{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,16]],"date-time":"2025-10-16T10:05:03Z","timestamp":1760609103928,"version":"build-2065373602"},"reference-count":57,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2018,8,17]],"date-time":"2018-08-17T00:00:00Z","timestamp":1534464000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61671384","61703338"],"award-info":[{"award-number":["61671384","61703338"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Fault diagnosis is an important issue in various fields and aims to detect and identify the faults of systems, products, and processes. The cause of a fault is complicated due to the uncertainty of the actual environment. Nevertheless, it is difficult to consider uncertain factors adequately with many traditional methods. In addition, the same fault may show multiple features and the same feature might be caused by different faults. In this paper, a neutrosophic set based fault diagnosis method based on multi-stage fault template data is proposed to solve this problem. For an unknown fault sample whose fault type is unknown and needs to be diagnosed, the neutrosophic set based on multi-stage fault template data is generated, and then the generated neutrosophic set is fused via the simplified neutrosophic weighted averaging (SNWA) operator. Afterwards, the fault diagnosis results can be determined by the application of defuzzification method for a defuzzying neutrosophic set. Most kinds of uncertain problems in the process of fault diagnosis, including uncertain information and inconsistent information, could be handled well with the integration of multi-stage fault template data and the neutrosophic set. Finally, the practicality and effectiveness of the proposed method are demonstrated via an illustrative example.<\/jats:p>","DOI":"10.3390\/sym10080346","type":"journal-article","created":{"date-parts":[[2018,8,17]],"date-time":"2018-08-17T10:54:25Z","timestamp":1534503265000},"page":"346","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["A Neutrosophic Set Based Fault Diagnosis Method Based on Multi-Stage Fault Template Data"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5429-2748","authenticated-orcid":false,"given":"Wen","family":"Jiang","sequence":"first","affiliation":[{"name":"School of Electronics and Information, Northwestern Polytechnical University, Xi\u2019an 710072, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yu","family":"Zhong","sequence":"additional","affiliation":[{"name":"School of Electronics and Information, Northwestern Polytechnical University, Xi\u2019an 710072, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xinyang","family":"Deng","sequence":"additional","affiliation":[{"name":"School of Electronics and Information, Northwestern Polytechnical University, Xi\u2019an 710072, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,8,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1155\/2014\/472395","article-title":"Actuator fault diagnosis in a Boeing 747 model via adaptive modified two-stage Kalman filter","volume":"2014","author":"Caliskan","year":"2014","journal-title":"Int. J. Aerosp. Eng."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1039","DOI":"10.21595\/jve.2017.18401","article-title":"Vibroacoustic technique for the fault diagnosis in a gear transmission of a military helicopter","volume":"19","author":"Zieja","year":"2017","journal-title":"J. Vibroeng."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"128","DOI":"10.1016\/j.mineng.2018.03.029","article-title":"Fault diagnosis and economic performance evaluation for a simulated base metal leaching operation","volume":"123","author":"Strydom","year":"2018","journal-title":"Miner. Eng."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"3419","DOI":"10.1109\/TIE.2013.2238871","article-title":"Bearing fault diagnosis for direct-drive wind turbines via current-demodulated signals","volume":"60","author":"Gong","year":"2013","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Zhang, C., Li, D., Broumi, S., and Sangaiah, A.K. (2018). Medical diagnosis based on single-valued neutrosophic probabilistic rough multisets over two universes. Symmetry, 10.","DOI":"10.3390\/sym10060213"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"467","DOI":"10.1007\/s10836-016-5602-4","article-title":"Fault diagnosis in highly dependable medical wearable systems","volume":"32","author":"Oliveira","year":"2016","journal-title":"J. Electron. Test."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"20","DOI":"10.1016\/j.apacoust.2016.10.012","article-title":"Diagnosis of stator faults of the single-phase induction motor using acoustic signals","volume":"117","author":"Glowacz","year":"2016","journal-title":"Appl. Acoust."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1155\/2018\/8218657","article-title":"Research on Fault Diagnosis Based on Singular Value Decomposition and Fuzzy Neural Network","volume":"2018","author":"Gai","year":"2018","journal-title":"Shock Vib."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"898","DOI":"10.1007\/s10489-016-0870-3","article-title":"An improved distance-based total uncertainty measure in belief function theory","volume":"46","author":"Deng","year":"2017","journal-title":"Appl. Intell."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1016\/j.anucene.2018.03.028","article-title":"Dependence assessment in human reliability analysis using an evidential network approach extended by belief rules and uncertainty measures","volume":"117","author":"Deng","year":"2018","journal-title":"Ann. Nucl. Energy"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1869","DOI":"10.1002\/int.21999","article-title":"Analyzing the monotonicity of belief interval based uncertainty measures in belief function theory","volume":"33","author":"Deng","year":"2018","journal-title":"Int. J. Intell. Syst."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"340","DOI":"10.1016\/j.apm.2017.07.032","article-title":"A modified Physarum-inspired model for the user equilibrium traffic assignment problem","volume":"55","author":"Xu","year":"2018","journal-title":"Appl. Math. Model."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1016\/j.inffus.2018.04.003","article-title":"Multi-sensor data fusion based on the belief divergence measure of evidences and the belief entropy","volume":"46","author":"Xiao","year":"2019","journal-title":"Inf. Fusion"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1016\/S0952-1976(03)00022-8","article-title":"Fault diagnosis based on rough set theory","volume":"16","author":"Tay","year":"2003","journal-title":"Eng. Appl. Artif. Intell."},{"key":"ref_15","first-page":"1","article-title":"Improving rolling bearing fault diagnosis by DS evidence theory based fusion model","volume":"2017","author":"Yao","year":"2017","journal-title":"J. Sens."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"501","DOI":"10.1002\/qre.2268","article-title":"Failure mode and effects analysis based on Dnumbers and TOPSIS","volume":"34","author":"Bian","year":"2018","journal-title":"Qual. Reliab. Eng. Int."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1007\/BF02683884","article-title":"Improving the dynamic range of real-time X-ray imaging systems via Bayesian fusion","volume":"16","author":"Dromigny","year":"1997","journal-title":"J. Nondestruct. Eval."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Rodrigues, M.A., Liu, Y., Bottaci, L., and Rigas, D.I. (2000, January 19\u201322). Learning and diagnosis in manufacturing processes through an executable Bayesian network. Proceedings of the International Conference on Industrial, Engineering and Other Applications of Applied Intelligent Systems, New Orleans, LA, USA.","DOI":"10.1007\/3-540-45049-1_47"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1016\/S0888-613X(01)00036-6","article-title":"Bayesian model-based diagnosis","volume":"27","author":"Lucas","year":"2001","journal-title":"Int. J. Approx. Reason."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1016\/j.inffus.2005.07.003","article-title":"Engine fault diagnosis based on multi-sensor information fusion using Dempster\u2013Shafer evidence theory","volume":"8","author":"Basir","year":"2007","journal-title":"Inf. Fusion"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1214\/aoms\/1177698950","article-title":"Upper and lower probabilities induced by a multivalued mapping","volume":"38","author":"Dempster","year":"1967","journal-title":"Ann. Math. Stat."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Shafer, G. (1976). A Mathematical Theory of Evidence, Princeton University Press.","DOI":"10.1515\/9780691214696"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Jiang, W., Chang, Y., and Wang, S. (2017). A method to identify the incomplete framework of discernment in evidence theory. Math. Probl. Eng., 2017.","DOI":"10.1155\/2017\/7635972"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1264","DOI":"10.1002\/int.21980","article-title":"An improved soft likelihood function for Dempster-Shafer belief structures","volume":"33","author":"Jiang","year":"2018","journal-title":"Int. J. Intell. Syst."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"547","DOI":"10.1016\/S0167-8655(02)00276-3","article-title":"Uncertainty modelling using Dempster\u2013Shafer theory for improving detection of weld defects","volume":"24","author":"Kaftandjian","year":"2003","journal-title":"Pattern Recognit. Lett."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"82","DOI":"10.1016\/j.apacoust.2018.03.010","article-title":"Acoustic based fault diagnosis of three-phase induction motor","volume":"137","author":"Glowacz","year":"2018","journal-title":"Appl. Acoust."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.measurement.2017.08.036","article-title":"Early fault diagnosis of bearing and stator faults of the single-phase induction motor using acoustic signals","volume":"113","author":"Glowacz","year":"2018","journal-title":"Measurement"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"83","DOI":"10.12911\/22998993\/79447","article-title":"Monitoring of the noise emitted by machine tools in industrial conditions","volume":"19","author":"Jozwik","year":"2018","journal-title":"J. Ecol. Eng."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"2368","DOI":"10.1109\/TDEI.2015.004855","article-title":"An integrated method of set pair analysis and association rule for fault diagnosis of power transformers","volume":"22","author":"Lee","year":"2015","journal-title":"IEEE Trans. Dielectr. Electr. Insul."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"651","DOI":"10.1016\/j.neucom.2017.06.024","article-title":"A novel fault diagnosis method based on optimal relevance vector machine","volume":"267","author":"He","year":"2017","journal-title":"Neurocomputing"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"429","DOI":"10.1016\/j.measurement.2017.11.035","article-title":"A feature extraction and visualization method for fault detection of marine diesel engines","volume":"116","author":"Xi","year":"2017","journal-title":"Meas. J. Int. Meas. Confed."},{"key":"ref_32","first-page":"447","article-title":"Effect of the disc processing technology on the vibration level of the chipper during operations","volume":"21","author":"Krolczyk","year":"2014","journal-title":"Teh. Vjesn."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Merizalde, Y., Hernandez-Callejo, L., and Duque-Perez, O. (2017). State of the art and trends in the monitoring, detection and diagnosis of failures in electric induction motors. Energies, 10.","DOI":"10.3390\/en10071056"},{"key":"ref_34","first-page":"489","article-title":"A unifying field in logics: Neutrosophic logic","volume":"8","author":"Smarandache","year":"1999","journal-title":"Mult. Valued Logic"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1817","DOI":"10.1007\/s00521-015-2154-y","article-title":"Complex neutrosophic set","volume":"28","author":"Ali","year":"2017","journal-title":"Neural Comput. Appl."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Zhang, X., Bo, C., Smarandache, F., and Park, C. (2018). New operations of totally dependent-neutrosophic sets and totally dependent-neutrosophic soft sets. Symmetry, 10.","DOI":"10.3390\/sym10060187"},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Ali, M., Smarandache, F., and Khan, M. (2017). Study on the development of neutrosophic triplet ting and neutrosophic triplet field. Mathematics, 6.","DOI":"10.3390\/math6040046"},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Li, X., Zhang, X., and Park, C. (2018). Generalized interval neutrosophic choquet aggregation operators and their applications. Symmetry, 10.","DOI":"10.3390\/sym10040085"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"338","DOI":"10.1016\/S0019-9958(65)90241-X","article-title":"Fuzzy sets","volume":"8","author":"Zadeh","year":"1965","journal-title":"Inf. Control"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1016\/S0165-0114(86)80034-3","article-title":"Intuitionistic fuzzy sets","volume":"20","author":"Atanassov","year":"1986","journal-title":"Fuzzy Sets Syst."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1002\/int.21939","article-title":"Intuitionistic fuzzy power aggregation operator based on entropy and its application in decision making","volume":"33","author":"Jiang","year":"2018","journal-title":"Int. J. Intell. Syst."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1016\/0165-0114(86)90077-1","article-title":"Interval valued fuzzy sets based on normal forms","volume":"20","author":"Turksen","year":"1986","journal-title":"Fuzzy Sets Syst."},{"key":"ref_43","unstructured":"Wang, H., Smarandache, F., Zhang, Y., and Sunderraman, R. (2005, January 21\u201326). Single valued neutrosophic sets. Proceedings of the 8th Joint Conference on Information Sciences, Salt Lake, UT, USA."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"2459","DOI":"10.3233\/IFS-130916","article-title":"A multicriteria decision-making method using aggregation operators for simplified neutrosophic sets","volume":"26","author":"Ye","year":"2014","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"2001","DOI":"10.1007\/s00521-014-1688-8","article-title":"Multiple attribute decision-making method based on single-valued neutrosophic normalized weighted Bonferroni mean","volume":"25","author":"Liu","year":"2014","journal-title":"Neural Comput. Appl."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"2342","DOI":"10.1080\/00207721.2014.994050","article-title":"Simplified neutrosophic sets and their applications in multi-criteria group decision-making problems","volume":"47","author":"Peng","year":"2016","journal-title":"Int. J. Syst. Sci."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"817","DOI":"10.1007\/s00500-015-1818-y","article-title":"Single-valued neutrosophic similarity measures based on cotangent function and their application in the fault diagnosis of steam turbine","volume":"21","author":"Ye","year":"2017","journal-title":"Soft Comput."},{"key":"ref_48","unstructured":"Ye, J. (2016). Fault diagnoses of hydraulic turbine using the dimension root similarity measure of single-valued neutrosophic sets. Intell. Autom. Soft Comput., 1\u20138."},{"key":"ref_49","first-page":"42","article-title":"Misfire fault diagnosis method of gasoline engines using the cosine similarity measure of neutrosophic numbers","volume":"8","author":"Kong","year":"2015","journal-title":"Neutrosophic Sets Syst."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"2829","DOI":"10.3233\/JIFS-169165","article-title":"Steam turbine fault diagnosis based on single-valued neutrosophic multigranulation rough sets over two universes","volume":"31","author":"Zhang","year":"2016","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"672","DOI":"10.1016\/j.asoc.2017.04.008","article-title":"Failure Mode and Effects Analysis based on a novel fuzzy evidential method","volume":"57","author":"Jiang","year":"2017","journal-title":"Appl. Soft Comput."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1016\/j.knosys.2018.03.014","article-title":"An evidential dynamical model to predict the interference effect of categorization on decision making","volume":"150","author":"He","year":"2018","journal-title":"Knowl. Based Syst."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"673","DOI":"10.1016\/j.anucene.2017.10.045","article-title":"Dependence Assessment in Human Reliability Analysis Based on Evidence Credibility Decay Model and IOWA Operator","volume":"112","author":"Zheng","year":"2018","journal-title":"Ann. Nucl. Energy"},{"key":"ref_54","first-page":"171","article-title":"Data fusion algorithm of fault diagnosis considering sensor measurement uncertainty","volume":"6","author":"Xu","year":"2013","journal-title":"Int. J. Smart Sens. Intell. Syst"},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1145\/584091.584093","article-title":"A mathematical theory of communication","volume":"5","author":"Shannon","year":"2001","journal-title":"ACM SIGMOBILE Mob. Comput. Commun. Rev."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"11363","DOI":"10.1016\/j.eswa.2009.03.039","article-title":"A multi-criteria intuitionistic fuzzy group decision making for supplier selection with TOPSIS method","volume":"36","author":"Boran","year":"2009","journal-title":"Expert Syst. Appl."},{"key":"ref_57","unstructured":"Xu, X., and Wen, C. (2012). Theory and Application of Multi-Source and Uncertain Information Fusion, Science Press."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/10\/8\/346\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:19:16Z","timestamp":1760195956000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/10\/8\/346"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,8,17]]},"references-count":57,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2018,8]]}},"alternative-id":["sym10080346"],"URL":"https:\/\/doi.org\/10.3390\/sym10080346","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2018,8,17]]}}}