{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,23]],"date-time":"2026-03-23T12:56:25Z","timestamp":1774270585713,"version":"3.50.1"},"reference-count":41,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2026,3,22]],"date-time":"2026-03-22T00:00:00Z","timestamp":1774137600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Chenguang Program","award":["20CGB15"],"award-info":[{"award-number":["20CGB15"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Failure Modes and Effects Analysis (FMEA) is crucial for complex system reliability. However, traditional FMEA and its existing enhancements face significant limitations. These notably include difficulties in handling diverse heterogeneous data, effectively coordinating large expert groups, and robustly propagating inherent uncertainties. To bridge these critical gaps, this paper proposes an innovative and robust FMEA framework, specifically designed for Large Group Decision Making (LGDM) under uncertainty, leveraging the Normal Cloud Model (NCM). First, LGDM is genuinely integrated into FMEA by involving an unprecedented number of experts (&gt;50). Second, a broad spectrum of heterogeneous data, including exact numbers, interval numbers, NCMs, linguistic terms, and linguistic expressions, is utilized to effectively model and manage diverse uncertainties. Third, a four-step data preprocessing method is incorporated to efficiently screen invalid and low-quality inputs, significantly enhancing the reliability of aggregated results. Fourth, an innovative and comprehensive expert weight determination method that judiciously combines subjective factors with objective data quality is proposed, ensuring more trustworthy and equitable aggregation of judgments. Distinctively, our method explicitly preserves and propagates uncertainty information across the entire computational process, yielding more insightful and informative results beyond simple rankings, encompassing detailed quantitative uncertainty analysis. A practical case study, alongside detailed result analysis, sensitivity analysis, both qualitative and quantitative comparative analysis, and advantages and limitations analysis, collectively confirms the effectiveness, practicality, rationality, and robustness of the proposed method. The sensitivity analyses demonstrate that the final risk rankings are highly stable even under varying trade-off coefficients, confirming the method\u2019s strong robustness and insensitivity to parameter fluctuations. Our framework provides a scientifically advanced and robust approach for FMEA in complex decision-making environments, particularly applicable to high-stakes industries such as modern aviation, thereby enabling more informed risk management decisions.<\/jats:p>","DOI":"10.3390\/e28030360","type":"journal-article","created":{"date-parts":[[2026,3,23]],"date-time":"2026-03-23T11:59:36Z","timestamp":1774267176000},"page":"360","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Failure Mode and Effect Analysis Using Large-Scale Group Decision Making and Normal Cloud Model"],"prefix":"10.3390","volume":"28","author":[{"given":"Lijie","family":"Wu","sequence":"first","affiliation":[{"name":"Department of Sino-German Engineer, Shanghai Technical Institute of Electronics and Information, Shanghai 201400, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Changchun","family":"Liu","sequence":"additional","affiliation":[{"name":"Department of Sino-German Engineer, Shanghai Technical Institute of Electronics and Information, Shanghai 201400, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hanwen","family":"Song","sequence":"additional","affiliation":[{"name":"Department of Sino-German Engineer, Shanghai Technical Institute of Electronics and Information, Shanghai 201400, China"},{"name":"Department of Aerospace and Mechanics, Tongji University, Shanghai 200092, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2026,3,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1195","DOI":"10.1016\/j.eswa.2007.11.028","article-title":"Risk evaluation in failure mode and effects analysis using fuzzy weighted geometric mean","volume":"36","author":"Wang","year":"2009","journal-title":"Expert Syst. Appl."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"425","DOI":"10.1016\/j.ress.2018.08.013","article-title":"Failure modes, mechanisms and effect analysis on temperature redundant sensor stage","volume":"180","author":"Catelani","year":"2018","journal-title":"Reliab. Eng. Syst. Saf."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"114444","DOI":"10.1109\/ACCESS.2025.3582537","article-title":"Dealing with heterogeneous information in multi-criteria group decision-making problems: A comprehensive design framework","volume":"13","author":"Ekel","year":"2025","journal-title":"IEEE Access"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"3527","DOI":"10.1016\/j.eswa.2013.10.058","article-title":"Risk analysis using FMEA: Fuzzy similarity value and possibility theory based approach","volume":"41","author":"Mandal","year":"2014","journal-title":"Expert Syst. Appl."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"242","DOI":"10.1016\/j.asoc.2018.10.033","article-title":"A new fuzzy methodology-based structured framework for RAM and risk analysis","volume":"74","author":"Panchal","year":"2019","journal-title":"Appl. Soft Comput."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"187","DOI":"10.31181\/sdmap31202642","article-title":"Assessing and prioritizing construction contracting risks with an extended FMEA decision-making model in uncertain environments","volume":"3","author":"Mohammadi","year":"2026","journal-title":"Spectr. Decis. Mak. Appl."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Liou, J.J.H., Guo, B.H.T., Huang, S.-W., and Yang, Y.-T. (2024). Failure mode and effect analysis using interval type-2 fuzzy and multiple-criteria decision-making methods. Mathematics, 12.","DOI":"10.3390\/math12243931"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"554","DOI":"10.1109\/TR.2018.2866029","article-title":"Failure mode and effects analysis using two-dimensional uncertain linguistic variables and alternative queuing method","volume":"68","author":"Liu","year":"2019","journal-title":"IEEE Trans. Reliab."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"566","DOI":"10.1109\/TR.2018.2869787","article-title":"Failure mode and effect analysis in a linguistic context: A consensus-based multiattribute group decision-making approach","volume":"68","author":"Zhang","year":"2019","journal-title":"IEEE Trans. Reliab."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1339","DOI":"10.1007\/s10845-019-01513-9","article-title":"A failure mode and risk assessment method based on cloud model","volume":"31","author":"Li","year":"2020","journal-title":"J. Intell. Manuf."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1058","DOI":"10.1109\/TR.2017.2754642","article-title":"Failure mode and effect analysis using cloud model theory and PROMETHEE method","volume":"66","author":"Liu","year":"2017","journal-title":"IEEE Trans. Reliab."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Ma, X., and Wang, C. (2025). Navigating cross-border E-commerce: Prioritizing logistics partners with hybrid MCGDM. Entropy, 27.","DOI":"10.3390\/e27080876"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"113174","DOI":"10.1016\/j.engappai.2025.113174","article-title":"Z-cloud fuzzy decision making approach for evaluating next generation agricultural decision support tools","volume":"164","author":"Muhsen","year":"2026","journal-title":"Eng. Appl. Artif. Intell."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1016\/j.asoc.2019.02.029","article-title":"Modified failure mode and effects analysis under uncertainty: A rough cloud theory-based approach","volume":"78","author":"Li","year":"2019","journal-title":"Appl. Soft Comput."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"110148","DOI":"10.1016\/j.asoc.2023.110148","article-title":"Decision-making model for failure modes and effect analysis based on rough fuzzy integrated clouds","volume":"136","author":"Sarwar","year":"2023","journal-title":"Appl. Soft Comput."},{"key":"ref_16","first-page":"73","article-title":"A novel multi-attribute group decision-making method for talent evaluation using heterogeneous data weighting and an extended cloud-VIKOR model","volume":"25","author":"Zhang","year":"2025","journal-title":"Oper. Res."},{"key":"ref_17","first-page":"100658","article-title":"Group decision making method for third-party logistics management: An interval rough cloud optimization model","volume":"41","author":"Sarwar","year":"2024","journal-title":"J. Ind. Inf. Integr."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"107876","DOI":"10.1016\/j.engfailanal.2023.107876","article-title":"A novel hybrid approach to explore the interaction among faults in production process with extended FMEA model using DEMATEL and cloud model theory","volume":"157","author":"Akhtar","year":"2024","journal-title":"Eng. Fail. Anal."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"84","DOI":"10.1109\/TFUZZ.2018.2861719","article-title":"Improving risk evaluation in FMEA with cloud model and hierarchical TOPSIS method","volume":"27","author":"Liu","year":"2019","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"106834","DOI":"10.1016\/j.asoc.2020.106834","article-title":"Failure mode and effect analysis: An interval-valued intuitionistic fuzzy cloud theory-based method","volume":"98","author":"Huang","year":"2021","journal-title":"Appl. Soft Comput."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"107350","DOI":"10.1016\/j.cie.2021.107350","article-title":"A new data envelopment analysis-based model for failure mode and effect analysis with heterogeneous information","volume":"157","author":"Yu","year":"2021","journal-title":"Comput. Ind. Eng."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"555","DOI":"10.1016\/j.psep.2021.09.047","article-title":"Risk assessment of submarine pipelines using modified FMEA approach based on cloud model and extended VIKOR method","volume":"155","author":"Yu","year":"2021","journal-title":"Process Saf. Environ. Prot."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"50037","DOI":"10.1109\/ACCESS.2022.3172513","article-title":"Efficient fine tuned trapezoidal fuzzy-based model for failure mode effect analysis risk prioritization","volume":"10","author":"Subramanian","year":"2022","journal-title":"IEEE Access"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"101803","DOI":"10.1016\/j.inffus.2023.101803","article-title":"Large-group failure mode and effects analysis for risk management of angle grinders in the construction industry","volume":"97","author":"Chen","year":"2023","journal-title":"Inf. Fusion"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"137620","DOI":"10.1016\/j.jclepro.2023.137620","article-title":"Risk evaluation of photovoltaic power systems: An improved failure mode and effect analysis under uncertainty","volume":"414","author":"Li","year":"2023","journal-title":"J. Clean. Prod."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"109943","DOI":"10.1016\/j.ress.2024.109943","article-title":"An improved failure mode and effect analysis method for group decision-making in utility tunnels construction project risk evaluation","volume":"244","author":"Zhang","year":"2024","journal-title":"Reliab. Eng. Syst. Saf."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"102353","DOI":"10.1016\/j.aei.2024.102353","article-title":"Failure mode and effect analysis with ORESTE method under large group probabilistic free double hierarchy hesitant linguistic environment","volume":"59","author":"Wan","year":"2024","journal-title":"Adv. Eng. Inform."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"120016","DOI":"10.1016\/j.ins.2023.120016","article-title":"Failure mode and effects analysis in consensus-based GDM for surface-guided deep inspiration breath-hold breast radiotherapy for breast cancer under the framework of linguistic Z-number","volume":"658","author":"Mandal","year":"2024","journal-title":"Inf. Sci."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Zhang, L., Du, B., and Wu, L. (2024, January 1\u20133). A normal cloud model-based method for failure mode and effect analysis utilizing heterogeneous information. Proceedings of the 4th International Conference on Computer, Internet of Things and Control Engineering (CITCE 2024), Wuhan, China.","DOI":"10.1145\/3705677.3705702"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"762","DOI":"10.1080\/08982112.2018.1448089","article-title":"An improved approach for failure mode and effect analysis involving large group of experts: An application to the healthcare field","volume":"30","author":"Liu","year":"2018","journal-title":"Qual. Eng."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"118782","DOI":"10.1016\/j.eswa.2022.118782","article-title":"Large-scale group Delphi method with heterogeneous decision information and dynamic weights","volume":"213","author":"Yang","year":"2023","journal-title":"Expert Syst. Appl."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"116649","DOI":"10.1016\/j.est.2025.116649","article-title":"The trapezium cloud-based method with heterogeneous information for selecting phase change materials in the latent heat energy storage system","volume":"123","author":"Weng","year":"2025","journal-title":"J. Energy Storage"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"18024","DOI":"10.1109\/ACCESS.2025.3532961","article-title":"Improving quality evaluation for control systems of machining line product processing with smart algorithmic techniques in intuitionistic fuzzy multiple-attribute group decision-making","volume":"13","author":"He","year":"2025","journal-title":"IEEE Access"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"101964","DOI":"10.1016\/j.aei.2023.101964","article-title":"Large group decision-making based on interval rough integrated cloud model","volume":"56","author":"Jiang","year":"2023","journal-title":"Adv. Eng. Inform."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"120994","DOI":"10.1016\/j.ins.2024.120994","article-title":"Large group decision-making with a rough integrated asymmetric cloud model under multi-granularity linguistic environment","volume":"678","author":"Jiang","year":"2024","journal-title":"Inf. Sci."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"357","DOI":"10.1002\/int.20340","article-title":"A new cognitive model: Cloud model","volume":"24","author":"Li","year":"2009","journal-title":"Int. J. Intell. Syst."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1109\/91.493904","article-title":"Fuzzy logic = computing with words","volume":"4","author":"Zadeh","year":"1996","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1016\/j.ins.2013.04.006","article-title":"A group decision making model dealing with comparative linguistic expressions based on hesitant fuzzy linguistic term sets","volume":"241","author":"Herrera","year":"2013","journal-title":"Inf. Sci."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"114","DOI":"10.1016\/j.knosys.2013.10.014","article-title":"Encoding words into cloud models from interval-valued data via fuzzy statistics and membership function fitting","volume":"55","author":"Yang","year":"2014","journal-title":"Knowl.-Based Syst."},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Yang, X.J., Xu, Z.F., He, R.M., and Xue, F.X. (2019, January 3\u20136). Credibility assessment of complex simulation models using cloud models to represent and aggregate diverse evaluation results. Proceedings of the 15th International Conference on Intelligent Computing, Nanchang, China.","DOI":"10.1007\/978-3-030-26766-7_28"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"349","DOI":"10.3233\/FI-2016-1340","article-title":"Representation of the pairwise comparisons in AHP using hesitant cloud linguistic term sets","volume":"144","author":"Huang","year":"2016","journal-title":"Fundam. Informaticae"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/28\/3\/360\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,23]],"date-time":"2026-03-23T12:04:50Z","timestamp":1774267490000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/28\/3\/360"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,3,22]]},"references-count":41,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2026,3]]}},"alternative-id":["e28030360"],"URL":"https:\/\/doi.org\/10.3390\/e28030360","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,3,22]]}}}