In this paper, we investigate the multiple attribute decision making problems for values evaluation of WTO multilateral trading system with the fuzzy number intuitionistic fuzzy information. We first introduce some operations on the fuzzy number intuitionistic fuzzy sets. Then, we further develop the induced fuzzy number intuitionistic fuzzy Hamacher ordered weighted geometric (IFNIFHOWG) operator based on the induced OWG (IOWG) operator. Then, we apply the IFNIFHOWG to deal with multiple attribute decision making with the fuzzy number intuitionistic fuzzy information. Finally an illustrative example for values evaluation of WTO multilateral trading system has been given to show the developed method.
LiD.F., Mathematical-programming approach to matrix games with payoffs represented by Atanassov’s interval-valued intuitionistic fuzzy sets, IEEE Transactions on Fuzzy Systems18 (2010), 1112–1128.
2.
WeiG.W. and WangJ.M., A comparative study of robust efficiency analysis and data envelopment analysis with imprecise data, Expert Systems with Applications81 (2017), 28–38.
3.
TangY.WenL.L.WeiG.W., Approaches to multiple attribute group decision making based on the generalized Dice similarity measures with intuitionistic fuzzy information, International Journal of Knowledge-Based and Intelligent Engineering Systems21(2) (2017), 85–95.
4.
WeiG.W.AlsaadiF.E.HayatT. and AlsaediA., Hesitant fuzzy linguistic arithmetic aggregation operators in multiple attribute decision making, Iranian Journal of Fuzzy Systems13(4) (2016), 1–16.
5.
SzmidtE. and KacprzykJ., A consensus-reaching process under intuitionistic fuzzy preference relations, International Journal of Intelligent Systems18 (2003), 837–852.
6.
LiD.F., TOPSIS-based nonlinear-programming methodology for multiattribute decision making with interval-valued intuitionistic fuzzy sets, IEEE Transactions on Fuzzy Systems18 (2010), 299–311.
7.
LiD.F., Closeness coefficient based nonlinear programming method for interval-valued intuitionistic fuzzy multiattribute decision making with incomplete preference information, Applied Soft Computing11 (2011), 3402–3418.
8.
GaoH., Pythagorean fuzzy hamacher prioritized aggregation operators in multiple attribute decision making, Journal of Intelligent and Fuzzy Systems35(2) (2018), 2229–2245.
9.
WeiG. and WeiY., Some single-valued neutrosophic dombi prioritized weighted aggregation operators in multiple attribute decision making, Journal of Intelligent and Fuzzy Systems35(2) (2018), 2001–2013.
10.
HuangY.H. and WeiG.W., TODIM method for pythagorean 2-tuple linguistic multiple attribute decision making, Journal of Intelligent and Fuzzy Systems35(1) (2018), 901–915.
11.
WeiG.W.GaoH.WangJ. and HuangY.H., Research on risk evaluation of enterprise human capital investment with interval-valued bipolar 2-tuple linguistic information, IEEE Access6 (2018), 35697–35712.
12.
WangW.Z. and LiuX.W., Intuitionistic fuzzy geometric aggregation operators based on einstein operations, International Journal of Intelligent Systems26 (2011), 1049–1075.
13.
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.
14.
WeiG.W., Interval valued hesitant fuzzy uncertain linguistic aggregation operators in multiple attribute decision making, International Journal of Machine Learning and Cybernetics7(6) (2016), 1093–1114.
15.
WuS.WangJ.WeiG. and WeiY., Research on construction engineering project risk assessment with some 2-tuple linguistic neutrosophic hamy mean operators, Sustainability10(5) (2018), 1536.
16.
WangJ.WeiG.W. and WeiY., Models for green supplier selection with some 2-tuple linguistic neutrosophic number Bonferroni mean operators, Symmetry10(5) (2018), 131.
17.
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.
18.
XiaM. and XuZ.S., Hesitant fuzzy information aggregation in decision making, International Journal of Approximate Reasoning52(3) (2011), 395–407.
19.
GaoH.WeiG.W. and HuangY.H., Dual hesitant bipolar fuzzy Hamacher prioritized aggregation operators in multiple attribute decision making, IEEE Access6(1) (2018), 11508–11522.
20.
XuZ.S. and DaQ.L., An overview of operators for aggregating information, International Journal of Intelligent System18 (2003), 953–969.
21.
WeiG.W. and ZhaoX.F., Induced hesitant interval-valued fuzzy einstein aggregation operators and their application to multiple attribute decision making, Journal of Intelligent and Fuzzy Systems24 (2013), 789–803.
22.
WeiG.W., Some induced geometric aggregation operators with intuitionistic fuzzy information and their application to group decision making, Applied Soft Computing10 (2010), 423–431.
23.
WeiG.W. and ZhaoX.F., Some induced correlated aggregating operators with intuitionistic fuzzy information and their application to multiple attribute group decision making, Expert Systems with Applications39(2) (2012), 2026–2034.
24.
LiuF. and YuanX.H., Fuzzy number intuitionistic fuzzy set, Fuzzy Systems and Mathematics21(1) (2007), 88–91.
25.
WangX.F., Fuzzy number intuitionistic fuzzy arithmetic aggregation operators, International Journal of Fuzzy Systems10(2) (2008)104–111.
26.
WangX.F., Fuzzy number intuitionistic fuzzy geometric aggregation operators and their application to decision making, Control and Decision23(6) (2008), 607–612.
27.
DeschrijverG.CornelisC. and KerreE.E., On the representation of intuitionistic fuzzy t-norms and t-conorms, IEEE Transactions on Fuzzy Systems12 (2004), 45–61.
28.
RoychowdhuryS. and WangB.H., On generalized Hamacher families of triangular operators, International Journal of Approximate Reasoning19 (1998), 419–439.
29.
DeschrijverG. and KerreE.E., A generalization of operators on intuitionistic fuzzy sets using triangular norms and conorms, Notes on intuitionistic Fuzzy Sets8 (2002), 19–27.
30.
HamacharH., Uber logische verknunpfungenn unssharfer Aussagen undderen Zugenhorige Bewertungsfunktione, in: Progress in Cybernatics and Systems ResearchTrapplR. and KlirG.J., eds, Hemisphere, Washington DC, 3, 1978, pp. 276–288.
31.
DeschrijverG. and KerreE.E., A generalization of operators on intuitionistic fuzzy sets using triangular norms and conorms, Notes on intuitionistic Fuzzy Sets8 (2002), 19–27.
32.
ZhaoX.F. and WeiG.W., Some intuitionistic fuzzy einstein hybrid aggregation operators and their application to multiple attribute decision making, Knowledge-Based Systems37 (2013), 472–479.
33.
ZhaoX.F.LiQ. and WeiG.W., Model for multiple attribute decision making based on the Einstein correlated information fusion with Hesitant fuzzy information, Journal of Intelligent and Fuzzy Systems26(6) (2014), 3057–3064.
34.
ZhaoX.F.LinR. and WeiG.W., Hesitant triangular fuzzy information aggregation based on Einstein operations and their application to multiple attribute decision making, Expert Systems with Applications41(4) (2014), 1086–1094.
35.
ZhouL.Y.ZhaoX.F. and WeiG.W., Hesitant fuzzy Hamacher aggregation operators and their application to multiple attribute decision making, Journal of Intelligent and Fuzzy Systems26(6) (2014), 2689–2699.
36.
LinR.ZhaoX.F. and WeiG.W., Fuzzy number intuitionistic fuzzy prioritized operators and their application to multiple attribute decision making, Journal of Intelligent and Fuzzy Systems24 (2013), 879–888.
37.
WangY.PengX.G. and BianJ., Study on the security of information system authentication scheme based on the fuzzy number intuitionistic fuzzy information, Journal of Intelligent and Fuzzy Systems28(5) (2015), 2225–2232.
38.
Olvera-GarcíaM.Á.Carbajal HernándezJ.J.Sánchez FernándezL.P. and Hernández-BautistaI., Air quality assessment using a weighted fuzzy inference system, Ecological Informatics33 (2016), 57–74.
39.
WeiG.W. and LuM., Pythagorean fuzzy power aggregation operators in multiple attribute decision making, International Journal of Intelligent Systems33(1) (2018), 169–186.
40.
WeiG.W., Picture fuzzy Hamacher aggregation operators and their application to multiple attribute decision making, Fundamenta Informaticae157(3) (2018), 271–320, DOI: 10.3233/FI-2018-1628.
41.
GuptaM. and MohantyB.K., An algorithmic approach to group decision making problems under fuzzy and dynamic environment, Expert Syst Appl55 (2016), 118–132.
42.
ZhaoN.XuZ. and RenZ., On typical Hesitant fuzzy prioritized “or” operator in multi-attribute decision making, Int J Intell Syst31(1) (2016), 73–100.
43.
WeiG.W., Picture uncertain linguistic Bonferroni mean operators and their application to multiple attribute decision making, Kybernetes46(10) (2017), 1777–1800.
44.
WeiG.W., Some cosine similarity measures for picture fuzzy sets and their applications to strategic decision making, Informatica28(3) (2017), 547–564.
45.
WangH. and XuZ., Admissible orders of typical hesitant fuzzy elements and their application in ordered information fusion in multi-criteria decision making, Information Fusion29 (2016), 98–104.
46.
WeiG.W. and LuM., Dual hesitant Pythagorean fuzzy Hamacher aggregation operators in multiple attribute decision making, Archives of Control Sciences27(3) (2017), 365–395.
47.
WeiG.W., Pythagorean fuzzy interaction aggregation operators and their application to multiple attribute decision making, Journal of Intelligent and Fuzzy Systems33(4) (2017), 2119–2132.
48.
GouX.XuZ. and LeiQ., New operational laws and aggregation method of intuitionistic fuzzy information, Journal of Intelligent and Fuzzy Systems30(1) (2016), 129–141.
49.
LiuH.XuZ. and LiaoH., The multiplicative consistency index of Hesitant fuzzy preference relation, IEEE Trans Fuzzy Systems24(1) (2016), 82–93.
50.
WeiG.W. and WangJ.M., A comparative study of robust efficiency analysis and data envelopment analysis with imprecise data, Expert Systems with Applications81 (2017), 28–38.
51.
WeiG.W. and GaoH., The generalized Dice similarity measures for picture fuzzy sets and their applications, Informatica29(1) (2018), 1–18.
52.
WeiG.W., Picture 2-tuple linguistic Bonferroni mean operators and their application to multiple attribute decision making, International Journal of Fuzzy System19(4) (2017), 997–1010.
53.
WeiG.W., Interval-valued dual hesitant fuzzy uncertain linguistic aggregation operators in multiple attribute decision making, Journal of Intelligent and Fuzzy Systems33(3) (2017), 1881–1893.
54.
WeiG.W.AlsaadiF.E.HayatT. and AlsaediA., A linear assignment method for multiple criteria decision analysis with hesitant fuzzy sets based on fuzzy measure, International Journal of Fuzzy Systems19(3) (2017), 607–614.
55.
NayagamV.L.G. and SivaramanG., Ranking of interval-valued intuitionistic fuzzy sets, Applied Soft Computing11 (2011), 3368–3372.
56.
WeiG.W.LuM.AlsaadiF.E.HayatT. and AlsaediA., Pythagorean 2-tuple linguistic aggregation operators in multiple attribute decision making, Journal of Intelligent and Fuzzy Systems33(2) (2017), 1129–1142.
57.
WeiG.W.AlsaadiF.E.HayatT. and AlsaediA., Hesitant bipolar fuzzy aggregation operators in multiple attribute decision making, Journal of Intelligent and Fuzzy Systems33(2) (2017), 1119–1128.
DengX.M.WeiG.W.GaoH. and WangJ., Models for safety assessment of construction project with some 2-tuple linguistic Pythagorean fuzzy Bonferroni mean operators, IEEE Access6 (2018), 52105–52137.
60.
WangJ.WeiG. and LuM., TODIM method for multiple attribute group decision making under 2-tuple linguistic neutrosophic environment, Symmetry10(10) (2018), 486.
61.
WeiG.W., Picture fuzzy aggregation operators and their application to multiple attribute decision making, Journal of Intelligent and Fuzzy Systems33(2) (2017), 713–724.
62.
MengF.Y. and ChenX.H., An approach to uncertain linguistic multi-attribute group decision making based on interactive index, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems23(3) (2015), 319–344.
63.
WangJ.WeiG. and LuM., An extended VIKOR method for multiple criteria group decision making with triangular fuzzy neutrosophic numbers, Symmetry10(10) (2018), 497.
64.
WangJ.WeiG. and GaoH., Approaches to multiple attribute decision making with interval-valued 2-tuple linguistic pythagorean fuzzy information, Mathematics6(10) (2018), 201.
65.
LinJ.ChenR.Q. and ZhangQ., Similarity-based approach for group decision making with multi-granularity linguistic information, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems24(6) (2016), 873–900.
66.
ParkD.G.KwunY.C.ParkJ.H. and ParkI.Y., Correlation coefficient of interval-valued intuitionistic fuzzy sets and its application to multiple attribute group decision making problems, Mathematical and Computer Modelling50 (2009), 1279–1293.
67.
ZhangN. and WeiG.W., Extension of VIKOR method for decision making problem based on hesitant fuzzy set, Applied Mathematical Modelling37 (2013), 4938–4947.
68.
LiZ.GaoH. and WeiG., Methods for multiple attribute group decision making based on intuitionistic fuzzy dombi hamy mean operators, Symmetry10(11) (2018), 574.
69.
DengX.WangJ.WeiG. and LuM., Models for multiple attribute decision making with some 2-tuple linguistic pythagorean fuzzy hamy mean operators, Mathematics6(11) (2018), 236.
70.
LiZ.WeiG. and GaoH., Methods for multiple attribute decision making with interval-valued pythagorean fuzzy information, Mathematics6(11) (2018), 228.
71.
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.
72.
ParkJ.H.ParkI.Y.KwunY.C. and TanX.G., Extension of the TOPSIS method for decision making problems under interval-valued intuitionistic fuzzy environment, Applied Mathematical Modelling35 (2011), 2544–2556.
