In this paper, we proposed the 2-tuple linguistic VIKOR method based on the fundamental theories of 2-tuple linguistic information and origin VIKOR model. Firstly, we introduce the concepts, operation formulas and the distance calculating method of 2-tuple linguistic information. Then we review some aggregation operator of 2-tuple linguistic number, thereafter, the calculating steps of the VIKOR model for 2-tuple linguistic MCGDM problems are simply presented, in our proposed method; it’s more scientific and reasonable for considering the conflicting attributes. Moreover, a numerical example for effect evaluation of ancient village landscape planning based on the heritage historical context has been proposed to illustrate the new method and some comparisons are also conducted to further illustrate advantages of the new method.
S.Opricovic and G.H.Tzeng, Compromise solution by MCDM methods: A comparative analysis of VIKOR and TOPSIS, European Journal of Operational Research156(2) (2007), 445–455.
2.
R.Benayoun, B.Roy and B.Sussman, ELECTRE: Une methode pour guider le choix en presence de points de vue multiples, Rev.franaise Informat.recherche Opérationnelle3 (1966), 31–56.
3.
B.Mareschal, J.P.Brans and P.Vincke, Promethee: A new family of outranking methods in multicriteria analysis. Ulb Institutional Repository, 1984.
4.
C.L.Hwang and K.Yoon, Multiple Attribute Decision Making. Economics and Mathematical Systems; Springer: Berlin, Germany, 1981.
5.
G.W.Wei, Extension of TOPSIS method for 2-tuple linguistic multiple attribute group decision making with incomplete weight information, Knowl Inf Syst25 (2010), 623–634.
6.
G.W.Wei, Grey relational analysis method for intuitionistic fuzzy multiple attribute decision making with preference information on alternatives, Int J Comput Intell Syst4 (2011), 164–173.
7.
G.W.Wei, Grey relational analysis model for dynamic hybrid multiple attribute decision making, Knowl Syst24 (2011), 672–679.
A.Balezentis, T.Balezentis and W.K.M. Brauers, Personnel selection based on computing with words and fuzzy MULTIMOORA, Expert Syst Appl39 (2012), 7961–7967.
10.
T.Balezentis, Group multi-criteria decision making based upon interval-valued fuzzy numbers: An extension of the MULTIMOORA method, Expert Syst Appl40 (2013), 543–550.
R.Bellman and L.A.Zadeh, Decision making in a fuzzy environment, Manag Sci17 (1970), 141–164.
13.
R.R.Yager, Multiple objective decision-making using fuzzy sets, Int JMan-Mach Stud9 (1997), 375–382.
14.
Y.Gong, N.Hu, J.Zhang, G.Liu and J.Deng, Multi-attribute group decision making method based on geometric bon-ferroni mean operator of trapezoidal interval type-2 fuzzy numbers, Comput IndEng81 (2015), 167–176.
15.
S.P.Wan, F.Wang, L.L.Lin and J.Y.Dong, Some new generalized aggregation operators for triangular intuition-istic fuzzy numbers and application to multi-attribute group decision making, Comput Ind Eng93 (2016), 286–301.
16.
F.Herrera and L.Martinez, A 2-tuple fuzzy linguistic representation model for computing with words, IEEE Trans Fuzzy Syst8 (2000), 746–752.
17.
R.R.Yager, On ordered weighted averaging aggregation operators in multicriteria decision making, IEEE Trans Syst Man Cybern18 (1988), 183–190.
18.
W.Jiang, B.Wei, Y.Tang and D.Zhou, Ordered visibility graph average aggregation operator: An application in produced water management, Chaos Interdiscip J Nonlinear Sci27 (2017), 023117.
19.
W.Jiang, B.Wei, J.Zhan, C.Xie and D.Zhou, A visibility graph power averaging aggregation operator: A methodology based on network analysis, Comput IndEng101 (2016), 260–268.
20.
H.Wang, H.Mo, R.Sadiq, Y.Hu and Y.Deng, Ordered visibility graph weighted averaging aggregation operator, Comput Ind Eng88 (2015), 181–190.
21.
C.Li, S.Zeng, T.Pan and L.Zheng, A method based on induced aggregation operators and distance measures to multiple attribute decision making under 2-tuple linguistic environment, J Comput Syst Sci80 (2014), 1339–1349.
22.
Y.Xu and H.Wang, Approaches based on 2-tuple linguistic power aggregation operators for multiple attribute group decision making under linguistic environment, Appl Soft Comput11 (2011), 3988–3997.
23.
Y.P.Jiang and Z.P.Fan, Property analysis of the aggregation operators for two-tuple linguistic information, Control Decis18 (2003), 754–757.
24.
S.Zeng, T.Balezentis and C.Zhang, A method based on owa operator and distance measures for multiple attribute decision making with 2-tuple linguistic information, Informatica4 (2012), 665–681.
25.
J.H.Wang and J.Hao, An approach to aggregation of ordinal information in multi-criteria multi-person decision making using choquet integral of fubini type, Fuzzy Optim Decis Mak8 (2009), 365–380.
26.
H.Liu, Q.Lin and J.Wu, Dependent interval 2-tuple linguistic aggregation operators and their application to multiple attribute group decision making, Int J Uncertain Fuzziness Knowl-Based Syst22 (2014), 717–735.
27.
S.Opricovic and G.-H.Tzeng, Extended VIKOR method in comparison with outranking methods, Eur J Oper Res178 (2007), 514–529.
28.
E.Cevikcan, S.Cebi and I.Kaya, Fuzzy VIKOR and Fuzzy Axiomatic Design Versus to Fuzzy Topsis: An Application of Candidate Assessment, Mul Valued Log Soft Comput15 (2009), 181–208.
29.
R.Bausys and E.K.Zavadskas, Multicriteria decision making approach by VIKOR under interval neutrosophic set environment, Economic Computation and Economic Cybernetics Studies and Research4 (2015), 33–48.
30.
J.H.Park, H.J.Cho and Y.C.Kwun, Extension of the VIKOR method for group decision making with interval-valued intu-itionistic fuzzy information, Fuzzy Optim Decis Mak10 (2011), 233–253.
31.
K.Selvakumari and Priyadharshini M. Ajitha, VIKOR method for decision making problem using octagonal neutrosophic soft matrix, International Journal of Latest Engineering Research and Applications2(7) (2017), 41–45.
32.
S.Wan, Q.Wang and J.Dong, The extended VIKOR method for multi-attribute group decision making with triangular intuitionistic fuzzy numbers, Knowl Based Syst52 (2013), 65–77.
33.
H.Liu, J.You, X.Fan and Y.Chen, Site selection in waste management by the VIKOR method using linguistic assessment, Appl Soft Comput21 (2014), 453–461.
34.
J.Qin, X.Liu and W.Pedrycz, An extended VIKOR method based on prospect theory for multiple attribute decision making under interval type-2 fuzzy environment, Knowl Based Syst86 (2015), 116–130.
35.
P.Liu and L.Zhang, The extended VIKOR method formultiple criteria decision making problem based on neutrosophic hesitant fuzzy set, 2014.
36.
H.Liao, Z.Xu and X.Zeng, Hesitant Fuzzy Linguistic VIKOR Method and Its Application in Qualitative Multiple Criteria Decision Making, IEEE Trans Fuzzy Syst23 (2015), 1343–1355.
37.
Z.Ren, Z.Xu and H.Wang, Dual hesitant fuzzy VIKOR method for multi-criteria group decision making based on fuzzy measure and new comparison method, Inf Sci388 (2017), 1–16.
38.
Z.Li, P.Liu and X.Qin, An extended VIKOR method for decision making problem with linguistic intuitionistic fuzzy numbers based on some new operational laws and entropy, JIntell Fuzzy Syst33 (2017), 1919–1931.
39.
H.Pouresmaeil, E.Shivanian, E.Khorram and H.S.Fathabadi, An extended method using TOPSIS and VIKOR for multiple attribute decision making with multiple decision makers and single valued neutrosophic numbers, Adv Appl Stat50 (2017), 261–292.
40.
Y.H.Huang, G.W.Wei and C.Wei, VIKOR Method for Interval Neutrosophic Multiple Attribute Group Decision-Making, Information8(4) (2018), 144.
41.
N.Zhang and G.Wei, Extension of VIKOR method for decision making problem based on hesitant fuzzy set, Applied Mathematical Modelling37(7) (2013), 4938–4947.
42.
S.Opricovic and G.-H.Tzeng, Compromise solution by MCDM methods: A comparative analysis of VIKOR and TOPSIS, Eur J Oper Res156 (2004), 445–455.
43.
J.Wang, G.Wei and H.Gao, Approaches to Multiple Attribute Decision Making with Interval-Valued 2-Tuple Linguistic Pythagorean Fuzzy Information, Mathematics6(10) (2018), 201.
44.
X.M.Deng, G.W.Wei, H.Gao and J.Wang, Models for safety assessment of construction project with some 2-tuple linguistic Pythagorean fuzzy Bonferroni mean operators, IEEE Access6 (2018), 52105–52137.
45.
X.Deng, J.Wang, G.Wei and M.Lu, Models for Multiple Attribute Decision Making with Some 2-Tuple Linguistic Pythagorean Fuzzy Hamy Mean Operators, Mathematics6(11) (2018), 236.
46.
M.Xia, Z.Xu and B.Zhu, Generalized intuitionistic fuzzy Bonferroni means, International Journal ofIntelligent Systems27(1) (2012), 23–47.
47.
Z.S.Xu and R.R.Yager, Intuitionistic fuzzy Bonferroni means, IEEE Transactions on Systems, Man and Cybernetics41 (2011), 568–578.
S.Wu, J.Wang, G.Wei and Y.Wei, Research on Construction Engineering Project Risk Assessment with Some 2-Tuple Linguistic Neutrosophic Hamy Mean Operators, Sustainability10(5) (2018), 1536. https://doi.org/10.3390/su10051536.
50.
R.R.Yager, On generalized Bonferroni mean operators for i-criteria aggregation, International Journal of Approximate-Reasoning50 (2009), 1279–1286.
51.
M.Xia, Z.Xu and B.Zhu, Generalized intuitionistic fuzzy Bonferroni means, International Journal of Intelligent Systems27(1) (2012), 23–47.
52.
J.Wang, G.Wei and M.Lu, TODIM Method for Multiple Attribute Group Decision Making under 2-Tuple Linguistic Neutrosophic Environment, Symmetry10(10) (2018), 486. https://doi.org/10.3390/sym10100486.
53.
Y.H.Huang and G.W.Wei, TODIM Method for Pythagorean 2-tuple Linguistic Multiple Attribute Decision Making, Journal of Intelligent and Fuzzy Systems35(1) (2018), 901–915.
54.
G.W.Wei, H.Gao, J.Wang and Y.H.Huang, Research on Risk Evaluation of Enterprise Human Capital Investment with Interval-valued bipolar 2-tuple linguistic Information, IEEE Access6 (2018), 35697–35712.
55.
J.M.Merigo and M.Casanovas, Induced aggregation operators in decision making with the Dempster-Shafer belief structure, International Journal ofIntelligent Systems24(8) (2009), 934–954.
56.
H.Gao, Pythagorean Fuzzy Hamacher Prioritized Aggregation Operators in Multiple Attribute Decision Making, Journal of Intelligent and Fuzzy Systems35(2) (2018), 2229–2245.
57.
J.Wang, G.W.Wei and Y.Wei, Models for Green Supplier Selection with Some 2-Tuple Linguistic Neutrosophic Number Bonferroni Mean Operators, Symmetry10(5) (2018), 131. doi:10.3390/sym10050131
58.
D.F.Li, Y.C.Wang, S.Liu and F.Shan, Fractional programming methodology for multi-attribute group decision making using IFS, Applied Soft Computing9 (2009), 219–225.
59.
X.Y.Tang and G.W.Wei, Models for green supplier selection in green supply chain management with Pythagorean 2-tuple linguistic information, IEEE Access6 (2018), 18042–18060.
60.
J.M.Merigo and M.Casanovas, Fuzzy Generalized Hybrid Aggregation Operators and its Application in Fuzzy Decision Making, International Journal of Fuzzzy Systems12 (2010), 15–24.
61.
G.W.Wei and H.Gao, The generalized Dice similarity measures for picture fuzzy sets and their applications, Informatica29(1) (2018), 107–124.
62.
F.E.Boran, S.Genc, M.Kurt and D.Akay, A multi-criteria intuitionistic fuzzy group decision making for supplier selection with TOPSIS method, Expert Systems with Applications36 (2009), 11363–11368.
63.
G.W.Wei, H.Gao and Y.Wei, Some q-Rung Orthopair Fuzzy Heronian Mean Operators in Multiple Attribute Decision Making, International Journal of Intelligent Systems33(7) (2018), 1426–1458.
64.
G.Wei and Y.Wei, Some single-valued neutrosophic dombi prioritized weighted aggregation operators in multiple attribute decision making, Journal of Intelligent and Fuzzy Systems35(2) (2018), 2001–2013.
65.
J.M.Merigo and M.Casanovas, Induced aggregation operators in decision making with the Dempster-Shafer belief structure, International Journal of Intelligent Systems24 (2009), 934–8.
