A Note on Fuzzy Set--Valued Brownian Motion

In this paper, we prove that a fuzzy set--valued Brownian motion $B_t$, as defined in [1], can be handle by an $R^d$--valued Wiener process $b_t$, in the sense that B_t =\indicator{b_t}; i.e. it is actually the indicator function of a Wiener process

Different linearity tests for a regression model with an imprecise response

Recently a new linear regression model with fuzzy response and scalar explanatory variables has been introduced and deeply analyzed. Since the inferences developed for such a model are meaningful only if the relationship is indeed linear, it is important to check the linearity for the regression model. Two different linearity tests have been introduced. The first one is based on the comparison of the simple linear regression model and the nonparametric regression. In details, the test statistic is constructed based on the variability explained by the two models. The second one consists in using the empirical process of the regressors marked by the residuals. Both tests have been analyzed by means of a bootstrap approach. In particular, a wild bootstrap and a residual bootstrap have been investigated

Testing linearity for a regression model with imprecise elements: a power analysis

A linearity test for a simple regression model with imprecise random elements is analyzed. The concept of LR fuzzy random variable is used to formalize imprecise random elements. The proposed linearity test is based on the comparison of the simple linear regression model and the nonparametric regression. In details, based on the variability explained by the above two models, the test statistic is constructed. The asymptotic significance level and the power under local alternatives are established. Since large samples are required to obtain suitable asymptotic results a bootstrap approach is investigated. Furthermore, in order to illustrate how the proposed test works in practice, some simulation and real-life examples are given

Presentadores tardíos de la infección por VIH en España: consecuencias médicas e impacto económico

Tesis inédita de la Universidad Complutense de Madrid, Facultad de Medicina, Departamento de Medicina, leída el 13-09-2012Depto. de MedicinaFac. de MedicinaTRUEunpu

Un divertido juego inventado por un matemático infeliz

En este artículo se presenta la posibilidad de introducir algunos temas de Matemáticas de Secundaria o Bachillerato, como pueden ser, entre otros, la Combinatoria, los Cuerpos Geométricos o incluso el propio Número Complejo, mediante la utilización del Juego Icosaédrico. Para ello se indica en primer lugar una breve biografía del descubridor de este juego: Sir William Rowan Hamilton, que pueda servirle al profesor como apoyo histórico para conseguir una mayor motivación del alumno a la hora de afrontar sus clases de Matemáticas; se muestran seguidamente las reglas de este juego, haciendo especial hincapié en las ventajas que puede ofrecer su uso en las clases de Matemáticas de Secundaria, fundamentalmente a la hora de introducir la Combinatoria; y se comentan también, finalmente, algunos otros juegos relacionados con el citado, que pueden ser utilizados por el profesor como soporte lúdico en la impartición de sus clases.In this article the possibility of introducing some mathematical topics characteristic of Secondary Education, like Combinatorial, Geometric Fields or Complex numbers, for example, by using the Icosian Game can be considered. We begin by giving a brief biography of the author of this game, Sir William Rowan Hamilton. Later, we show the advantages which this game can supply when dealing with the mathematical topics previously mentioned, basically when the Combinatorial is taught. Finally, other games related to it, which can be also used by the teacher to motivate and interest his pupils to study are also indicated

A linear regression model for imprecise response

A linear regression model with imprecise response and p real explanatory variables is analyzed. The imprecision of the response variable is functionally described by means of certain kinds of fuzzy sets, the LR fuzzy sets. The LR fuzzy random variables are introduced to model usual random experiments when the characteristic observed on each result can be described with fuzzy numbers of a particular class, determined by 3 random values: the center, the left spread and the right spread. In fact, these constitute a natural generalization of the interval data. To deal with the estimation problem the space of the LR fuzzy numbers is proved to be isometric to a closed and convex cone of R3 with respect to a generalization of the most used metric for LR fuzzy numbers. The expression of the estimators in terms of moments is established, their limit distribution and asymptotic properties are analyzed and applied to the determination of confidence regions and hypothesis testing procedures. The results are illustrated by means of some case-studies. © 2010 Elsevier Inc. All rights reserved

Predicting the Risk of Mortality in Children using a Fuzzy-Probabilistic Hybrid Model

Publisher Copyright: © 2022 Corsino Rey et al.Introduction. The mortality risk in children admitted to Pediatric Intensive Care Units (PICU) is usually estimated by means of validated scales, which only include objective data among their items. Human perceptions may also add relevant information to prognosticate the risk of death, and the tool to use this subjective data is fuzzy logic. The objective of our study was to develop a mathematical model to predict mortality risk based on the subjective perception of PICU staff and to evaluate its accuracy compared to validated scales. Methods. A prospective observational study in two PICUs (one in Spain and another in Latvia) was performed. Children were consecutively included regardless of the cause of admission along a two-year period. A fuzzy set program was developed for the PICU staff to record the subjective assessment of the patients' mortality risk expressed through a short range and a long range, both between 0% and 100%. Pediatric Index of Mortality 2 (PIM2) and Therapeutic Intervention Scoring System 28 (TISS28) were also prospectively calculated for each patient. Subjective and objective predictions were compared using the logistic regression analysis. To assess the prognostication ability of the models a stratified B-random K-fold cross-validation was performed. Results. Five hundred ninety-nine patients were included, 308 in Spain (293 survivors, 15 nonsurvivors) and 291 in Latvia (282 survivors, 9 nonsurvivors). The best logistic classification model for subjective information was the one based on MID (midpoint of the short range), whereas objective information was the one based on PIM2. Mortality estimation performance was 86.3% for PIM2, 92.6% for MID, and the combination of MID and PIM2 reached 96.4%. Conclusions. Subjective assessment was as useful as validated scales to estimate the risk of mortality. A hybrid model including fuzzy information and probabilistic scales (PIM2) seems to increase the accuracy of prognosticating mortality in PICU.publishersversionPeer reviewe