Nie-Tan Method and its Improved Version: A Counterexample

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dc.contributor.authorSalazar, Omarspa
dc.contributor.authorRojas, Juan Diegospa
dc.contributor.authorSerrano, Humbertospa
dc.date2016-05-26
dc.date.accessioned2019-09-19T21:38:59Z
dc.date.available2019-09-19T21:38:59Z
dc.descriptionContext: The bottleneck on interval type-2 fuzzy logic systems is the output processing when using Centroid Type-Reduction + Defuzzification (CTR+D method). Nie and Tan proposed an approximation to CTR+D (NT method). Recently, Mendel and Liu improved the NT method (INT method). Numerical examples (due to Mendel and Liu) exhibit the NT and INT methods as good approximations to CTR+D.Method: Normalization to the unit interval of membership function domains (examples and counterexample) and variables involved in the calculations for the three methods. Examples (due to Mendel and Liu) taken from the literature. Counterexample with piecewise linear membership functions. Comparison by means of error and percentage relative error.Results: NT vs. CTR+D: Our counterexample showed an error of 0.1014 and a percentage relative error of 30.53%. This is respectively 23 and 32 times higher than the worst case obtained in the examples. INT vs. CTR+D: Our counterexample showed an error of 0.0725 and a percentage relative error of 21.83%. This is respectively 363 and 546 times higher than the worst case obtained in the examples.Conclusions: NT and INT methods are not necessarily good approximations to the CTR+D method.en-US
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dc.identifierhttps://revistas.udistrital.edu.co/index.php/reving/article/view/9370
dc.identifier10.14483/udistrital.jour.reving.2016.2.a02
dc.identifier.urihttp://hdl.handle.net/11349/19844
dc.languageeng
dc.languagespa
dc.publisherUniversidad Distrital Francisco José de Caldasen-US
dc.relationhttps://revistas.udistrital.edu.co/index.php/reving/article/view/9370/11561
dc.relationhttps://revistas.udistrital.edu.co/index.php/reving/article/view/9370/13797
dc.rightsCopyright (c) 2016 Ingenieríaen-US
dc.sourceIngeniería; Vol 21 No 2 (2016): May - August; 138-153en-US
dc.sourceIngeniería; Vol. 21 Núm. 2 (2016): Mayo - Agosto; 138-153es-ES
dc.source2344-8393
dc.source0121-750X
dc.subjectType-2 fuzzy logic systemen-US
dc.subjecttype-2fuzzy seten-US
dc.subjectcentroiden-US
dc.subjectdefuzzificationen-US
dc.subjectNie-Tanmethod.en-US
dc.titleNie-Tan Method and its Improved Version: A Counterexampleen-US
dc.typeinfo:eu-repo/semantics/article
dc.typeinfo:eu-repo/semantics/publishedVersion
dc.typeArticleen-US
dc.typeArtículoes-ES
dc.type.coarhttp://purl.org/coar/resource_type/c_6501

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