Métodos de regresión borrosa posibilística. Aplicaciones
Fecha
2014-07-08
Autores
Brito Seoane, Salvador
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Editor
Universidad Central “Marta Abreu” de Las Villas
Resumen
En esta tesis se presentan de manera resumida los conceptos fundamentales de la teoría de conjuntos borrosos. Se definen los detalles y definiciones fundamentales de los números borrosos L-R de Dubois y Prade, los números borrosos triangulares y los números borrosos triangulares simétricos.
Se exponen los elementos fundamentales de la regresión borrosa y se muestran diferentes modelos de regresión reportados en la literatura haciendo énfasis en las medidas de bondad de ajuste.
Se presentan los aspectos principales en la modificación del análisis, diseño e implementación del software “efuzzy 1.0” obteniéndose de esta manera la nueva versión 2.0.
Se explica la utilización de la biblioteca commons-math3-3.2 para dar solución a problemas de optimización lineal y eliminar la dependencia total con el software Mathematica. Se expone algunas características y ventajas del software Lingo, así como la estructura que debe tener un fichero con extensión .lg4 para resolver el modelo de Nadimi utilizando el Lingo.
Se muestra una aplicación con datos reales para el diagnóstico de la hipertensión arterial en niños considerando si tienen alto o bajo riesgo de ser hipertensos. Se obtienen varios modelos de regresión borrosa a partir de los métodos estudiados y se compara con la regresión clásica.
In this thesis, a summary of the basic concepts of the theory of fuzzy sets is presented. Details and definitions of the fuzzy numbers of LR Dubois and Prade, triangular fuzzy numbers and the symmetric triangular fuzzy numbers are defined. The fundamentals of fuzzy set and different regression models reported in the literature with emphasis on measures of goodness of fit are exposed. The main aspects are presented in the modification of the analysis, design and implementation of the software "efuzzy 1.0" obtaining as a result, the new version 2.0. The use of commons-math3-3.2 library is explained for solving linear optimization problems and to eliminate total dependence with the Mathematica software. Some features and advantages of the software Lingo are exposed, and also the structure that must have a file with .lg4 to solve the Nadimi model using the Lingo. An application is displayed, which has real data for the diagnosis of hypertension in children considering whether they have high or low risk of being hypertensive. Several fuzzy regression models are obtained from the methods studied and a comparison is made with classical regression.
In this thesis, a summary of the basic concepts of the theory of fuzzy sets is presented. Details and definitions of the fuzzy numbers of LR Dubois and Prade, triangular fuzzy numbers and the symmetric triangular fuzzy numbers are defined. The fundamentals of fuzzy set and different regression models reported in the literature with emphasis on measures of goodness of fit are exposed. The main aspects are presented in the modification of the analysis, design and implementation of the software "efuzzy 1.0" obtaining as a result, the new version 2.0. The use of commons-math3-3.2 library is explained for solving linear optimization problems and to eliminate total dependence with the Mathematica software. Some features and advantages of the software Lingo are exposed, and also the structure that must have a file with .lg4 to solve the Nadimi model using the Lingo. An application is displayed, which has real data for the diagnosis of hypertension in children considering whether they have high or low risk of being hypertensive. Several fuzzy regression models are obtained from the methods studied and a comparison is made with classical regression.
Descripción
Palabras clave
Regresión Borrosa, Efuzzy 1.0, Métodos Estadísticos, Hipertensión Arterial, Niños