Comparación entre el Índice de Yager y el Centroide para Reducción de tipo de un Número Difuso Tipo-2 de Intervalo

A Comparison Between the Centroid and the Yager Index Rank for Type Reduction of an Interval Type-2 Fuzzy Number

  • Diego Pachon Neira
  • Juan Carlos Figueroa Universidad Distrital Francisco José de Caldas
Keywords: Interval Type-2 Fuzzy numbers, Yager Index, Ranking (en_US)
Keywords: Números Difusos Tipo-2 de Intervalo, Índice de Yager, Ranking (es_ES)

Abstract (es_ES)

Contexto: Hay una necesidad por defuzzificar y rankear Conjuntos Difusos Tipo-2 de Intervalo (IT2FS), en particular Números Difusos Tipo-2 de Intervalo (IT2FN). Para ello, usamos el Índice de Yager (YIR) para conjuntos difusos aplicado a IT2FNs con el fin de encontrar una alternativa al centroide de un IT2FN.

Método: Usamos una estrategia de simulación para comparar los resultados del centroide y del YIR de un IT2FN. Así pues, simulamos 1000 IT2FNs de cada uno de los siguientes tres tipos: gausianos, triangulares y asimétricos para comparar sus centroides y YIRs.

Resultados: Después de realizar las simulaciones, se calculan algunas estadísticas de su comportamiento como el grado de cobertura y de igualdad relativas del YIR respecto al centroide así como el tamaño de la Huella de Incertidumbre (FOU) de un IT2FN. La descripción de los resultados obtenidos muestra que el YIR es menos amplio que el centroide.

Conclusiones: En general, el YIR es menos complejo de obtener que el centroide de un IT2FN, lo cual es altamente deseable en aplicaciones prácticas como toma de decisiones y control. Otras propiedades relacionadas con su tamaño y ubicación también son discutidas.

Abstract (en_US)

Context: There is a need for ranking and defuzzification of Interval Type-2 fuzzy sets (IT2FS), in particular Interval Type-2 fuzzy numbers (IT2FN). To do so, we use the classical Yager Index Rank (YIR) for fuzzy sets to IT2FNs in order to find an alternative to the centroid of an IT2FN.


Method: We use a simulation strategy to compare the results of the centroid and the YIR of an IT2FN. This way, we simulate 1000 IT2FNs of the following three kinds: gaussian, triangular, and non symmetrical in order to compare their centroids and YIRs.

Results: After performing the simulations, we compute some statistics about its behavior such as the degree of subsethood, equality and the size of the Footprint of Uncertainty (FOU) of an IT2FN. A description of the obtained results shows that the YIR is less wide than centroid of an IT2FN.

Conclusions: In general, YIR is less complex to obtain than the centroid of an IT2FN, which is highly desirable in practical applications such as fuzzy decision making and control. Some other properties regarding its size and location are also discussed.

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How to Cite
Pachon Neira, D., & Figueroa, J. C. (2016). A Comparison Between the Centroid and the Yager Index Rank for Type Reduction of an Interval Type-2 Fuzzy Number. Ingeniería, 21(2), 225-234. https://doi.org/10.14483/udistrital.jour.reving.2016.2.a08
Published: 2016-05-26
Section
Special Section: Best Extended Articles - WEA 2015