Análisis borroso de datos: aplicaciones
Fecha
2014-06-25
Autores
Denoda Pérez, Lisset
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Editor
Universidad Central “Marta Abreu” de Las Villas. Facultad de Matemática, Física y Computación. Departamento Ciencias de la Computación
Resumen
Bajo el nombre “análisis de datos” se agrupa una gran cantidad de métodos estadísticos cuyo propósito es extraer conclusiones a partir de un conjunto de datos. A este proceso se le denomina “descubrimiento de conocimiento”. Con frecuencia los datos recogidos son imprecisos o tienen asociado cierto grado de incertidumbre. Para procesarlos existe un conjunto de métodos que combinan los análisis estadísticos tradicionales con la teoría de la Lógica Borrosa. A ello se le denomina “análisis borroso de datos”.
En esta tesis se presentan de manera resumida los conceptos fundamentales de la teoría de conjuntos borrosos. Se definen los números borrosos triangulares, trapezoidales, así como sus operaciones fundamentales. Se muestran variantes para realizar el cálculo de medidas descriptivas borrosas como la media, moda, mediana y varianza. Se exponen diferentes modelos de regresión lineal borrosa reportadas en la literatura así como las medidas de bondad de ajuste para los mismos.
Se explica las medidas de riesgo borrosas y se propone una nueva técnica borrosa para obtener los canales endémicos. Se detallan las herramientas computacionales utilizadas haciendo énfasis en el diseño de la versión 2.0 del efuzzy.
Se mostraron numerosas aplicaciones de los métodos desarrollados a la solución de problemas reales.
The name “Data Analysis” groups many statistical methods to obtain information from data. This process is called “knowledge discovering”. Frequently the data are imprecise or have certain degree of inexactitude. To process it, there is a set of methods combining Traditional Statistical Analysis with the Fuzzy Logic Theory. This is the “Fuzzy Data Analysis”. In this thesis, a summary of the basic concepts of the theory of fuzzy sets is presented. Triangular fuzzy numbers and trapezoidal fuzzy numbers and their operations are defined. Several ways to calculate fuzzy descriptive statistics like mean, median, mode and variance, are shown. Many different fuzzy linear regression models and measures of goodness of fit reported in the literature are exposed. Some fuzzy risk measures are explained and a new fuzzy technique for obtaining endemic channel is presented. The computational tools used in the investigation are detailed, making emphasis in a new efuzzy version 2.0. Several applications of the developed methods to the solution of real problems are displayed.
The name “Data Analysis” groups many statistical methods to obtain information from data. This process is called “knowledge discovering”. Frequently the data are imprecise or have certain degree of inexactitude. To process it, there is a set of methods combining Traditional Statistical Analysis with the Fuzzy Logic Theory. This is the “Fuzzy Data Analysis”. In this thesis, a summary of the basic concepts of the theory of fuzzy sets is presented. Triangular fuzzy numbers and trapezoidal fuzzy numbers and their operations are defined. Several ways to calculate fuzzy descriptive statistics like mean, median, mode and variance, are shown. Many different fuzzy linear regression models and measures of goodness of fit reported in the literature are exposed. Some fuzzy risk measures are explained and a new fuzzy technique for obtaining endemic channel is presented. The computational tools used in the investigation are detailed, making emphasis in a new efuzzy version 2.0. Several applications of the developed methods to the solution of real problems are displayed.
Descripción
Palabras clave
Lógica Borrosa, Regresión Lineal, Análisis de datos