{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,4]],"date-time":"2026-06-04T03:35:08Z","timestamp":1780544108474,"version":"3.54.1"},"reference-count":52,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2023,1,3]],"date-time":"2023-01-03T00:00:00Z","timestamp":1672704000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Science and Technology Council, Taiwan","award":["MOST 110-2410-H-145-001"],"award-info":[{"award-number":["MOST 110-2410-H-145-001"]}]},{"name":"National Science and Technology Council, Taiwan","award":["MOST 111-2221-E-145-003"],"award-info":[{"award-number":["MOST 111-2221-E-145-003"]}]},{"name":"National Science and Technology Council, Taiwan","award":["MOST 111-2221-E-145-004"],"award-info":[{"award-number":["MOST 111-2221-E-145-004"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>Risk evaluation is an important part of the product design and product manufacturing process; it entails the pursuit of the highest product quality and preventing failure under the constraints of limited resources. The failure mode and effects analysis approach is one of the most widely applied risk evaluation tools that uses the product of the three risk elements of product failure items, severity, occurrence probability, and detection probability, to calculate the risk priority number, the priority of failure risk. However, the typical failure mode and effects analysis method ignores the consideration of objective weights, which may lead to incorrect evaluation results. Moreover, the method of expressing information about product failure provided by experts also directly affects the results of risk assessment. To comprehensively assess the risk of product failure, in this study, the hybrid of the Fermatean fuzzy set and entropy method was used to prioritize product failure items risk. This study used a service failure mode and effects analysis numerical example of self-service electric vehicles to illustrate and test the correctness of the proposed new hybrid Fermatean fuzzy set and entropy method. The mathematical operation results were also compared with the listing of different calculation methods. The test results prove that the proposed new hybrid Fermatean fuzzy set and entropy method can fully consider the cognitive information provided by experts to provide more accurate risk ranking results of failure items.<\/jats:p>","DOI":"10.3390\/axioms12010058","type":"journal-article","created":{"date-parts":[[2023,1,4]],"date-time":"2023-01-04T03:27:44Z","timestamp":1672802864000},"page":"58","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":19,"title":["A New Hybrid Fermatean Fuzzy Set and Entropy Method for Risk Assessment"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9630-7386","authenticated-orcid":false,"given":"Kuei-Hu","family":"Chang","sequence":"first","affiliation":[{"name":"Department of Management Sciences, R.O.C. Military Academy, Kaohsiung 830, Taiwan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hsiang-Yu","family":"Chung","sequence":"additional","affiliation":[{"name":"Department of Management Sciences, R.O.C. Military Academy, Kaohsiung 830, Taiwan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2374-3830","authenticated-orcid":false,"given":"Chia-Nan","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Industrial Engineering and Management, National Kaohsiung University of Science and Technology, Kaohsiung 807618, Taiwan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yu-Dian","family":"Lai","sequence":"additional","affiliation":[{"name":"Department of Leisure Industry Management, National Chin-Yi University of Technology, Taichung 411, Taiwan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chi-Hung","family":"Wu","sequence":"additional","affiliation":[{"name":"Department of Management Sciences, R.O.C. Military Academy, Kaohsiung 830, Taiwan"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,1,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2625","DOI":"10.3233\/JIFS-17594","article-title":"Soft failure mode and effects analysis using the OWG operator and hesitant fuzzy linguistic term sets","volume":"34","author":"Chang","year":"2018","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"609","DOI":"10.1007\/s10661-022-10248-9","article-title":"Risk assessment of physical unit operations of wastewater treatment plant using fuzzy FMEA method: A case study in the northwest of Iran","volume":"194","author":"Alizadeh","year":"2022","journal-title":"Environ. Monit. 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