A Comparison Between the Centroid and the Yager Index Rank for Type Reduction of an Interval Type-2 Fuzzy Number
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| Format: | Artículo científico |
| Language: | en |
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Universidad Distrital Francisco José de Caldas
2016
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| _version_ | 1876473169989074944 |
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| author | Diego Fernando Pachón-Neira |
| author_facet | Diego Fernando Pachón-Neira |
| contents | A Comparison Between the Centroid and the Yager Index Rank for Type Reduction of an Interval Type-2 Fuzzy Number Diego Fernando Pachón-Neira Juan Carlos Figueroa-García Ingeniería Ranking Yager Index Interval Type 2 Fuzzy numbers 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 sym- metrical 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. 2016 artículo científico 0121-750X https://www.redalyc.org/articulo.oa?id=498853953010 https://www.redalyc.org/journal/4988/498853953010/ https://www.redalyc.org/journal/4988/498853953010/html/ https://www.redalyc.org/journal/4988/498853953010/498853953010.epub https://www.redalyc.org/journal/4988/498853953010/movil en http://www.redalyc.org/revista.oa?id=4988 Ingeniería application/pdf Universidad Distrital Francisco José de Caldas Ingeniería (Colombia) Num.2 Vol.21 |
| format | Artículo científico |
| id | redalyc_498853953010 |
| institution | Redalyc |
| language | en |
| publishDate | 2016 |
| publisher | Universidad Distrital Francisco José de Caldas |
| spellingShingle | A Comparison Between the Centroid and the Yager Index Rank for Type Reduction of an Interval Type-2 Fuzzy Number Diego Fernando Pachón-Neira Ingeniería Ranking Yager Index Interval Type 2 Fuzzy numbers A Comparison Between the Centroid and the Yager Index Rank for Type Reduction of an Interval Type-2 Fuzzy Number Diego Fernando Pachón-Neira Juan Carlos Figueroa-García Ingeniería Ranking Yager Index Interval Type 2 Fuzzy numbers 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 sym- metrical 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. 2016 artículo científico 0121-750X https://www.redalyc.org/articulo.oa?id=498853953010 https://www.redalyc.org/journal/4988/498853953010/ https://www.redalyc.org/journal/4988/498853953010/html/ https://www.redalyc.org/journal/4988/498853953010/498853953010.epub https://www.redalyc.org/journal/4988/498853953010/movil en http://www.redalyc.org/revista.oa?id=4988 Ingeniería application/pdf Universidad Distrital Francisco José de Caldas Ingeniería (Colombia) Num.2 Vol.21 |
| title | A Comparison Between the Centroid and the Yager Index Rank for Type Reduction of an Interval Type-2 Fuzzy Number |
| topic | Ingeniería Ranking Yager Index Interval Type 2 Fuzzy numbers |
| url | https://www.redalyc.org/articulo.oa?id=498853953010 https://www.redalyc.org/journal/4988/498853953010/ https://www.redalyc.org/journal/4988/498853953010/html/ https://www.redalyc.org/journal/4988/498853953010/498853953010.epub https://www.redalyc.org/journal/4988/498853953010/movil |