{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,7]],"date-time":"2026-05-07T04:18:50Z","timestamp":1778127530377,"version":"3.51.4"},"reference-count":60,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2023,5,15]],"date-time":"2023-05-15T00:00:00Z","timestamp":1684108800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Natural Science Basic Research Program of Shaanxi","award":["2023-JC-QN-0689"],"award-info":[{"award-number":["2023-JC-QN-0689"]}]},{"name":"Natural Science Basic Research Program of Shaanxi","award":["G2022WD01010"],"award-info":[{"award-number":["G2022WD01010"]}]},{"name":"NWPU Research Fund for Young Scholars","award":["2023-JC-QN-0689"],"award-info":[{"award-number":["2023-JC-QN-0689"]}]},{"name":"NWPU Research Fund for Young Scholars","award":["G2022WD01010"],"award-info":[{"award-number":["G2022WD01010"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The failure mode and effects analysis (FMEA) is a commonly adopted approach in engineering failure analysis, wherein the risk priority number (RPN) is utilized to rank failure modes. However, assessments made by FMEA experts are full of uncertainty. To deal with this issue, we propose a new uncertainty management approach for the assessments given by experts based on negation information and belief entropy in the Dempster\u2013Shafer evidence theory framework. First, the assessments of FMEA experts are modeled as basic probability assignments (BPA) in evidence theory. Next, the negation of BPA is calculated to extract more valuable information from a new perspective of uncertain information. Then, by utilizing the belief entropy, the degree of uncertainty of the negation information is measured to represent the uncertainty of different risk factors in the RPN. Finally, the new RPN value of each failure mode is calculated for the ranking of each FMEA item in risk analysis. The rationality and effectiveness of the proposed method is verified through its application in a risk analysis conducted for an aircraft turbine rotor blade.<\/jats:p>","DOI":"10.3390\/e25050800","type":"journal-article","created":{"date-parts":[[2023,5,15]],"date-time":"2023-05-15T03:40:26Z","timestamp":1684122026000},"page":"800","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Uncertainty Management in Assessment of FMEA Expert Based on Negation Information and Belief Entropy"],"prefix":"10.3390","volume":"25","author":[{"given":"Lei","family":"Wu","sequence":"first","affiliation":[{"name":"School of Information Science and Engineering, Zaozhuang University, Zaozhuang 277160, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2568-9628","authenticated-orcid":false,"given":"Yongchuan","family":"Tang","sequence":"additional","affiliation":[{"name":"School of Microelectronics, Northwestern Polytechnical University, Xi\u2019an 710072, China"}]},{"given":"Liuyuan","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Big Data and Software Engineering, Chongqing University, Chongqing 401331, China"}]},{"given":"Yubo","family":"Huang","sequence":"additional","affiliation":[{"name":"School of Engineering, University of Warwick, Coventry CV4 7AL, UK"}]}],"member":"1968","published-online":{"date-parts":[[2023,5,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"520","DOI":"10.1016\/j.ins.2022.03.013","article-title":"A novel fault diagnosis method of smart grids based on memory spiking neural P systems considering measurement tampering attacks","volume":"596","author":"Wang","year":"2022","journal-title":"Inf. Sci."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1214\/aoms\/1177698950","article-title":"Upper and Lower Probabilities Induced by a Multi-valued Mapping","volume":"38","author":"Dempster","year":"1967","journal-title":"Ann. Math. Stat."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Shafer, G. (1976). A Mathematical Theory of Evidence, Princeton University Press.","DOI":"10.1515\/9780691214696"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"103680","DOI":"10.1016\/j.engappai.2020.103680","article-title":"A weighted corrective fuzzy reasoning spiking neural P system for fault diagnosis in power systems with variable topologies","volume":"92","author":"Wang","year":"2020","journal-title":"Eng. Appl. Artif. Intell."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"540","DOI":"10.1016\/j.ins.2022.08.077","article-title":"Interpretable fuzzy clustering using unsupervised fuzzy decision trees","volume":"611","author":"Jiao","year":"2022","journal-title":"Inf. Sci."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1007\/s13198-013-0145-x","article-title":"Fuzzy fault tree analysis: A review of concept and application","volume":"4","author":"Mahmood","year":"2013","journal-title":"Int. J. Syst. Assur. Eng. Manag."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"352","DOI":"10.17531\/ein.2020.2.18","article-title":"Estimation of maintenance costs of a pipeline for a U-shaped hazard rate function in the imprecise setting","volume":"22","author":"Romaniuk","year":"2020","journal-title":"Eksploat. I Niezawodn."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1607","DOI":"10.1109\/TCYB.2021.3107040","article-title":"Enhanced fuzzy fault estimation of discrete-time nonlinear systems via a new real-time gain-scheduling mechanism","volume":"53","author":"Xie","year":"2021","journal-title":"IEEE Trans. Cybern."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"121907","DOI":"10.1016\/j.energy.2021.121907","article-title":"Risk assessment of renewable energy investments: A modified failure mode and effect analysis based on prospect theory and intuitionistic fuzzy AHP","volume":"239","author":"Ilbahar","year":"2022","journal-title":"Energy"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1007\/BF01001956","article-title":"Rough sets","volume":"11","author":"Pawlak","year":"1982","journal-title":"Int. J. Comput. Inf. Sci."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0169-7439(98)00200-7","article-title":"Rough sets theory","volume":"47","author":"Walczak","year":"1999","journal-title":"Chemom. Intell. Lab. Syst."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"501","DOI":"10.1002\/qre.2268","article-title":"Failure mode and effects analysis based on D numbers and TOPSIS","volume":"34","author":"Bian","year":"2018","journal-title":"Qual. Reliab. Eng. Int."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1016\/j.ins.2020.04.006","article-title":"A novel linguistic approach for multi-granular information fusion and decision-making using risk-based linguistic D numbers","volume":"530","author":"Seiti","year":"2020","journal-title":"Inf. Sci."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"206","DOI":"10.1016\/j.ins.2019.01.006","article-title":"R-numbers, a new risk modeling associated with fuzzy numbers and its application to decision making","volume":"483","author":"Seiti","year":"2019","journal-title":"Inf. Sci."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"130146","DOI":"10.1016\/j.jclepro.2021.130146","article-title":"An integrated framework for new sustainable waste-to-energy technology selection and risk assessment: An R-TODIM-R-MULTIMOOSRAL approach","volume":"335","author":"Mousavi","year":"2022","journal-title":"J. Clean. Prod."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"9793","DOI":"10.1007\/s00500-019-03804-y","article-title":"A new rule to combine dependent bodies of evidence","volume":"23","author":"Su","year":"2019","journal-title":"Soft Comput."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Tang, Y., Chen, Y., and Zhou, D. (2022). Measuring Uncertainty in the Negation Evidence for Multi-Source Information Fusion. Entropy, 24.","DOI":"10.3390\/e24111596"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1016\/j.ins.2020.01.021","article-title":"Multiple criteria group decision making based on group satisfaction","volume":"518","author":"Fu","year":"2020","journal-title":"Inf. Sci."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1016\/j.eswa.2015.09.006","article-title":"A hybrid fuzzy evaluation method for curtain grouting efficiency assessment based on an AHP method extended by D numbers","volume":"44","author":"Fan","year":"2016","journal-title":"Expert Syst. Appl."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1683","DOI":"10.1007\/s11227-022-04739-2","article-title":"Decision-making for the anomalies in IIoTs based on 1D convolutional neural networks and Dempster\u2013Shafer theory (DS-1DCNN)","volume":"79","author":"Ebrahimpour","year":"2023","journal-title":"J. Supercomput."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"618","DOI":"10.1109\/TFUZZ.2019.2911915","article-title":"Evidence combination based on credal belief redistribution for pattern classification","volume":"28","author":"Liu","year":"2019","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"18182","DOI":"10.1109\/ACCESS.2020.2966260","article-title":"Fault diagnosis based on non-negative sparse constrained deep neural networks and Dempster\u2013Shafer theory","volume":"8","author":"Zhang","year":"2020","journal-title":"IEEE Access"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"095002","DOI":"10.1088\/1361-6501\/ab842f","article-title":"A fault diagnosis model based on singular value manifold features, optimized SVMs and multi-sensor information fusion","volume":"31","author":"Su","year":"2020","journal-title":"Meas. Sci. Technol."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Alhijazi, M., Zeeshan, Q., and Ghasemian, H. (2019, January 2\u20133). Failure Mode and Effect Analysis (FMEA) of Vertical Axis Wind Turbines. Proceedings of the Industrial Engineering in the Digital Disruption Era: Selected papers from the Global Joint Conference on Industrial Engineering and Its Application Areas, GJCIE 2019, Gazimagusa, North Cyprus, Turkey.","DOI":"10.1007\/978-3-030-42416-9_6"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Demirci, M., Saka, M., Gozde, H., Dursun, M., and Taplamacioglu, M.C. (2022, January 29\u201331). Dempster Shafer Evidence Theory Application for Fault Diagnosis of Power Transformers. Proceedings of the 2022 9th International Conference on Electrical and Electronics Engineering (ICEEE), Alanya, Turkey.","DOI":"10.1109\/ICEEE55327.2022.9772608"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"220","DOI":"10.1016\/j.ejor.2014.06.033","article-title":"Evaluating risk of water mains failure using a Bayesian belief network model","volume":"240","author":"Kabir","year":"2015","journal-title":"Eur. J. Oper. Res."},{"key":"ref_27","first-page":"77","article-title":"Development of a hybrid AHP and Dempster-Shafer theory of evidence for project risk assessment problem","volume":"7","author":"Albogami","year":"2022","journal-title":"J. Proj. Manag."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"7163","DOI":"10.1007\/s13369-022-07560-4","article-title":"An Improved Failure Mode and Effects Analysis Method Using Belief Jensen\u2013Shannon Divergence and Entropy Measure in the Evidence Theory","volume":"48","author":"Tang","year":"2023","journal-title":"Arab. J. Sci. Eng."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Shams, G., Hatefi, S.M., and Nemati, S. (2022). A Dempster-Shafer evidence theory for environmental risk assessment in failure modes and effects analysis of Oil and Gas Exploitation Plant. Sci. Iran.","DOI":"10.24200\/sci.2022.56162.4580"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Fabis-Domagala, J., Domagala, M., and Momeni, H. (2021). A Concept of Risk Prioritization in FMEA Analysis for Fluid Power Systems. Energies, 14.","DOI":"10.3390\/en14206482"},{"key":"ref_31","first-page":"85","article-title":"A simple view of the Dempster-Shafer theory of evidence and its implication for the rule of combination","volume":"7","author":"Zadeh","year":"1986","journal-title":"AI Mag."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"210201","DOI":"10.1007\/s11432-020-3006-9","article-title":"Uncertainty measure in evidence theory","volume":"63","author":"Deng","year":"2020","journal-title":"Sci. China Inf. Sci."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"549","DOI":"10.1016\/j.chaos.2016.07.014","article-title":"Deng entropy","volume":"91","author":"Deng","year":"2016","journal-title":"Chaos, Solitons Fractals"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"890","DOI":"10.1109\/TSMCA.2005.853483","article-title":"Measuring ambiguity in the evidence theory","volume":"36","author":"Jousselme","year":"2006","journal-title":"IEEE Trans. Syst. Man Cybern. Part A Syst. Humans"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1016\/j.ijar.2017.10.010","article-title":"A new definition of entropy of belief functions in the Dempster\u2013Shafer theory","volume":"92","author":"Shenoy","year":"2018","journal-title":"Int. J. Approx. Reason."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"260","DOI":"10.1016\/j.ijar.2020.01.004","article-title":"On properties of a new decomposable entropy of Dempster-Shafer belief functions","volume":"119","author":"Shenoy","year":"2020","journal-title":"Int. J. Approx. Reason."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"94","DOI":"10.1016\/j.ijar.2018.09.001","article-title":"A correlation coefficient for belief functions","volume":"103","author":"Jiang","year":"2018","journal-title":"Int. J. Approx. Reason."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1016\/j.ress.2017.11.024","article-title":"Improving failure analysis efficiency by combining FTA and FMEA in a recursive manner","volume":"172","author":"Peeters","year":"2018","journal-title":"Reliab. Eng. Syst. Saf."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"74628","DOI":"10.1109\/ACCESS.2018.2883115","article-title":"Application of a Genetic-Fuzzy FMEA to Rainfed Lowland Rice Production in Sarawak: Environmental, Health, and Safety Perspectives","volume":"6","author":"Sang","year":"2018","journal-title":"IEEE Access"},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Batbayar, K., Tak\u00e1cs, M., and Kozlovszky, M. (2016, January 12\u201314). Medical device software risk assessment using FMEA and fuzzy linguistic approach: Case study. Proceedings of the 2016 IEEE 11th International Symposium on Applied Computational Intelligence and Informatics (SACI), Timisoara, Romania.","DOI":"10.1109\/SACI.2016.7507369"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"1242","DOI":"10.1016\/j.ifacol.2019.11.368","article-title":"Application of a FMEA method combining interval 2-tuple linguistic variables and grey relational analysis in preoperative medical service process","volume":"52","author":"Shi","year":"2019","journal-title":"IFAC-PapersOnLine"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"890","DOI":"10.1002\/qre.2607","article-title":"Fuzzy smart failure modes and effects analysis to improve safety performance of system: Case study of an aircraft landing system","volume":"36","author":"Daneshvar","year":"2020","journal-title":"Qual. Reliab. Eng. Int."},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Anes, V., Morgado, T., Abreu, A., Calado, J., and Reis, L. (2022). Updating the FMEA Approach with Mitigation Assessment Capabilities. Appl. Sci., 12.","DOI":"10.3390\/app122211407"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1016\/j.procs.2021.01.160","article-title":"Optimization of condition-based maintenance strategy prediction for aging automotive industrial equipment using FMEA","volume":"180","author":"Ramere","year":"2021","journal-title":"Procedia Comput. Sci."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"106019","DOI":"10.1016\/j.engfailanal.2021.106019","article-title":"Application of 8D methodology: An approach to reduce failures in automotive industry","volume":"134","year":"2022","journal-title":"Eng. Fail. Anal."},{"key":"ref_46","doi-asserted-by":"crossref","unstructured":"Takahashi, M., Anang, Y., and Watanabe, Y. (2021). A safety analysis method for control software in coordination with FMEA and FTA. Information, 12.","DOI":"10.3390\/info12020079"},{"key":"ref_47","doi-asserted-by":"crossref","unstructured":"Kadena, E., Ko\u00e7ak, S., Tak\u00e1cs-Gy\u00f6rgy, K., and Keszthelyi, A. (2022). FMEA in Smartphones: A Fuzzy Approach. Mathematics, 10.","DOI":"10.3390\/math10030513"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"19144","DOI":"10.1109\/ACCESS.2017.2751505","article-title":"Hydro-pneumatic suspension system hybrid reliability modeling considering the temperature influence","volume":"5","author":"Jiao","year":"2017","journal-title":"IEEE Access"},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"4512383","DOI":"10.1155\/2016\/4512383","article-title":"A Modified Model of Failure Mode and Effects Analysis Based on Generalized Evidence Theory","volume":"2016","author":"Zhou","year":"2016","journal-title":"Math. Probl. Eng."},{"key":"ref_50","doi-asserted-by":"crossref","unstructured":"Liu, H.C. (2016). FMEA Using Uncertainty Theories and MCDM Methods, Springer.","DOI":"10.1007\/978-981-10-1466-6"},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"579","DOI":"10.1016\/j.asoc.2014.11.036","article-title":"A novel approach for failure mode and effects analysis using combination weighting and fuzzy VIKOR method","volume":"28","author":"Liu","year":"2015","journal-title":"Appl. Soft Comput."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"257","DOI":"10.1016\/j.jsm.2019.08.002","article-title":"Fuzzy-FMEA risk evaluation approach for LHD machine\u2013A case study","volume":"18","author":"Balaraju","year":"2019","journal-title":"J. Sustain. Min."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"4779","DOI":"10.1007\/s00500-017-2664-x","article-title":"A new method to evaluate risk in failure mode and effects analysis under fuzzy information","volume":"22","author":"Huang","year":"2018","journal-title":"Soft Comput."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1109\/TFUZZ.2018.2871756","article-title":"The negation of a basic probability assignment","volume":"27","author":"Yin","year":"2018","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"869","DOI":"10.3233\/IFS-151809","article-title":"A risk assessment approach for failure mode and effects analysis based on intuitionistic fuzzy sets and evidence theory","volume":"30","author":"Guo","year":"2016","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"1162","DOI":"10.1016\/j.engfailanal.2011.02.004","article-title":"Multiple failure modes analysis and weighted risk priority number evaluation in FMEA","volume":"18","author":"Xiao","year":"2011","journal-title":"Eng. Fail. Anal."},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0888-613X(02)00066-X","article-title":"The application of the matrix calculus to belief functions","volume":"31","author":"Smets","year":"2002","journal-title":"Int. J. Approx. Reason."},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"2084","DOI":"10.1016\/j.engfailanal.2011.06.014","article-title":"Risk evaluation in failure mode and effects analysis of aircraft turbine rotor blades using Dempster\u2013Shafer evidence theory under uncertainty","volume":"18","author":"Yang","year":"2011","journal-title":"Eng. Fail. Anal."},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"27103","DOI":"10.1109\/ACCESS.2018.2836139","article-title":"AMWRPN: Ambiguity measure weighted risk priority number model for failure mode and effects analysis","volume":"6","author":"Tang","year":"2018","journal-title":"IEEE Access"},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"164","DOI":"10.1016\/j.engfailanal.2012.07.009","article-title":"An improved method for risk evaluation in failure modes and effects analysis of aircraft engine rotor blades","volume":"26","author":"Su","year":"2012","journal-title":"Eng. Fail. Anal."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/25\/5\/800\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T19:35:04Z","timestamp":1760124904000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/25\/5\/800"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,5,15]]},"references-count":60,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2023,5]]}},"alternative-id":["e25050800"],"URL":"https:\/\/doi.org\/10.3390\/e25050800","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,5,15]]}}}