To address the issues of inaccurate expert weight allocation in existing large-group decision-making methods and information loss in multi-attribute group emergency decision-making processes, we propose a clustering-based method using the probabilistic hesitant fuzzy set. Recognizing the diverse contributions of the decision makers within each cluster-to-cluster consistency and the varied impacts of preferences in different clusters on overall group preference, we introduce a two-layer weight model. Specifically, from a two-dimensional viewpoint, we determine the weights of decision members within each cluster using an expert evaluation distance formula and the weights of each cluster using fuzzy entropy. Subsequently, by incorporating the Maclaurin symmetric mean operator (MSMO), we establish the ranking of decision alternatives. Finally, we assess the effectiveness and applicability of the proposed method by applying it to analyze the case of the Tonga volcanic eruption.
National Work Safety Emergency Rescue Center. Chongqing Energy Investment Chongqing New Energy Company Songzao Coal Mine “9·27” major fire accident rescue. (2021-06-25) [2021-06-25]. https://www.nwserc.cn/aqyj/jyal/202106/t20210625_389929.shtml
3.
Ministry of EmergencyManagement of China. The National Defense Headquarters specially dispatched and deployed the defense work against Typhoon “Dusuri” to upgrade the flood prevention and typhoon emergency response to Level 2. (2023-7-27) [2023-7-27]. https://www.mem.gov.cn/xw/yjyw/202307/t20230727_457533.shtml
ZhuB., Decision method for research and application based on preference relation, Working Paper, Nanjing: Southeast University, 2014.
6.
WuZ. and XuJ., A consensus model for large-scale group decision making with hesitant fuzzy information and changeable clusters, Information Fusion41 (2018), 217–231.
7.
ZhangS., XuZ. and HeY., Operations and integrations of probabilistic hesitant fuzzy information in decision making, Information Fusion38 (2017), 1–11.
8.
DingQ., WangY.M. and GohM., TODIM dynamic emergency decision-making method based on hybrid weighted distance under probabilistic hesitant fuzzy information, International Journal of Fuzzy Systems23 (2021), 474–491.
9.
SongG.X. and YangH., Decision behavior analysis in group decision making, Academic Exploration13(3) (2000), 48–49.
ZhouK. and YangS., Effect of cluster size distribution on clustering: A comparative study of k-means and fuzzy c-means clustering, Pattern Analysis and Applications23 (2020), 455–466.
12.
MengüçK.,
AydinN. and
UluM., Optimisation of COVID-19 vaccination process using GIS, machine learning, and the multi-layered transportation model, International Journal of Production Research (2023), 1–14.
13.
WangZ., RodríguezR.M., WangY., et al. A two-stage minimum adjustment consensus model for large scale decision making based on reliability modeled by two-dimension 2-tuple linguistic information, Computers & Industrial Engineering151 (2021), 106973.
14.
PangJ. and SongP., Multi-attribute group decision making method for interval-valued intuitionistic uncertain language with completely unknown experts’ weights, Computer Science45(1) (2018), 47–54.
15.
WanJ., XingH. and ZhangX., Algorithm of adjusting weights of decision-makers in multi-attribute group decision-making based on entropy theory, Control and Decision25(6) (2010), 907–910.
16.
ZhuY., Determination of bidirectional objective weight of expert based on interval two-tuple linguistic group decision making, Computing Technology and Automation37(3) (2018), 106–110.
17.
LiangW. and WangY., Generalized TODIM emergency group decision making method for basic uncertain information interval-valued hesitant fuzzy set based on reliability degree, Control and Decision38(07) (2023), 1988–1996.
18.
ChenZ.S., ZhouJ., ZhuC.Y., et al. Prioritizing real estate enterprises based on credit risk assessment: an integrated multi-criteria group decision support framework [J], Financial Innovation9(1) (2023), 120.
19.
ChenZ.S., LuJ.Y., WangX.J., et al. Identifying digital transformation barriers in small and medium-sized construction enterprises: A multi-criteria perspective [J], Journal of the Knowledge Economy (2024), 1–37.
20.
ChenZ.S., ZhuZ., WangZ.J., et al. Fairness-aware large-scale collective opinion generation paradigm: A case study of evaluating blockchain adoption barriers in medical supply chain [J], Information Sciences635 (2023), 257–278.
21.
AgrawalA., SehA.H., BazA., et al. Software security estimation using the hybrid fuzzy ANP-TOPSIS approach: Design tactics perspective [J], Symmetry12(4) (2020), 598.
22.
SahuK. and SrivastavaR.K., Needs and importance of reliability prediction: An industrial perspective [J], Information Sciences Letters9(1) (2020), 33–37.
23.
SahuK. and SrivastavaR.K., Predicting software bugs of newly and large datasets through a unified neuro-fuzzy approach: Reliability perspective [J], Advances in Mathematics: Scientific Journal10(1) (2021), 543–555.
24.
KumarR., KhanS.A., AgrawalA., et al. Measuring the security attributes through fuzzy analytic hierarchy process: Durability perspective [J], ICIC Express Letters12(6) (2018), 615–620.
25.
KumarR., KhanS.A. and KhanR.A., Durable security in software development: Needs and importance [J], CSI Communication39(7) (2015), 34–36.
26.
KumarR., AleneziM., AnsariM.T.J., et al. Evaluating the impact of malware analysis techniques for securing web applications through a decision-making framework under fuzzy environment [J], Int. J. Intell. Eng. Syst13(6) (2020), 94–109.
27.
LiuP., HeL. and YuX., Generalized hybrid aggregation operators based on the 2-dimension uncertain linguistic information for multiple attribute group decision making, Group Decision and Negotiation25 (2016), 103–126.
28.
YinK., WangP. and LiX., The multi-attribute group decision-making method based on interval grey trapezoid fuzzy linguistic variables, International Journal of Environmental Research and Public Health14(12) (2017), 1561.
29.
WuQ., WangF., ZhouL., et al. Method of multiple attribute group decision making based on 2-dimension interval type-2 fuzzy aggregation operators with multi-granularity linguistic information, International Journal of Fuzzy Systems19 (2017), 1880–1903.
30.
SahuK., SrivastavaR.K., KumarS., et al. Integrated hesitant fuzzy-based decision-making framework for evaluating sustainable and renewable energy [J], International Journal of Data Science and Analytics16(3) (2023), 371–390.
31.
KumarR., BazA., AlhakamiH., et al. A hybrid fuzzy rule-based multi-criteria framework for sustainable-security assessment of web application [J], Ain Shams Engineering Journal12(2) (2021), 2227–2240.
32.
WangJ., YangY. and LiL., Multi-criteria decision-making method based on single-valued neutrosophic linguistic Maclaurin symmetric mean operators, Neural Computing and Applications30 (2018), 1529–1547.
33.
DeTempleD.W. and RobertsonJ.M., On generalized symmetric means of two variables, Publikacije Elektrotehničkog fakulteta. Serija Matematika i fizika (634/677) (1979), 236–238.
34.
WangJ., YangY. and LiL., Multi-criteria decision-making method based on single-valued neutrosophic linguistic Maclaurin symmetric mean operators, Neural Computing and Applications30 (2018), 1529–1547.
35.
JuY., LiuX. and JuD., Some new intuitionistic linguistic aggregation operators based on Maclaurin symmetric mean and their applications to multiple attribute group decision making, Soft Computing20 (2016), 4521–4548.
36.
LiuP. and QinX., Maclaurin symmetric mean operators of linguistic intuitionistic fuzzy numbers and their application to multiple-attribute decision-making, Journal of Experimental & Theoretical Artificial Intelligence29(6) (2017), 1173–1202.
37.
ShannonC.E., A mathematical theory of communication, The Bell System Technical Journal27(3) (1948), 379–423.
38.
WangP., ZhangJ. and ZhangW., Multi-granularity linguistic large group decision-making based on cloud model and multi-layer weight determination, Control and Decision36(09) (2021), 2257–2266.
39.
XuX. and SunQ., Two-layer weight large group decision-making method based on multigranularity attributes, Control and Decision31(10) (2016), 1908–1914.
