Una versión del teorema de Stone-Weierstrass en análisis difuso

Treball final de Màster Universitari en Matemàtica Computacional. Codi: SIQ027. Curs acadèmic 2015-201

Bases de datos relacionales difusas

Treball final de Grau en Matemàtica Computacional. Codi: MT1030. Curs acadèmic 2014-2015Este documento consta de dos partes, primero presenta un informe de la estancia en pr acticas donde se especi can los objetivos y las tareas realizadas correspondientes a dicho periodo de pr acticas, y a continuaci on, presenta un modelo de Bases de Datos Relacionales Difusas cuyas caracter sticas principales son: la integraci on en un entorno com un de modelos precedentes, la capacidad de representaci on de una amplia gama de informaci on difusa y el tratamiento coherente y exible de la misma. Todo ellos con el animo de ofrecer un modelo con el que resolver cada problema de representaci on y manipulaci on de informaci on difusa, atendiendo a la naturaleza del mismo, pudiendo modelar la consulta, mediante la elecci on del operador de comparaci on y de la medida de compatibilidad difusa a emplear. Adem as, te ofrece la posibilidad de actuar de forma selectiva sobre la precisi on con la que los atributos han de satisfacer las condiciones de una consulta

A version of the Stone-Weierstrass theorem in fuzzy analysis

Let C ( K , E 1 ) be the space of continuous functions defined between a compact Hausdorff space K and the space of fuzzy numbers E 1 endowed with the supremum metric. We provide a set of sufficient conditions on a subspace of C ( K , E 1 ) in order that it be dense. We also obtain a similar result for interpolating families of C ( K , E 1 ) . As a corollary of the above results we prove that certain fuzzy-number-valued neural networks can approximate any continuous fuzzy-number-valued function defined on a compact subspace of R

Completeness, metrizability and compactness in spaces of fuzzy-number-valued functions

Fuzzy-number-valued functions, that is, functions defined on a topological space taking values in the space of fuzzy numbers, play a central role in the development of Fuzzy Analysis. In this paper we study completeness, metrizability and compactness of spaces of continuous fuzzy-number-valued functions

A version of Stone-Weierstrass theorem in Fuzzy Analysis

[EN] Let C(K, E1) be the space of continuous functions defined between a compact Hausdorff space K and the space of fuzzy numbers E1 endowed with the supremum metric. We provide a sufficient set of conditions on a subspace of C(K, E1) in order that it be dense. We also obtain a similar result for interpolating families of C(K, E1).This research is supported by Spanish Government (MTM2016-77143-P), Universitat Jaume I (Projecte P1-1B2014-35) and Generalitat Valenciana (Projecte AICO/2016/030).Font, JJ.; Sanchis, D.; Sanchis, M. (2017). A version of Stone-Weierstrass theorem in Fuzzy Analysis. En Proceedings of the Workshop on Applied Topological Structures. Editorial Universitat Politècnica de València. 41-46. http://hdl.handle.net/10251/128026OCS414

Espacios de funciones continuas con valores difusos

En esta tesis abordamos tres aspectos importantes de los espacios de funciones difusas que son continuas respecto a la métrica supremo cuando están dotados de las topologías más habituales en este contexto. Estudiamos su completitud, metrizabilidad y compacidad. Este último concepto está claramente relacionado con el teorema de Ascoli cuyo resultado generalizamos a un marco más amplio. Por otra parte, estudiamos los problemas de aproximación en los espacios de funciones difusas continuas, no solo utilizando redes neuronales, sino probando resultados más generales, tipo Stone-Weierstrass. Cabe destacar que estos resultados se prueban para funciones difusas que son continuas tanto respecto a la métrica supremo como respecto a la topología de la convergencia de nivel.In this thesis we deal with three important aspects of the spaces of diffuse functions that are continuous with respect to the supreme metric when they are endowed with the most common topologies in this context. We study its completeness, metrizability and compactness. This last concept is clearly related to the Ascoli theorem whose result we generalize to a wider framework. On the other hand, we studied the problems of approximation in the spaces of continuous diffuse functions, not only using neural networks, but testing more general results, such as Stone-Weierstrass. It should be noted that these results are tested for fuzzy functions that are continuous both with respect to the supreme metric and with respect to the topology of the level convergence.Programa de Doctorat en Cièncie

Constructive approximation of level continuous fuzzy functions 1

We consider the space of continuous functions defined between a locally compact Hausdorff space and the space of fuzzy numbers endowed with the level convergence topology. We obtain a Stone-Weierstrass type theorem for such space of functions equipped with the compact open topology. As a corollary of the above results, we prove that such functions can be approximated by certain fuzzy-number-valued neural networks and sums of fuzzy-number-valued ridge functions

Early detection of mechanical damage in mango using NIR hyperspectral images and machine learning

Mango fruit are sensitive and can easily develop brown spots after suffering mechanical stress during postharvest handling, transport and marketing. The manual inspection of this fruit used today cannot detect the damage in very early stages of maturity and to date no automatic tool capable of such detection has been developed, since current systems based on machine vision only detect very visible damage. The application of hyperspectral imaging to the postharvest quality inspection of fruit is relatively recent and research is still underway to find a method of estimating internal properties or detecting invisible damage. This work describes a new system to evaluate mechanically induced damage in the pericarp of ‘Manila’ mangos at different stages of ripeness based on the analysis of hyperspectral images. Images of damaged and intact areas of mangos were acquired in the range 650–1100 nm using a hyperspectral computer vision system and then analysed to select the most discriminating wavelengths for distinguishing and classifying the two zones. Eleven feature-selection methods were used and compared to determine the wavelengths, while another five classification methods were used to segment the resulting multispectral images and classify the skin of the mangos as sound or damaged. A 97.9% rate of correct classification of pixels was achieved on the third day after the damage had been caused using k-Nearest Neighbours and the whole spectra and the figure dropped to 91.4% when only the most discriminant bands were used