Gil González-Rodríguez

University of Oviedo | UNIOVI · Department of Statistics and Operational Research and Mathematics Didactics

Star-shaped sets represent a large class of sets that contains compact and convex ones as a particular case. The center-radial characterization of these sets is very useful to identify their original shape. The complexity of these data lies in the fact that several aspects of the data are considered in a single representation. Since in some situati...

Se seleccionan y describen los diferentes hábitats de interés comunitario (HIC) y prioritarios presentes en Asturias, así como el grado de relación que tienen con las unidades EUNIS correspondientes.

We provide the first list of terrestrial and littoral habitats present in the Principality of Asturias, following the habitat types defined at European level by the hierarchical habitat classification system EUNIS (European Nature Information System), at national level by the Spanish standard list of terrestrial habitats (ES units), and at regional...

El tratamiento experimental de Eucalyptus globulus se realizó sobre cuatro parcelas con diferentes técnicas. En tres de ellas se cubrieron los tocones de árboles recién talados con lona negra hasta la base del tocón, en dos de estas se aplicaron previamente diferentes salmueras en la sección de los troncos (sal con agua en una y sal con agua y con...

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 ob...

This chapter describes the methodological bases used and presents novel economic information we have gathered in order to quantify the direct contribution that brown bears have on local economies and also to measure the current economic and occupational dependence of this resource on different activities and businesses. In contrast to previous stud...

Este capítulo describe las bases metodológicas y recoge información económica novedosa que permite cuantificar la contribución directa del oso pardo a las economías locales, y mide la dependencia económica y laboral que distintas actividades y negocios tienen de este recurso en la actualidad. A diferencia de estudios precedentes, hemos abordado la...

Alien and invasive plants are one of the mayor threats for the alluvial forests with Alnus glutinosa and Fraxinus excelsior (Alno-Padion, Alnion incanae, Salicion albae) (priority habitat 91E0*) of NW of the Iberian Peninsula river corridors. A correct management is required to improve the actual conservation status of this riparian habitat. The ai...

Some hypothesis tests for analyzing the degree of overlap between the expected value of random intervals are provided. For this purpose, a suitable measure to quantify the overlapping grade between intervals is considered on the basis of the Szymkiewicz-Simpson coefficient defined for general sets. It can be seen as a kind of likeness index to meas...

River corridors are subject to numerous pressures such as invasive species, plant diseases, intensification of uses, artificial structures and activities, etc. These pressures affect their functions as reservoirs of diversity of flora and fauna species, flood peak damping, hydrological cycle regulators and ecosystem service providers. Edaphological...

Seismic data are typically employed to monitor earthquake activity, but they can also be exploited in order to investigate the existing links betweenthe seismic signal and a broad range of physical processes occurring in the nearby rivers. For instance, the noise related to water turbulence duringhigh discharges has a clear impact on the seismic si...

Sensory analysis entails subjective valuations provided by qualified experts which in most of the cases are given by means of a real value. However personal valuations usually present an uncertainty in their meaning which is difficult to capture by using a unique value. In this work some statistical techniques to deal with such kind of information...

Coastal sand dune ecosystems are facing threats and pressures across Europe, but the quantification of the exact impacts is not easy, particularly when natural and anthropic effects are overlapping. In order to tackle this question, during two years sand movement has been measured in pilot dune plots located in the Northern Spanish coast. We aimed...

The river channel in the Esva basin, a coastal catchment of the Cantabrian region (Northwest of Spain), has experienced a slight active channelwidth decrease from 1957 to 1985 (<1%) and more important decrease (close to 13%) from 1985 to 2003. This trend is well related to the main changes in the forest cover, which also increases slightly from 195...

Fluvial systems draining the northern watershed of Cantabrian mountains (NW Spain) to the Bay of Biscay are characterized by single-thread channels with short paths and steep slopes. During the last decades, they have experienced riverbed's incision, channel narrowing, vegetal colonization, loss of active gravels and abandonment of secondary c...

The river channel in the Esva basin, a coastal catchment of the Cantabrian region (North Iberian Peninsula) with a surface of 464 km2 and maximum high close to 1300 m, has experienced riverbed’s incision, channel narrowing, vegetal colonization and loss of active gravels. This trend has been described in other rivers from Spain and Europe, and they...

Fluvial systems draining the northern watershed of Cantabrian mountains (NW Spain) are characterized by short paths and steep slopes. During the last decades, the morphology of the river channel has experienced several changes: riverbed's incision, channel narrowing, vegetal colonization, loss of active gravels and abandonment of secondary channels...

During the last decades, fluvial systems of the Cantabrian region (Northwest of Spain) have experienced important geomorphological changes. These changes are characterized by main channel incision and narrowing, vegetal colonization of fluvial bars and channel morphology simplification. This trend has been described in other spanish and Atlantic Eu...

Los ríos que fluyen por las cuencas septentrionales de la Cordillera Cantábrica (noroeste de España), caracterizados por cortos recorridos y elevados gradientes de pendiente, han experimentado durante los últimos años cambios en su morfología. Al igual que otras regiones montañosas de España y Europa, la tendencia observada es hacia la incisión ver...

The usual estimators of the regression under isotonicity assumptions are too sensitive at the tails. In order to avoid this problem, some new strategies for fixed designs are analyzed. The uniform consistency of certain estimators on a closed and bounded working interval are obtained. It is shown that the usual isotonic regression can be employed w...

The convenient theoretical properties of the support function and the Minkowski addition-based arithmetic have been shown to be useful when dealing with compact and convex sets on Rp. However, both concepts present several drawbacks in certain contexts. The use of the radial function instead of the support function is suggested as an alternative to...

The space of nonempty convex and compact (fuzzy) subsets of Rp, Kc(Rp), has been traditionally used to handle imprecise data. Its elements can be characterized via the support function, which agrees with the usual Minkowski addition, and naturally embeds Kc(Rp) into a cone of a separable Hilbert space. The support function embedding holds interesti...

M-estimators of location are widely used robust estimators of the center of univariate or multivariate real-valued data. This paper aims to study M-estimates of location in the framework of functional data analysis. To this end, recent developments for robust nonparametric density estimation by means of M-estimators are considered. These results ca...

One of the most common spaces to model imprecise data through (fuzzy) sets is that of convex and compact (fuzzy) subsets in \(\mathbb {R}^p\). The properties of compactness and convexity allow the identification of such elements by means of the so-called support function, through an embedding into a functional space. This embedding satisfies certai...

Hilbert spaces are frequently used in statistics as a framework to deal with general random elements, specially with functional-valued random variables. The scarcity of common parametric distribution models in this context makes it important to develop non-parametric techniques, and among them, bootstrap has already proved to be specially valuable....

The first aim is to empathize the use of fuzziness in data analysis to capture information that has been traditionally disregarded with a cost in the precision of the conclusions. Fuzziness can be considered in the data analysis process at various stages, but the main target in this paper will be fuzziness in the data. Depending on the nature of th...

In response to our paper "Pyrogenic organic matter production from wildfires: a missing sink in the global carbon cycle" (Santín et al. 2015), Billings & Schlesinger (2015) argue that pyrogenic organic matter (PyOM) formation is not a missing C sink. This article is protected by copyright. All rights reserved. This article is protected by copyright...

The fuzzy rating method has been introduced in psychometric studies as a tool allowing to capture and accurately reflect the diversity, subjectivity and imprecision inherent to human responses to many questionnaires. The lack of statistical techniques to analyze in depth these responses has been for years an important barrier. At present, this barr...

An extension of the inclusion test of the expected value of a real random variable in an interval to the case of general random intervals is introduced. The hypothesis of strict inclusion is relaxed by considering a measure of the degree of inclusion. Thus, partial inclusions are also tested. Asymptotic and bootstrap techniques are established. The...

Wildfires release substantial quantities of carbon (C) into the atmosphere but they also convert part of the burnt biomass into pyrogenic organic matter (PyOM). This is richer in C and, overall, more resistant to environmental degradation than the original biomass, and, therefore, PyOM production is an efficient mechanism for C sequestration. The m...

Real-life data associated with experimental outcomes are not always real-valued. In particular, opinions, perceptions, ratings, etc. are often assumed to be imprecise in nature, especially when they come from human valuations. Fuzzy numbers have long been considered to provide us with a convenient scale to express these imprecise data. In analyzing...

This note is a rejoinder on our paper in this issue. It attempts to provide some clarifications and thoughts in connection with the discussions/comments made about it by Didier Dubois and Sebastien Destercke. We hope our comments are at the level of the discussants'.

Inferential studies for the regression coefficients of a linear model for interval-valued random variables are addressed. Confidence sets and hypothesis tests are investigated and solved through asymptotic and bootstrap techniques. The inferences are based on the least-squares estimators of the model which have been shown to be coherent with the in...

A hypothesis test for the inclusion of the expected value of a fuzzy-valued random element in a given fuzzy set is provided. The exclusion, or the empty intersection of the expected value of a random fuzzy set and a fuzzy set, is also tested, that allows us to define one-sided tests for this expected value without the need of considering any restri...

A model in which the response is monotonically related to a given exposure or predictor is considered. This is motivated by dose–response analysis, however it also applies to survival distributions depending on a series of ordered multinomial parameters or, in a more general context, to change-point problems. In these contexts, although the monoton...

Confidence intervals for the parameters of a linear regression model with a fuzzy response variable and a set of real and/or fuzzy explanatory variables are investigated. The family of LR fuzzy random variables is considered and an appropriate metric is suggested for coping with this type of variables. A class of linear regression models is then pr...

Most of the research developed in the last years by the SMIRE Research Group concerns the statistical analysis of imprecisely (set- and fuzzy set)-valued experimental data. This analysis has been based on an approach considering the usual arithmetic for these data as well as suitable metrics between them. The research perfectly fits into the resear...

When working with real-valued data regression analysis allows to model and forecast the values of a random variable in terms of the values of either another one or several other random variables defined on the same probability space. When data are not real-valued, regression techniques should be extended and adapted to model simply relationships in...

Since the Aumann-type expected value of a random interval is not robust, the aim of this paper is to propose a new central tendency measure for interval-valued data. The median of a random interval has already been defined as the interval minimizing the mean distance, in terms of an L 1 metric extending the Euclidean distance, to the values of the...

A methodology for analyzing the variability of the tidal fluctuation in a specific area is proposed in this work. The idea is to consider intervals determined by the minimum and maximum height reached by the tides in a day. Thus, the theoretical aim is to develop hypothesis tests about the variance of one or more interval-valued random elements (i....

The problem of testing the equality of variances of k random fuzzy sets has been recently developed on the basis of Levene's classical procedure. Asymptotic and bootstrap approaches have been carried out in this framework, and the proposed test was compared with a Bartlett-type test. In this work, a deeper comparison between some bootstrap statisti...

New measures of skewness for real-valued random variables are proposed. The measures are based on a functional representation of real-valued random variables. Specifically, the expected value of the transformed random variable can be used to characterize the distribution of the original variable. Firstly, estimators of the proposed skewness measure...

Functional data have been the subject of many research works over the last years. Functional regression is one of the most discussed issues. Specifically, significant advances have been made for functional linear regression models with scalar response. Let $(\mathcal{H},<\cdot,\cdot>)$ be a separable Hilbert space. We focus on the model $Y=<\Theta,...

The prediction of a response random interval-valued set from an explanatory one has been examined in previous developments. These developments have considered an interval arithmetic-based linear model between the random interval-valued sets and a least squares regression analysis. The least squares approach involves a generalized L2-metric between...

The construction of confidence sets for the parameters of a flexible simple linear regression model for interval-valued random sets is addressed. For that purpose, the asymptotic distribution of the least-squares estimators is analyzed. A simulation study is conducted to investigate the performance of those confidence sets. In particular, the empir...

The importance of the historical information in flood analysis has previously been underlined. In this context, we present an integral methodology aimed at the establishment of return periods of different flood units on the unique basis of historical data. Specifically, the reconstruction of the flood chronology extended back to 1900, complemented...

The use of the fuzzy scale of measurement to describe an important number of observations from real-life attributes or variables is first explored. In contrast to other well-known scales (like nominal or ordinal), a wide class of statistical measures and techniques can be properly applied to analyze fuzzy data. This fact is connected with the possi...

Likert scales or associated codings are often used in connection with opinions/valuations/ratings, and especially with questionnaires with a pre-specified response format.A guideline to design questionnaires allowing free fuzzy-numbered response format is now given, the fuzzy numbers scale being very rich and expressive and enabling to describe in...

The supervised classification of fuzzy data obtained from a random experiment is discussed. The data generation process is modelled through random fuzzy sets which, from a formal point of view, can be identified with certain function-valued random elements. First, one of the most versatile discriminant approaches in the context of functional data a...

A methodology for analyzing the quality of a specific kind of cheese is proposed in this work. The idea consists in extending the well-known categorical scale corresponding to the possible perceptions of qualified experts (that commonly ranges from “very bad quality” to “very high quality”) to a more flexible scale. In addition, some statistical in...

Se presenta una metodología basada en el estudio evolutivo del medio fluvial, comparando la situación actual con, al menos, la disponible en el vuelo americano realizado durante los años 1956/57, así como la reconstrucciónde series históricas de inundaciones y la estimación de frecuencias de inundación en tramos concretos.

The estimation of a simple linear regression model when both the independent and dependent variable are interval valued is addressed. The regression model is defined by using the interval arithmetic, it considers the possibility of interval-valued disturbances, and it is less restrictive than existing models. After the theoretical formalization, th...

Fuzzy sets are often used to handle the imprecision/vagueness that affects some characteristics in environmental sciences. A determination coefficient is introduced in order to quantify the degree of relationship between an imprecise response variable and a scalar explanatory predictor in a linear regression problem. An estimator of such coefficien...

Different methods to assess the flood return period are available in the literature. The hydrological-hydraulic approaches, among the best-known quantitative methods, oversimplify the complex characteristics of the fluvial systems. Additionally, they rely on data that are usually criticized because of their low quality and representativity. In cont...

Setting species priorities is commonly based on the assessment of multiple conservation criteria, and point-scoring methods are broadly used for obtaining ranked species lists. However, the implications of different procedures in the performance and application of resulting lists have been scarcely investigated. In this study, we test the effect of...

Least-squares estimation of various linear models for interval data has already been considered in the literature. One of these models allows different slopes for mid-points and spreads (or radii) integrated in a unique equation based on interval arithmetic. A preliminary study about the construction of confidence regions for the parameters of that...

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...

A new method for estimating shallow landslide susceptibility by combining Geographical Information System (GIS), nonparametric kernel density estimation and logistic regression is described. Specifically, a logistic regression is applied to predict the spatial distribution by estimating the probability of occurrence of a landslide in a 16km2 area....

This work concerns the contingent valuation of endangered species. Specifically, it is devoted to quantify and model the value of the brown bear and its habitat in a society in the north of Spain. A single-bound dichotomous choice format for the valuation problem has been chosen. The main models to deal with this format will be recalled. In order t...

A procedure to test hypotheses about the population variance of a fuzzy random variable is analyzed. The procedure is based on the theory of UH-statistics. The variance is defined in terms of a general metric to quantify the variability of the fuzzy values about its (fuzzy) mean. An asymptotic one-sample test in a wide setting is developed and a bo...

Some tools for testing hypotheses about the variance of random fuzzy sets are already available. Asymptotically correct procedures for the k-sample homoscedasticity tests have been recently developed. However, the power of such procedures has not been analyzed yet. In this paper, some studies about the power function of the asymptotic procedure for...

Interpretability is acknowledged as the main advantage of fuzzy systems and it should be given a main role in fuzzy modeling. Classical systems are viewed as black boxes because mathematical formulas set the mapping between inputs and outputs. On the contrary, fuzzy systems (if they are built regarding some constraints) can be seen as gray boxes in...

One of the most important aspects of the (statistical) analysis of imprecise data is the usage of a suitable distance on the family of all compact, convex fuzzy sets, which is not too hard to calculate and which reflects the intuitive meaning of fuzzy sets. On the basis of expressing the metric of Bertoluzza et al. [C. Bertoluzza, N. Corral, A. Sal...

A clustering method to group independent fuzzy random variables observed on a sample by focusing on their expected values is developed. The procedure is iterative and based on the p-value of a multi-sample bootstrap test. Thus, it simultaneously takes into account fuzziness and stochastic variability. Moreover, an objective stopping criterion leadi...

This work deals with the simulation of fuzzy random variables, which can be used to model various realistic situations, where uncertainty is not only present in form of randomness but also in form of imprecision, described by means of fuzzy sets. Utilizing the common arithmetics in the space of all fuzzy sets only induces a conical structure. As a...

A generalized simple linear regression statistical/probabilistic model in which both input and output data can be fuzzy subsets of Rp is dealt with. The regression model is based on a fuzzy-arithmetic approach and it considers the possibility of fuzzy-valued random errors. Specifically, the least-squares estimation problem in terms of a versatile m...

The aim of this paper is to extend the classical prob- lem of confidence interval estimation for the mean of a random vari- able to the case of a fuzzy random variable. The key idea consists in considering a confidence region defined as a ball w.r.t. a given metric, which is centered in the sample mean and whose radius is determined via bootstrappi...

This communication is concerned with the problem of supervised classification of fuzzy data obtained from a random ex- periment. The data generation process is modelled through fuzzy random variables which, from a formal point of view, can be identi- fied with a kind of functional random element. We propose to adapt one of the most versatile discri...

Susceptibility or hazard models are often established by means of logistic regression techniques in order to describe the effect of a group of explanatory variables on the probability of a dichotomous or binary response. Since the available variables do not always meet the assumptions of logit-linearity of the logistic regression, a modified approa...

The linear relationship between interval-valued random sets can arise in different ways. Recently, a linear model based on the natural arithmetic for intervals has been studied. In order to test whether the explanatory random set contributes significantly to explain the response random set through that linear model, an asymptotic testing procedure...

In this communication we present a procedure to test whether the variance of a fuzzy random variable (FRV) is a given value or not by using asymptotic techniques. The variance considered here is defined in terms of a generalized metric in order to quantify the variability of the fuzzy values of the FRV about its expected value. We present some simu...

A new measure of skewness for real-valued random variables based on fuzzy tools has been recently introduced. The measure is derived from certain fuzzy representations of real-valued random variables which can be used to characterize the distribution of the original variables through the expected value of the ‘fuzzified’ random variables. In this c...

The suitability of the family of d K -distances for intervals to quantify and estimate the variability of a random interval with respect to its Aumann expectation is discussed. To be precise, we will review some properties of the metrics and the associated variance. Then, we will show that the sample variance is a consistent estimator of the popul...