Nie-Tan Method and its Improved Version: A Counterexample<br><br><i>Método Nie-Tan y su Versión Mejorada: Un contraejemplo</i>
Abstract Context: 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 e...
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| Format: | Article |
| Language: | Spanish |
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Universidad Distrital Francisco José de Caldas
2016-05-01
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| Series: | Ingeniería |
| Subjects: | |
| Online Access: | http://revistas.udistrital.edu.co/ojs/index.php/reving/article/view/9370 |
| _version_ | 1811320054584705024 |
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| author | Omar Salazar Juan Diego Rojas Humberto Serrano |
| author_facet | Omar Salazar Juan Diego Rojas Humberto Serrano |
| author_sort | Omar Salazar |
| collection | DOAJ |
| description | Abstract
Context: 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. |
| first_indexed | 2024-04-13T12:52:44Z |
| format | Article |
| id | doaj.art-257416e30226466d8ead003be40bf99e |
| institution | Directory Open Access Journal |
| issn | 0121-750X 2344-8393 |
| language | Spanish |
| last_indexed | 2024-04-13T12:52:44Z |
| publishDate | 2016-05-01 |
| publisher | Universidad Distrital Francisco José de Caldas |
| record_format | Article |
| series | Ingeniería |
| spelling | doaj.art-257416e30226466d8ead003be40bf99e2022-12-22T02:46:09ZspaUniversidad Distrital Francisco José de CaldasIngeniería0121-750X2344-83932016-05-012127963Nie-Tan Method and its Improved Version: A Counterexample<br><br><i>Método Nie-Tan y su Versión Mejorada: Un contraejemplo</i>Omar Salazar0Juan Diego Rojas1Humberto Serrano2Universidad Disitrital Francisco Jose de CaldasUniversidad Distrital Francisco Jose de CaldasUniversidad Distrital Francisco Jose de CaldasAbstract Context: 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.http://revistas.udistrital.edu.co/ojs/index.php/reving/article/view/9370Type-2 fuzzy logic systemtype-2fuzzy setcentroiddefuzzificationNie-Tanmethod. |
| spellingShingle | Omar Salazar Juan Diego Rojas Humberto Serrano Nie-Tan Method and its Improved Version: A Counterexample<br><br><i>Método Nie-Tan y su Versión Mejorada: Un contraejemplo</i> Ingeniería Type-2 fuzzy logic system type-2fuzzy set centroid defuzzification Nie-Tanmethod. |
| title | Nie-Tan Method and its Improved Version: A Counterexample<br><br><i>Método Nie-Tan y su Versión Mejorada: Un contraejemplo</i> |
| title_full | Nie-Tan Method and its Improved Version: A Counterexample<br><br><i>Método Nie-Tan y su Versión Mejorada: Un contraejemplo</i> |
| title_fullStr | Nie-Tan Method and its Improved Version: A Counterexample<br><br><i>Método Nie-Tan y su Versión Mejorada: Un contraejemplo</i> |
| title_full_unstemmed | Nie-Tan Method and its Improved Version: A Counterexample<br><br><i>Método Nie-Tan y su Versión Mejorada: Un contraejemplo</i> |
| title_short | Nie-Tan Method and its Improved Version: A Counterexample<br><br><i>Método Nie-Tan y su Versión Mejorada: Un contraejemplo</i> |
| title_sort | nie tan method and its improved version a counterexample br br i metodo nie tan y su version mejorada un contraejemplo i |
| topic | Type-2 fuzzy logic system type-2fuzzy set centroid defuzzification Nie-Tanmethod. |
| url | http://revistas.udistrital.edu.co/ojs/index.php/reving/article/view/9370 |
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