{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:06:53Z","timestamp":1760234813004,"version":"build-2065373602"},"reference-count":37,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2021,6,17]],"date-time":"2021-06-17T00:00:00Z","timestamp":1623888000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>In this paper, we develop fuzzy, possibilistic hypothesis tests for testing crisp hypotheses for a distribution parameter from crisp data. In these tests, fuzzy statistics are used, which are produced by the possibility distribution of the estimated parameter, constructed by the known from crisp statistics confidence intervals. The results of these tests are in much better agreement with crisp statistics than the ones produced by the respective tests of a popular book on fuzzy statistics, which uses fuzzy critical values. We also present an error that we found in the implementation of the unbiased fuzzy estimator of the variance in this book, due to a poor interpretation of its mathematical content, which leads to disagreement of some fuzzy hypotheses tests with their respective crisp ones. Implementing correctly this estimator, we produce test statistics that achieve results in hypotheses tests that are in much better agreement with the results of the respective crisp ones.<\/jats:p>","DOI":"10.3390\/a14060185","type":"journal-article","created":{"date-parts":[[2021,6,17]],"date-time":"2021-06-17T11:20:26Z","timestamp":1623928826000},"page":"185","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Unbiased Fuzzy Estimators in Fuzzy Hypothesis Testing"],"prefix":"10.3390","volume":"14","author":[{"given":"Nikos","family":"Mylonas","sequence":"first","affiliation":[{"name":"Department of Civil Engineering, Democritus University of Thrace, 67100 Xanthi, Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6519-895X","authenticated-orcid":false,"given":"Basil","family":"Papadopoulos","sequence":"additional","affiliation":[{"name":"Department of Civil Engineering, Democritus University of Thrace, 67100 Xanthi, Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,6,17]]},"reference":[{"key":"ref_1","unstructured":"Hogg, R.V., and Tanis, E.A. (2001). Probability and Statistical Inference, Prentice Hall. [6th ed.]."},{"key":"ref_2","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_3","doi-asserted-by":"crossref","first-page":"239","DOI":"10.17713\/ajs.v32i3.459","article-title":"Trends in fuzzy statistics","volume":"32","author":"Taheri","year":"2003","journal-title":"Aust. J. Stat."},{"key":"ref_4","unstructured":"Gupta, M.M., Ragade, R.K., and Yager R., R. (1979). Fuzzy information and decision in a statistical model. Advances in Fuzzy Set Theory and Applications, North-Holland."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1016\/0165-0114(86)90076-X","article-title":"On the use of Zadeh\u2019s probabilistic definition for testing statistical hypotheses from fuzzy information","volume":"20","author":"Casals","year":"1986","journal-title":"Fuzzy Sets Syst."},{"key":"ref_6","first-page":"189","article-title":"Bayesian testing of fuzzy parametric hypotheses from fuzzy information","volume":"27","author":"Casals","year":"1993","journal-title":"Oper. Res."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1016\/0165-0114(93)90170-M","article-title":"A fuzzy statistical test of fuzzy hypotheses","volume":"53","author":"Watanabe","year":"1993","journal-title":"Fuzzy Sets Syst."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1007\/BF02614060","article-title":"An approach to fuzzy hypothesis testing","volume":"44","author":"Arnold","year":"1996","journal-title":"Metrika"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"323","DOI":"10.1016\/S0165-0114(96)00258-8","article-title":"Testing fuzzy hypotheses with crisp data","volume":"94","author":"Arnold","year":"1998","journal-title":"Fuzzy Sets Syst."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1007\/s001840050021","article-title":"Neyman-Pearson Lemma for fuzzy hypotheses testing","volume":"49","author":"Taheri","year":"1999","journal-title":"Metrika"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1016\/S0165-0114(00)00134-2","article-title":"ABayesian approach to fuzzy hypotheses testing","volume":"123","author":"Taheri","year":"2001","journal-title":"Fuzzy Sets Syst."},{"key":"ref_12","first-page":"27","article-title":"Optimal statistical tests based on fuzzy random variables","volume":"15","author":"Chachi","year":"2018","journal-title":"Iran. J. Fuzzy Syst."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"10385","DOI":"10.1007\/s00500-018-3590-2","article-title":"Testing statistical hypotheses for intuitionistic fuzzy data","volume":"23","author":"Akbari","year":"2019","journal-title":"Soft Comput."},{"key":"ref_14","first-page":"153","article-title":"Testing statistical hypotheses under fuzzy data and based on a new signed distance","volume":"15","author":"Arefi","year":"2018","journal-title":"Iran. J. Fuzzy Syst."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Hung, J.-L., Chen, C.-C., and Lai, C.-M. (2020). Possibility Measure of Accepting Statistical Hypothesis. Mathematics, 8.","DOI":"10.3390\/math8040551"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1016\/j.fss.2019.02.017","article-title":"Fuzzy hypothesis testing for a population proportion based on set-valued information","volume":"387","author":"Chukhrova","year":"2020","journal-title":"Fuzzy Sets Syst."},{"key":"ref_17","first-page":"1","article-title":"Randomized versus non-randomized hypergeometric hypothesis testing with crisp and fuzzy hypotheses","volume":"61","author":"Chukhrova","year":"2018","journal-title":"Stat. Pap."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1007\/s001840300269","article-title":"Testing hypotheses with fuzzy data: The fuzzy p-value","volume":"59","author":"Filzmoser","year":"2004","journal-title":"Metrika"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1007\/s00362-008-0133-4","article-title":"Fuzzy p-value in testing fuzzy hypotheses with crisp data","volume":"51","author":"Parchami","year":"2010","journal-title":"Stat Pap."},{"key":"ref_20","first-page":"1","article-title":"Fuzzy p-value of Hypotheses Tests with Crisp Data Using Non-Asymptotic Fuzzy Estimators","volume":"2","author":"Mylonas","year":"2021","journal-title":"J. Stoch. Anal."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"240","DOI":"10.1016\/j.ijar.2010.07.009","article-title":"Mark-recapture techniques in statistical tests for imprecise data","volume":"52","author":"Couso","year":"2011","journal-title":"Internat. J. Approx. Reason."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1007\/978-3-7908-1814-7_4","article-title":"Soft methods in hypotheses testing","volume":"Volume 76","author":"Ruan","year":"2001","journal-title":"Soft Computing for Risk Evaluation and Management: Applications in Technology, Environment and Finance, in Studies in Fuzziness and Soft Computing"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"2665","DOI":"10.1016\/j.fss.2003.08.009","article-title":"Possibilistic decisions and fuzzy statistical tests","volume":"157","author":"Hryniewicz","year":"2006","journal-title":"Fuzzy Sets Syst."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"544","DOI":"10.1016\/j.ijar.2017.12.003","article-title":"Statistical properties of the fuzzy p-value","volume":"93","author":"Hryniewicz","year":"2018","journal-title":"Internat. J. Approx. Reason."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Meier, A., Portmann, E., and Teran, L. (2019). Testing hypotheses by fuzzy methods: A comparison with the classical approach. Applying Fuzzy Logic for the Digital Economy and Society, in Fuzzy Management Methods, Springer.","DOI":"10.1007\/978-3-030-03368-2"},{"key":"ref_26","first-page":"67","article-title":"Fuzzy decision making in testing hypotheses: An introduction to the packages FPV and fuzzy.p.value with practical examples","volume":"17","author":"Parchami","year":"2020","journal-title":"Iran. J. Fuzzy Syst."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"107331","DOI":"10.1016\/j.asoc.2021.107331","article-title":"Fuzzy hypothesis testing: Systematic review and bibliography","volume":"106","author":"Chukhrova","year":"2021","journal-title":"Appl. Soft Comput."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"512","DOI":"10.1007\/s00500-004-0368-5","article-title":"Fuzzy statistics: Hypotheses testing","volume":"9","author":"Buckley","year":"2005","journal-title":"Soft Comput."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Buckley, J.J. (2004). Fuzzy Statistics, Springer.","DOI":"10.1007\/978-3-540-39919-3"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Mylonas, N., and Papadopoulos, B. (2021). Fuzzy hypotheses tests for crisp data using non-asymptotic fuzzy estimators and a degree of rejection or acceptance. Evol. Syst., 1\u201318.","DOI":"10.31390\/josa.2.1.01"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"446","DOI":"10.1016\/j.ins.2014.03.131","article-title":"Non-asymptotic fuzzy estimators based on confidence intervals","volume":"279","author":"Sfiris","year":"2014","journal-title":"Inf. Sci."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1023\/B:REOM.0000032115.22510.b5","article-title":"Probability-possibility transformations, triangular fuzzy-sets and probabilistic inequalities","volume":"10","author":"Dubois","year":"2004","journal-title":"Reliab. Comput."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"4593","DOI":"10.1016\/j.eswa.2009.12.049","article-title":"A new perspective on fuzzy process capability indices: Robustness","volume":"37","author":"Kaya","year":"2010","journal-title":"Expert Syst. Appl."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"483","DOI":"10.1007\/978-3-642-12052-7_20","article-title":"Fuzzy Process Capability Analysis and Applications","volume":"Volume 252","author":"Kahraman","year":"2010","journal-title":"Production Engineering and Management under Fuzziness, Studies in Fuzziness and Soft Computing"},{"key":"ref_35","unstructured":"Fuerstner, I. (2010). Process Capability and Six Sigma Methodology Including Fuzzy and Lean Approaches. Products and Services from R and D to Final Solutions, IntechOpen. Available online: https:\/\/www.intechopen.com\/books\/products-and-services\u2013from-r-d-to-final-solutions\/process-capability-and-six-sigma-methodology-including-fuzzy-and-lean-approaches."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1016\/0020-0255(83)90025-7","article-title":"Ranking of fuzzy numbers in the setting of possibility theory","volume":"30","author":"Dubois","year":"1983","journal-title":"Inf. Sci."},{"key":"ref_37","unstructured":"(2020, January 01). Hellenic National Meteorological Service. Available online: http:\/\/www.hnms.gr\/emy\/el\/climatology\/climatologymonth."}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/14\/6\/185\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T06:17:34Z","timestamp":1760163454000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/14\/6\/185"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,6,17]]},"references-count":37,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2021,6]]}},"alternative-id":["a14060185"],"URL":"https:\/\/doi.org\/10.3390\/a14060185","relation":{},"ISSN":["1999-4893"],"issn-type":[{"type":"electronic","value":"1999-4893"}],"subject":[],"published":{"date-parts":[[2021,6,17]]}}}