A normal wiggly hesitant fuzzy set (NWHFS) is a powerful and useful tool to dig the potential indeterminacy of decision makers (DMs) in the process of expressing their preferences, which can be considered as an extended form of the traditional hesitant fuzzy set (HFS). The NWHFSs can not only retain the original hesitant fuzzy information completely, but also explore potential uncertainty of theses information. TODIM is an effective method to capture the psychological behavior based on prospect theory. Considering the advantages of NWHFS and TODIM method, in this paper, we define the distance measure of any two normal wiggly hesitant fuzzy elements (NWHFEs), and put forward an extended normal wiggly hesitant fuzzy TODIM (NWHF-TODIM) approach to handle multiple attribute decision making (MADM) problems with normal wiggly hesitant fuzzy (NWHF) information. Then we use the extended NWHF-TODIM method to rank alternatives and select an ideal one. Lastly, we compare it with two existing approaches to verify the rationality and validity of the proposed approach.
ChenN. and XuZ., Hesitant fuzzy ELECTRE II approach: a new way to handle multi-criteria decision making problems, Information Sciences292 (2015), 175–197.
4.
DahooieJ.H., ZavadskasE.K., FiroozfarH.R., et al., An improved fuzzy MULTIMOORA approach for multi-criteria decision making based on objective weighting method (CCSD) and its application to technological forecasting method selection, Engineering Applications of Artificial Intelligence79 (2019), 114–128.
5.
GomesL. and LimaM., TODIM: Basics and application to multicriteria ranking of projects with environmental impacts, Foundations of Computing and Decision Sciences16(4) (1992), 113–127.
6.
HerreraF. and MartínezL., A 2-tuple fuzzy linguistic representation model for computing with words, IEEE Transactions on Fuzzy Systems8(6) (2000), 746–752.
7.
JiP., ZhangH. and WangJ., A projection-based TODIM method under multi-valued neutrosophic environments and its application in personnel selection, Neural Computing and Applications29(1) (2018), 221–234.
8.
KahnemanD. and TverskyA., Prospect theory: an analysis of decision under risk, Econometrica: Journal of the Econometric Society47(2) (1979), 263–291.
9.
LiM.Y. and CaoP.P., Extended TODIM method for multi-attribute risk decision making problems in emergency response, Computers & Industrial Engineering135 (2019), 1286–1293.
10.
LiangQ. and MendelJ.M., Interval type-2 fuzzy logic systems: theory and design, IEEE Trans Fuzzy Syst8 (2000), 535–550.
11.
LiuP. and QinX., An extended VIKOR method for decision making problem with interval-valued linguistic intuitionistic fuzzy numbers based on entropy, Informatica28(4) (2017), 665–685.
12.
LiaoH., et al., Score-HeDLiSF: A score function of hesitant fuzzy linguistic term set based on hesitant degrees and linguistic scale functions: An application to unbalanced hesitant fuzzy linguistic MULTIMOORA, Information Fusion48 (2019), 39–54.
13.
LiaoH. and XuZ., A VIKOR-based method for hesitant fuzzy multi-criteria decision making, Fuzzy Optimization and Decision Making12(4) (2013), 373–392.
14.
MemariA., DargiA., JokarM.R.A., et al., Sustainable supplier selection: A multi-criteria intuitionistic fuzzy TOPSIS method, Journal of Manufacturing Systems50 (2019), 9–24.
15.
QinJ., LiuX. and PedryczW., An extended TODIM multi-criteria group decision making method for green supplier selection in interval type-2 fuzzy environment, European Journal of Operational Research258(2) (2017), 626–638.
16.
PengH., ShenK., HeS., et al., Investment risk evaluation for new energy resources: An integrated decision support model based on regret theory and ELECTRE III, Energy Conversion and Management183 (2019), 332–348.
17.
SahinR. and LiuP., Correlation coefficient of single-valued neutrosophic hesitant fuzzy sets and its applications in decision making, Neural Computing and Applications28(6) (2017), 1387–1395.
18.
RenZ., XuZ. and WangH., Normal wiggly hesitant fuzzy sets and their application to environmental quality evaluation, Knowledge-Based Systems159 (2018), 286–297.
19.
TorraV., Hesitant fuzzy sets, International Journal of Intelligent Systems25(6) (2010), 529–539.
20.
TrivediA., JhaS.K., ChoudharyS. and ShandleyR., Fuzzy TOPSIS Multi-criteria Decision Making for Selection of Electric Molding Machine. Innovations in Computer Science and Engineering. In book: Innovations in Computer Science and Engineering, Springer, Singapore (2019), 325–332.
21.
WangJ., WuJ., WangJ., et al., Interval-valued hesitant fuzzy linguistic sets and their applications in multi-criteria decision-making problems, Information Sciences288 (2014), 55–72.
22.
WeiG., WangJ., LuJ., et al., VIKOR method for multiple criteria group decision making under 2-tuple linguistic neutrosophic environment, Economic Research-Ekonomska Istraživanja (2019), 1–24.
23.
XiaM. and XuZ., Hesitant fuzzy information aggregation in decision making, International Journal of Approximate Reasoning52(3) (2011), 395–407.
24.
XuZ. and ZhangX., Hesitant fuzzy multi-attribute decision making based on TOPSIS with incomplete weight information, Knowledge-Based Systems52 (2013), 53–64.
25.
YagerR.R., On ordered weighted averaging aggregation operators in multicriteria decision making, IEEE Trans Syst Man Cybern18(1) (1988), 183–190.
26.
ZadehL.A., Fuzzy sets, Information and Control8(3) (1965), 338–353.
27.
ZhangY. and XuZ., Efficiency evaluation of sustainable water management using the HF-TODIM method, International Transactions in Operational Research26(2) (2019), 747–764.
28.
ZhangW., ZhuY., WangD., et al., A Multi-attribute Decision Making Method Based on Interval Pythagorean Fuzzy Language and thePROMETHEEMethod. The International Conference on Natural Computation, Fuzzy Systems and Knowledge Discovery. Springer, Cham, (2019), 818–826.
29.
ZhaoJ., ZhuH., LiH., 2-Dimension linguistic PROMETHEE methods for multiple attribute decision making, Expert Systems with Applications127 (2019), 97–108.
30.
ZhuJ., ShuaiB., WangR., et al., Risk Assessment for Failure Mode and Effects Analysis Using the Bonferroni Mean and TODIM Method, Mathematics7(6) (2019), 536.
31.
LiuP., WangP., Multiple-Attribute Decision Making based on Archimedean Bonferroni Operators of q-Rung Orthopair Fuzzy Numbers, IEEE Transactions on Fuzzy Systems27(5) (2019), 834–848.
32.
LiuP., ChenS.M., WangP., Multiple-Attribute Group Decision-Making Based on q-Rung Orthopair Fuzzy Power Maclaurin Symmetric Mean Operators, IEEE Transactions on Systems, Man, and Cybernetics: Systems, In Press. DOI: 10.1109/TSMC.2018.2852948
33.
LiuP., TangG., Some Intuitionistic Fuzzy Prioritized Interactive Einstein Choquet Operators and Their Application in Decision Making, IEEE ACCESS6 (2019), 72357–72371.
34.
LiuP., LiuJ., Some q-Rung Orthopai Fuzzy Bonferroni Mean Operators and Their Application to Multi-Attribute Group Decision Making, International Journal of Intelligent Systems33(2) (2018), 315–347.
35.
LiuP., ChengS., ZhangY., An extended multi-criteria group decision-making PROMETHEE method based on probability multi-valued neutrosophic sets, International Journal of Fuzzy Systems21(2) (2019), 388–406.
36.
LiuP., LiY., The PROMETHEE II method based on probabilistic linguistic information and their application to Decision Making, Informatica29(2) (2018), 303–320.
37.
LiuP. and LiY., An extended MULTIMOORA method for probabilistic linguistic multi-criteria group decision-making based on prospect theory, Computers & Industrial Engineering136 (2019), 528–545.
