y., Fundamental properties of Pythagorean fuzzy aggregation operators, Fundam Inform147(4) (2016), 415–446.
38.
RahmanK. et al., Pythagorean fuzzy Einstein weighted geometric aggregation operator and their application to multiple attribute group decision making, Journal of Intelligent and Fuzzy Systems33(1) (2017), 635–647.
39.
WeiG.W., Pythagorean fuzzy hamacher power aggregation operators in multiple attribute decision making, Fundamenta Informaticae166(1) (2019), 57–85.
40.
WeiG.W. and LuM., Pythagorean fuzzy maclaurin symmetric mean operators in multiple attribute decision making, International Journal of Intelligent Systems33(5) (2018), 1043–1070.
41.
WangJ. et al., Dual hesitant q-Rung orthopair fuzzy muirhead mean operators in multiple attribute decision making, IEEE Access7(1) (2019), 67139–67166.
42.
ZengS.Z.MuZ.M. and BalezentisT., A novel aggregation method for Pythagorean fuzzy multiple attribute group decision making, Int J Intell Syst33(3) (2018), 573–585.
43.
WangJ. et al., Methods for multiple-attribute group decision making with q-rung interval-valued orthopair fuzzy information and their applications to the selection of green suppliers, Symmetry11(1) (2019), 56.
44.
MohagheghiV.MousaviS.M. and VahdaniB., Enhancing decision-making flexibility by introducing a new last aggregation evaluating approach based on multi-criteria group decision making and Pythagorean fuzzy sets, Appl Soft Comput61 (2017), 527–535.
45.
GargH., Confidence levels based Pythagorean fuzzy aggregation operators and its application to decision-making process, Computational & Mathematical Organization Theory23(4) (2017), 546–571.
46.
GargH., Generalized Pythagorean fuzzy geometric aggregation operators using einstein t-Norm and t-Conorm for multicriteria decision-making process, Int J Intell Syst32(6) (2017), 597–630.
47.
TangM. et al., Dual hesitant pythagorean fuzzy heronian mean operators in multiple attribute decision making, Mathematics7(4) (2019), 344.
48.
LiangD.C. et al., Pythagorean fuzzy Bonferroni mean aggregation operator and its accelerative calculating algorithm with the multithreading, Int J Intell Syst33(3) (2018), 615–633.
49.
LiZ.WeiG. and LuM., Pythagorean fuzzy hamy mean operators in multiple attribute group decision making and their application to supplier selection, Symmetry10(10) (2018), 505.
50.
GargH., New exponential operational laws and their aggregation operators for interval-valued Pythagorean fuzzy multicriteria decision-making, Int J Intell Syst33(3) (2018), 653–683.
51.
GargH., Some methods for strategic decision-making problems with immediate probabilities in Pythagorean fuzzy environment, Int J Intell Syst33(4) (2018), 687–712.
52.
GargH., A novel improved accuracy function for interval valued Pythagorean fuzzy sets and its applications in the decision-making process, Int J Intell Syst32(12) (2017), 1247–1260.
53.
TangX.Y.HuangY.H. and WeiG.W., Approaches to multiple-attribute decision-making based on Pythagorean 2-tuple linguistic bonferroni mean operators, Algorithms11(1) (2018),5.
54.
TangX.Y. and WeiG.W., Models for green supplier selection in green supply chain management with Pythagorean 2-tuple linguistic information, IEEE Access6 (2018), 18042–18060.
55.
GaoH. and WeiG.W., Multiple attribute decision making based on interval-valued Pythagorean uncertain linguistic aggregation operators, International Journal of Knowledge-based and Intelligent Engineering Systems22(1) (2018), 59–81.
56.
WeiG.W. et al., Pythagorean 2-tuple linguistic aggregation operators in multiple attribute decision making, Journal of Intelligent and Fuzzy Systems33(2) (2017), 1129–1142.
57.
WeiG.W.GaoH. and WeiY., Some q-Rung orthopair fuzzy heronian mean operators in multiple attribute decision making, International Journal of Intelligent Systems33(7) (2018), 1426–1458.
58.
LuM. et al., Ahmed alsaedi, hesitant Pythagorean fuzzy hamacher aggregation operators and their application to multiple attribute decision making, Journal of Intelligent and Fuzzy Systems33(2) (2017), 1105–1117.
59.
WeiG.W. et al., Pythagorean Hesitant Fuzzy Hamacher Aggregation Operators and Their Application to Multiple Attribute Decision Making, International Journal of Intelligent Systems33(6) (2018), 1197–1233.
60.
DengX. et al., Models for multiple attribute decision making with some 2-tuple linguistic Pythagorean fuzzy hamy mean operators, Mathematics6(11) (2018), 236.
61.
DengX.M.WangJ. and WeiG.W., Some 2-tuple linguistic Pythagorean Heronian mean operators and their application to multiple attribute decision making, Journal of Experimental & Theoretical Artificial Intelligence31(4) (2019), 555–574.
62.
DengM. and GaoH., TODIM method for multiple attribute decision making with 2-tuple linguistic Pythagorean fuzzy information, Journal of Intelligent and Fuzzy Systems (2019), 1–12.
63.
WangJ.WeiG. and GaoH., Approaches to multiple attribute decision making with interval-valued 2-tuple linguistic Pythagorean fuzzy information, Mathematics6(10) (2018), 201.
64.
BonferroniC., Sulle medie multiple di potenze, Bolletino Matematica Italiana5 (1950), 267–270.
65.
BeliakovG. et al., Generalized Bonferroni mean operators in multicriteria aggregation, Fuzzy Sets and Systems161 (2010), 2227–2242.
66.
WeiG.W., The generalized dice similarity measures for multiple attribute decision making with hesitant fuzzy linguistic information, Economic Research-Ekonomska Istraživanja32(1) (2019), 1498–1520.
67.
ZhuB.XuZ.S. and XiaM.M., Hesitant fuzzy geometric Bonferroni means, Information sciences205 (2012), 72–85.
68.
ZhangR.T. et al., Some generalized Pythagorean fuzzy bonferroni mean aggregation operators with their application to multiattribute group decision-making, Complexity2017 (2017), 1–16.
69.
MohagheghiV.MousaviS.M. and VahdaniB., Enhancing decision-making flexibility by introducing a new last aggregation evaluating approach based on multi-criteria group decision making and Pythagorean fuzzy sets, Appl Soft Comput61 (2017), 527–535.
70.
WuL.P.WangJ. and GaoH., Models for competiveness evaluation of tourist destination with some interval-valued intuitionistic fuzzy Hamy mean operators, Journal of Intelligent and Fuzzy Systems36(6) (2019), 5693–5709.
71.
HaoY.H. and ChenX.G., Study on the ranking problems in multiple attribute decision making based on interval-valued intuitionistic fuzzy numbers, Int J Intell Syst33(3) (2018), 560–572.
72.
GaoH., Pythagorean fuzzy hamacher prioritized aggregation operators in multiple attribute decision making, Journal of Intelligent and Fuzzy Systems35(2) (2018), 2229–2245.
73.
BalogluU.B. and DemirY., An agent-based Pythagorean fuzzy approach for demand analysis with incomplete information, Int J Intell Syst33(5) (2018), 983–997.
74.
WeiY. et al., Oil price fluctuation, stock market and macroeconomic fundamentals: Evidence from China before and after the financial crisis, Finance Research Letters30 (2019), 23–29.
75.
WeiY. et al., Hot money and China’s stock market volatility: Further evidence using the GARCH-MIDAS model, Physica A: Statistical Mechanics and its Applications492 (2018), 923–930.
76.
WuL. et al., Some interval-valued intuitionistic fuzzy dombi hamy mean operators and their application for evaluating the elderly tourism service quality in tourism destination, Mathematics6(12) (2018), 294.
