|
|
An overview on the applications of the hesitant fuzzy sets in group decision-making: theory, support and methods |
Zeshui XU(), Shen ZHANG |
Business School, Sichuan University, Chengdu 610064, China |
|
|
Abstract Due to the characteristics of hesitant fuzzy sets (HFSs), one hesitant fuzzy element (HFE), which is the basic component of HFSs, can express the evaluation values of multiple decision makers (DMs) on the same alternative under a certain attribute. Thus, the HFS has its unique advantages in group decision making (GDM). Based on which, many scholars have conducted in-depth research on the applications of HFSs in GDM. We have viewed lots of relevant literature and divided the existing studies into three categories: theory, support and methods. In this paper, we elaborate on hesitant fuzzy GDM from these three aspects. The first aspect is mainly about the introduction of HFSs, HFPRs and some hesitant fuzzy aggregation operators. The second aspect describes the consensus process under hesitant fuzzy environment, which is an important support for a complete decision-making process. In the third aspect, we introduce seven hesitant fuzzy GDM approaches, which can be applied in GDM under different decision-making conditions. Finally, we summarize the research status of hesitant fuzzy GDM and put forward some directions of future research.
|
Keywords
hesitant fuzzy set
hesitant fuzzy preference relation
group decision-making
|
Corresponding Author(s):
Zeshui XU
|
Online First Date: 03 April 2019
Issue Date: 17 May 2019
|
|
1 |
CAcar, A Beskese, G TTemur (2018). Sustainability analysis of different hydrogen production options using hesitant fuzzy AHP. International Journal of Hydrogen Energy, 43(39): 18059–18076
https://doi.org/10.1016/j.ijhydene.2018.08.024
|
2 |
J C RAlcantud, AGiarlotta (2019). Necessary and possible hesitant fuzzy sets: A novel model for group decision making. Information Fusion, 46: 63–76
https://doi.org/10.1016/j.inffus.2018.05.005
|
3 |
UAsan, C Kadaifci, EBozdag, ASoyer, SSerdarasan (2018). A new approach to DEMATEL based on interval-valued hesitant fuzzy sets. Applied Soft Computing, 66: 34–49
https://doi.org/10.1016/j.asoc.2018.01.018
|
4 |
MAshtiani, M A Azgomi (2016). A hesitant fuzzy model of computational trust considering hesitancy, vagueness and uncertainty. Applied Soft Computing, 42: 18–37
https://doi.org/10.1016/j.asoc.2016.01.023
|
5 |
CCamerer (1998). Bounded rationality in individual decision making. Experimental Economics, 1(2): 163–183
https://doi.org/10.1023/A:1009944326196
|
6 |
NChen, Z S Xu (2015). Hesitant fuzzy ELECTRE II Approach: A new way to handle multi-criteria decision making problems. Information Sciences, 292: 175–197
https://doi.org/10.1016/j.ins.2014.08.054
|
7 |
NChen, Z S Xu, M M Xia (2013a). Correlation coefficients of hesitant fuzzy sets and their applications to clustering analysis. Applied Mathematical Modelling, 37(4): 2197–2211
https://doi.org/10.1016/j.apm.2012.04.031
|
8 |
NChen, Z S Xu, M M Xia (2013b). Interval-valued hesitant preference relations and their applications to group decision making. Knowledge-Based Systems, 37: 528–540
https://doi.org/10.1016/j.knosys.2012.09.009
|
9 |
NChen, Z S Xu, M M Xia (2015). The ELECTRE I multi-criteria decision making method based on hesitant fuzzy sets. International Journal of Information Technology & Decision Making, 14(03): 621–657
https://doi.org/10.1142/S0219622014500187
|
10 |
S HCheng (2018). Autocratic decision making using group recommendations based on hesitant fuzzy sets for green hotels selection and bidders selection. Information Sciences, 467: 604–617
https://doi.org/10.1016/j.ins.2018.08.014
|
11 |
S KDe, S S Sana (2017). Multi-criterion multi-attribute decision-making for an EOQ model in a hesitant fuzzy environment. Pacific Science Review A. Natural Science and Engineering, 17: 61–68
|
12 |
HDincer, S Yuksel, LMartinez (2019). Balanced scorecard-based analysis about European energy investment policies: A hybrid hesitant fuzzy decision-making approach with Quality Function Deployment. Expert Systems with Applications, 115: 152–171
https://doi.org/10.1016/j.eswa.2018.07.072
|
13 |
JDing, Z S Xu, N Zhao (2017). An interactive approach to probabilistic hesitant fuzzy multi-attribute group decision-making with incomplete weight information. Journal of Intelligent & Fuzzy Systems, 32(3): 2523–2536
https://doi.org/10.3233/JIFS-16503
|
14 |
BFarhadinia (2014). Distance and similarity measures for higher order hesitant fuzzy sets. Knowledge-Based Systems, 55: 43–48
https://doi.org/10.1016/j.knosys.2013.10.008
|
15 |
BFarhadinia (2016a). Hesitant fuzzy set lexicographical ordering and its application to multi-attribute decision making. Information Sciences, 327: 233–245
https://doi.org/10.1016/j.ins.2015.07.057
|
16 |
BFarhadinia (2016b). Utility of correlation measures for weighted hesitant fuzzy sets in medical diagnosis problems. Mathematical Modelling and Applications, 1(2): 36–45
|
17 |
N RGalo, L D D R Calache, L C R Carpinetti (2018). A group decision approach for supplier categorization based on hesitant fuzzy and ELECTRI TRI. International Journal of Production Economics, 202: 182–196
https://doi.org/10.1016/j.ijpe.2018.05.023
|
18 |
Y DHe, Z He, L XShi, S SMeng (2016). Multiple attribute group decision making based on IVHFPBMs and a new ranking method for interval-valued hesitant fuzzy information. Computers & Industrial Engineering, 99: 63–77
https://doi.org/10.1016/j.cie.2016.07.004
|
19 |
YHe, Z S Xu (2017). A consensus reaching model for hesitant information with different preference structures. Knowledge-Based Systems, 135: 99–112
https://doi.org/10.1016/j.knosys.2017.08.007
|
20 |
YHe, Z S Xu, J Gu (2016). An approach to group decision making with hesitant information and its application in credit risk evaluation of enterprises. Applied Soft Computing, 43: 159–169
https://doi.org/10.1016/j.asoc.2016.02.010
|
21 |
C LHwang, K Yoon (1981). Multiple Attribute Decision Making Methods and Applications. Berlin: Springer
|
22 |
H MJiang, C K Kwong, W Y Park (2017). Probabilistic fuzzy regression approach for preference modeling. Engineering Applications of Artificial Intelligence, 64: 286–294
https://doi.org/10.1016/j.engappai.2017.06.019
|
23 |
F FJin, Z W Ni, H Y Chen, Y P Li, L G Zhou (2016). Multiple attribute group decision making based on interval-valued hesitant fuzzy information measures. Computers & Industrial Engineering, 101: 103–115
https://doi.org/10.1016/j.cie.2016.08.019
|
24 |
J BLan, R F Jin, A Y Zheng, M M Hu (2017). Priority degrees for hesitant fuzzy sets: Applications to multiple attribute decision making. Operations Research Perspectives, 4: 67–73
https://doi.org/10.1016/j.orp.2017.05.001
|
25 |
D QLi, W Y Zeng, J H Li (2015). New distance and similarity measures on hesitant fuzzy sets and their applications in multiple criteria decision making. Engineering Applications of Artificial Intelligence, 40: 11–16
https://doi.org/10.1016/j.engappai.2014.12.012
|
26 |
D CLiang, Z S Xu (2017). The new extension of TOPSIS method for multiple criteria decision making with hesitant Pythagorean fuzzy sets. Applied Soft Computing, 60: 167–179
https://doi.org/10.1016/j.asoc.2017.06.034
|
27 |
H CLiao, Z S Xu (2013). A VIKOR-based method for hesitant fuzzy multi-criteria decision making. Fuzzy Optimization and Decision Making, 12(4): 373–392
https://doi.org/10.1007/s10700-013-9162-0
|
28 |
H CLiao, Z S Xu (2014a). Some new hybrid weighted aggregation operators under hesitant fuzzy multi-criteria decision making environment. Journal of Intelligent & Fuzzy Systems, 26(4): 1601–1617
|
29 |
H CLiao, Z S Xu (2014b). Subtraction and division operations over hesitant fuzzy sets. Journal of Intelligent & Fuzzy Systems, 27(1): 65–72
|
30 |
H CLiao, Z S Xu, M M Xia (2014). Multiplicative consistency of hesitant fuzzy preference relation and its application in group decision making. International Journal of Information Technology & Decision Making, 13(1): 47–76
https://doi.org/10.1142/S0219622014500035
|
31 |
AMahmoudi, S Sadi-Nezhad, AMakui, M RVakili (2016). An extension on PROMETHEE based on the typical hesitant fuzzy sets to solve multi-attribute decision-making problem. Kybernetes, 45(8): 1213–1231
https://doi.org/10.1108/K-10-2015-0271
|
32 |
F YMeng, Q X An (2017). A new approach for group decision making method with hesitant fuzzy preference relations. Knowledge-Based Systems, 127: 1–15
https://doi.org/10.1016/j.knosys.2017.03.010
|
33 |
F YMeng, X H Chen, Q Zhang (2015). Induced generalized hesitant fuzzy Shapley hybrid operators and their application in multi-attribute decision making. Applied Soft Computing, 28: 599–607
https://doi.org/10.1016/j.asoc.2014.11.017
|
34 |
LOsiro, F R Lima-Junior, L C R Carpinetti (2018). A group decision model based on quality function deployment and hesitant fuzzy for selecting supply chain sustainability metrics. Journal of Cleaner Production, 183: 964–978
https://doi.org/10.1016/j.jclepro.2018.02.197
|
35 |
D HPeng, C Y Gao, Z F Gao (2013). Generalized hesitant fuzzy synergetic weighted distance measures and their application to multiple criteria decision-making. Applied Mathematical Modelling, 37(8): 5837–5850
https://doi.org/10.1016/j.apm.2012.11.016
|
36 |
J JPeng, J Q Wang, J Wang, L JYang, X HChen (2015). An extension of ELECTRE to multi-criteria decision-making problems with multi-hesitant fuzzy sets. Information Sciences, 307: 113–126
https://doi.org/10.1016/j.ins.2015.02.030
|
37 |
RPerez-Fernandez, P Alonso, HBustince, IDiaz, S Montes (2016). Applications of finite interval-valued hesitant fuzzy preference relations in group decision making. Information Sciences, 326: 89–101
https://doi.org/10.1016/j.ins.2015.07.039
|
38 |
GQian, H Wang, X QFeng (2013). Generalized hesitant fuzzy sets and their application in decision support system. Knowledge-Based Systems, 37: 357–365
https://doi.org/10.1016/j.knosys.2012.08.019
|
39 |
J DQin, X W Liu, W Pedrycy (2016). Frank aggregation operators and their application to hesitant fuzzy multiple attribute decision making. Applied Soft Computing, 41: 428–452
https://doi.org/10.1016/j.asoc.2015.12.030
|
40 |
PSevastjanov, L Dymova (2015). Generalized operations on hesitant fuzzy values in the framework of Dempster-Shafer theory. Information Sciences, 311: 39–58
https://doi.org/10.1016/j.ins.2015.03.041
|
41 |
G DSun, X Guan, XYi, ZZhou (2018). An innovative TOPSIS approach based on hesitant fuzzy correlation coefficient and its applications. Applied Soft Computing, 68: 249–267
https://doi.org/10.1016/j.asoc.2018.04.004
|
42 |
C QTan, W T Yi, X H Chen (2015). Hesitant fuzzy Hamacher aggregation operators for multicriteria decision making. Applied Soft Computing, 26: 325–349
https://doi.org/10.1016/j.asoc.2014.10.007
|
43 |
X LTian, Z S Xu, H Fujita (2018). Sequential funding the venture project or not? A prospect consensus process with probabilistic hesitant fuzzy preference information. Knowledge-Based Systems, 161: 172–184
https://doi.org/10.1016/j.knosys.2018.08.002
|
44 |
VTorra (2010). Hesitant fuzzy sets. International Journal of Intelligent Systems, 25: 529–539
|
45 |
S PWan, Y L Qin, J Y Dong (2017). A hesitant fuzzy mathematical programming method for hybrid multi-criteria group decision making with hesitant fuzzy truth degrees. Knowledge-Based Systems, 138: 232–248
https://doi.org/10.1016/j.knosys.2017.10.002
|
46 |
G WWei (2012). Hesitant fuzzy prioritized operators and their application to multiple attribute decision making. Knowledge-Based Systems, 31: 176–182
https://doi.org/10.1016/j.knosys.2012.03.011
|
47 |
Z BWu, B M Jin, J P Xu (2018). Local feedback strategy for consensus building with probability-hesitant fuzzy preference relations. Applied Soft Computing, 67: 691–705
https://doi.org/10.1016/j.asoc.2017.06.011
|
48 |
Z BWu, J P Xu (2018). A consensus model for large-scale group decision making with hesitant fuzzy information and changeable clusters. Information Fusion, 41: 217–231
https://doi.org/10.1016/j.inffus.2017.09.011
|
49 |
M MXia, Z S Xu (2013). Managing hesitant information GDM problems under fuzzy and multiplicative preference relations. International Journal of Uncertainty, Fuzziness and Knowledge-based Systems, 21(06): 865–897
https://doi.org/10.1142/S0218488513500402
|
50 |
M MXia, Z S Xu (2011a). Some techniques for aggregating hesitant and intuitionistic information based on Sasty’s 1-9 scale. Technical report
|
51 |
M MXia, Z S Xu (2011b). Hesitant fuzzy information aggregation in decision making. International Journal of Approximate Reasoning, 52(3): 395–407
https://doi.org/10.1016/j.ijar.2010.09.002
|
52 |
M MXia, Z S Xu, N Chen (2013). Some hesitant fuzzy aggregation operators with their application in group decision making. Group Decision and Negotiation, 22(2): 259–279
https://doi.org/10.1007/s10726-011-9261-7
|
53 |
Y JXu, C Y Li, X W Wen (2018). Missing values estimation and consensus building for incomplete hesitant fuzzy preference relations with multiplicative consistency. International Journal of Computational Intelligence Systems, 11(1): 101–119
https://doi.org/10.2991/ijcis.11.1.9
|
54 |
Y JXu, D Rui, H MWang (2017). A dynamically weight adjustment in the consensus reaching process for group decision-making with hesitant fuzzy preference relations. International Journal of Systems Science, 48(6): 1311–1321
https://doi.org/10.1080/00207721.2016.1255803
|
55 |
Y JXu, F J Cabrerizo, N Herrera-Viedma (2017). A consensus model for hesitant fuzzy preference relations and its application in water allocation management. Applied Soft Computing, 58: 265–284
https://doi.org/10.1016/j.asoc.2017.04.068
|
56 |
Y JXu, L Chen, R MRodriguez, FHerrera, H MWang (2016). Deriving the priority weights from incomplete hesitant fuzzy preference relations in group decision making. Knowledge-Based Systems, 99: 71–78
https://doi.org/10.1016/j.knosys.2016.01.047
|
57 |
Z SXu, M M Xia (2011). On distance and correlation measures of hesitant fuzzy information. International Journal of Intelligent Systems, 26(5): 410–425
https://doi.org/10.1002/int.20474
|
58 |
Z SXu, W Zhou (2017). Consensus building with a group of decision makers under the hesitant probabilistic fuzzy environment. Fuzzy Optimization and Decision Making, 16(4): 481–503
https://doi.org/10.1007/s10700-016-9257-5
|
59 |
Z SXu, X L Zhang (2013). Hesitant fuzzy multi-attribute decision making based on TOPSIS with incomplete weight information. Knowledge-Based Systems, 52: 53–64
https://doi.org/10.1016/j.knosys.2013.05.011
|
60 |
D JYu, W Y Zhang, Y J Xu (2013). Group decision making under hesitant fuzzy environment with application to personnel evaluation. Knowledge-Based Systems, 52: 1–10
https://doi.org/10.1016/j.knosys.2013.04.010
|
61 |
SZhang, Z S Xu, H Y Wu (2018). Fusions and preference relations based on probabilistic interval-valued hesitant fuzzy information in group decision making. Soft Computing, DOI: http://doi.org/10.1007/s00500-018-3465-6
|
62 |
SZhang, Z S Xu, Y He (2017). Operations and integrations of probabilistic hesitant fuzzy information in decision making. Information Fusion, 38: 1–11
https://doi.org/10.1016/j.inffus.2017.02.001
|
63 |
X LZhang, Z S Xu (2014a). Interval programming method for hesitant fuzzy multi-attribute group decision making with incomplete preference over alternatives. Computers & Industrial Engineering, 75: 217–229
https://doi.org/10.1016/j.cie.2014.07.002
|
64 |
X LZhang, Z S Xu (2014b). The TODIM analysis approach based on novel measured functions under hesitant fuzzy environment. Knowledge-Based Systems, 61: 48–58
https://doi.org/10.1016/j.knosys.2014.02.006
|
65 |
X LZhang, Z S Xu (2015). Hesitant fuzzy QUALIFLEX approach with a signed distance-based comparison method for multiple criteria decision analysis. Expert Systems with Applications, 42(2): 873–884
https://doi.org/10.1016/j.eswa.2014.08.056
|
66 |
Z MZhang (2013). Hesitant fuzzy power aggregation operators and their application to multiple attribute group decision making. Information Sciences, 234: 150–181
https://doi.org/10.1016/j.ins.2013.01.002
|
67 |
Z MZhang (2016). Deriving the priority weights from incomplete hesitant fuzzy preference relations based on multiplicative consistency. Applied Soft Computing, 46: 37–59
https://doi.org/10.1016/j.asoc.2016.04.010
|
68 |
Z MZhang, C Wang, D ZTian, KLi (2014). Induced generalized hesitant fuzzy operators and their application to multiple attribute group decision making. Computers & Industrial Engineering, 67: 116–138
https://doi.org/10.1016/j.cie.2013.10.011
|
69 |
Z MZhang, C Wang, X DTian (2015a). A decision support model for group decision making with hesitant fuzzy preference relations. Knowledge-Based Systems, 86: 77–101
https://doi.org/10.1016/j.knosys.2015.05.023
|
70 |
Z MZhang, C Wang, X DTian (2015b). Multi-criteria group decision making with incomplete hesitant fuzzy preference relations. Applied Soft Computing, 36: 1–23
https://doi.org/10.1016/j.asoc.2015.06.047
|
71 |
Z MZhang, C Wu (2014a). Deriving the priority weights from hesitant multiplicative preference relations in group decision making. Applied Soft Computing, 25: 107–117
https://doi.org/10.1016/j.asoc.2014.08.062
|
72 |
Z MZhang, C Wu (2014b). Weighted hesitant fuzzy sets and their application to multi-criteria decision making. British Journal of Mathematics and Computer Science, 4(8): 1091–1123
https://doi.org/10.9734/BJMCS/2014/8533
|
73 |
ZZhang, X Y Kou, Q X Dong (2018). Additive consistency analysis and improvement for hesitant fuzzy preference relations. Expert Systems with Applications, 98: 118–128
https://doi.org/10.1016/j.eswa.2018.01.016
|
74 |
ZZhang, X Y Kou, W Y Yu, C H Guo (2018). On priority weights and consistency for incomplete hesitant fuzzy preference relations. Knowledge-Based Systems, 143: 115–126
https://doi.org/10.1016/j.knosys.2017.12.010
|
75 |
NZhao, Z S Xu, Z L Ren (2015). On typical hesitant fuzzy prioritized “or” operator in multi-attribute decision making. International Journal of Intelligent Systems, 31(1): 73–100
https://doi.org/10.1002/int.21754
|
76 |
X FZhao, R Lin, G WWei (2014). Hesitant triangular fuzzy information aggregation based on Einstein operations and their application to multiple attribute decision making. Expert Systems with Applications, 41(4): 1086–1094
https://doi.org/10.1016/j.eswa.2013.07.104
|
77 |
WZhou, Z S Xu (2017a). Expected hesitant VaR for tail decision making under probabilistic hesitant fuzzy environment. Applied Soft Computing, 60: 297–311
https://doi.org/10.1016/j.asoc.2017.06.057
|
78 |
WZhou, Z S Xu (2017b). Group consistency and group decision making under uncertain probabilistic hesitant fuzzy preference environment. Information Sciences, 414: 276–288
https://doi.org/10.1016/j.ins.2017.06.004
|
79 |
WZhou, Z S Xu (2018). Probability calculation and element optimization of probabilistic hesitant fuzzy preference relations based on expected consistency. IEEE Transactions on Fuzzy Systems, 26(3): 1367–1378
https://doi.org/10.1109/TFUZZ.2017.2723349
|
80 |
WZhou, Z S Xu, M H Chen (2015). Preference relations based on hesitant-intuitionistic fuzzy information and their application in group decision making. Computers & Industrial Engineering, 87: 163–175
https://doi.org/10.1016/j.cie.2015.04.020
|
81 |
BZhu (2014). Decision method for research and application based on preference relations. Nanjing: Southeast University
|
82 |
BZhu, Z S Xu (2014). Analytic hierarchy process-hesitant group decision making. European Journal of Operational Research, 239(3): 794–801
https://doi.org/10.1016/j.ejor.2014.06.019
|
83 |
BZhu, Z S Xu (2018). Probability-hesitant fuzzy sets and the representation of preference relations. Technological and Economic Development of Economy, 24(3): 1029–1040
https://doi.org/10.3846/20294913.2016.1266529
|
84 |
BZhu, Z S Xu, J P Xu (2014). Deriving a ranking from hesitant fuzzy preference relations under group decision making. IEEE Transactions on Cybernetics, 44(8): 1328–1337
https://doi.org/10.1109/TCYB.2013.2283021
|
85 |
BZhu, Z S Xu, M M Xia (2012). Hesitant fuzzy geometric Bonferroni means. Information Sciences, 2015: 72–85
https://doi.org/10.1016/j.ins.2012.01.048
|
86 |
BZhu, Z S Xu, M M Xia (2013). Hesitant fuzzy Bonferroni means for multi-criteria decision making. Journal of the Operational Research Society, 64(12): 1831–1840
https://doi.org/10.1057/jors.2013.7
|
87 |
BZhu, Z S Xu, R Zhang, MHong (2015). Generalized analytic network process. European Journal of Operational Research, 244(1): 277–288
https://doi.org/10.1016/j.ejor.2015.01.011
|
88 |
BZhu, Z S Xu, R Zhang, MHong (2016). Hesitant analytic hierarchy process. European Journal of Operational Research, 250(2): 602–614
https://doi.org/10.1016/j.ejor.2015.09.063
|
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
Cited |
|
|
|
|
|
Shared |
|
|
|
|
|
Discussed |
|
|
|
|