{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:52:08Z","timestamp":1753887128134,"version":"3.41.2"},"reference-count":17,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2018,10,8]],"date-time":"2018-10-08T00:00:00Z","timestamp":1538956800000},"content-version":"vor","delay-in-days":280,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100009092","name":"Universidad de Alicante","doi-asserted-by":"publisher","award":["GRE14-02"],"award-info":[{"award-number":["GRE14-02"]}],"id":[{"id":"10.13039\/100009092","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Complexity"],"published-print":{"date-parts":[[2018,1]]},"abstract":"<jats:p>In a data mining process, outlier detection aims to use the high marginality of these elements to identify them by measuring their degree of deviation from representative patterns, thereby yielding relevant knowledge. Whereas rough sets (RS) theory has been applied to the field of knowledge discovery in databases (KDD) since its formulation in the 1980s; in recent years, outlier detection has been increasingly regarded as a KDD process with its own usefulness. The application of RS theory as a basis to characterise and detect outliers is a novel approach with great theoretical relevance and practical applicability. However, algorithms whose spatial and temporal complexity allows their application to realistic scenarios involving vast amounts of data and requiring very fast responses are difficult to develop. This study presents a theoretical framework based on a generalisation of RS theory, termed the variable precision rough sets model (VPRS), which allows the establishment of a stochastic approach to solving the problem of assessing whether a given element is an outlier within a specific universe of data. An algorithm derived from quasi\u2010linearisation is developed based on this theoretical framework, thus enabling its application to large volumes of data. The experiments conducted demonstrate the feasibility of the proposed algorithm, whose usefulness is contextualised by comparison to different algorithms analysed in the literature.<\/jats:p>","DOI":"10.1155\/2018\/4867607","type":"journal-article","created":{"date-parts":[[2018,10,8]],"date-time":"2018-10-08T23:39:00Z","timestamp":1539041940000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Application of the Variable Precision Rough Sets Model to Estimate the Outlier Probability of Each Element"],"prefix":"10.1155","volume":"2018","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2516-4728","authenticated-orcid":false,"given":"Francisco Maci\u00e1","family":"P\u00e9rez","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9007-6054","authenticated-orcid":false,"given":"Jose Vicente Berna","family":"Martienz","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alberto Fern\u00e1ndez","family":"Oliva","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Miguel Abreu","family":"Ortega","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2018,10,8]]},"reference":[{"key":"e_1_2_10_1_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01001956"},{"key":"e_1_2_10_2_2","doi-asserted-by":"crossref","unstructured":"HanS. 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Classifying initial returns of electronic Firm_s IPOs using entropy based rough sets in Taiwan trading systems Second International Conference on Innovative Computing Informatio and Control (ICICIC 2007) 2007 Kumamoto Japan IEEE Computer Societyhttps:\/\/doi.org\/10.1109\/ICICIC.2007.215 2-s2.0-39049153358.","DOI":"10.1109\/ICICIC.2007.215"},{"key":"e_1_2_10_4_2","doi-asserted-by":"publisher","DOI":"10.1002\/scj.20405"},{"key":"e_1_2_10_5_2","doi-asserted-by":"publisher","DOI":"10.1007\/11548706_9"},{"key":"e_1_2_10_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.dss.2015.05.002"},{"key":"e_1_2_10_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0000(93)90048-2"},{"key":"e_1_2_10_8_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4471-3238-7"},{"key":"e_1_2_10_9_2","doi-asserted-by":"publisher","DOI":"10.1111\/0824-7935.00165"},{"key":"e_1_2_10_10_2","unstructured":"Fern\u00e1ndez OlivaA. Abreu OrtegaM. Fern\u00e1ndez Baiz\u00e1nM. C. andMaci\u00e1 P\u00e9rezF. M\u00e9todo de detecci\u00f3n no determinista de outliers basado en el modelo de conjuntos aproximados de precisi\u00f3n variable Jornadas para el Desarrollo de Grandes Aplicaciones de Red (JDARE\u201909) 2009 Alicante Espa\u00f1a 131\u2013148."},{"key":"e_1_2_10_11_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-011-3534-4"},{"key":"e_1_2_10_12_2","unstructured":"UCI machine learning repository May 2009 https:\/\/cml.ics.uci.edu."},{"key":"e_1_2_10_13_2","doi-asserted-by":"crossref","unstructured":"GongZ. T. SunB. Z. ShaoY. B. ChenD. G. andHeQ. Variable precision rough set model based on general relation Proceedings of 2004 International Conference on Machine Learning and Cybernetics (IEEE Cat. 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