Maria Angeles Gil

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Maria Angeles verified their affiliation via an institutional email.

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• PhD in Maths
• Professor Emeritus at University of Oviedo

Abstrac Measuring psychological variables (attitudes, opinions, perceptions, feelings, etc.) there is a need for rating scales coping with both the natural imprecision and individual differences. In this respect, the so-called fuzzy rating scales have been introduced as a doubly continuous instrument allowing to capture both imprecision and individ...

In evaluating aspects like quality perception, satisfaction or attitude which are intrinsically imprecise, the fuzzy rating scale has been introduced as a psychometric tool that allows evaluators to give flexible and quite accurate, albeit non numerical, ratings. The fuzzy rating scale integrates the skills associated with the visual analogue scale...

The fuzzy rating scale was introduced as a tool to measure intrinsically ill-defined/ imprecisely-valued attributes in a free way. Thus, users do not have to choose a value from a class of prefixed ones (like it happens when a fuzzy semantic representation of a linguistic term set is considered), but just to draw the fuzzy number that better repres...

Print Request Permissions The Aumann-type mean has been shown to possess valuable properties as a measure of the location or central tendency of fuzzy data associated with a random experiment. However, concerning robustness its behavior is not appropriate. The Aumann-type mean is highly affected by slight changes in the fuzzy data or when outliers...

Share Link – URL providing free access to the article: https://authors.elsevier.com/a/1kpus,KD6ZjV-K

Supplementary material to the manuscript "On some properties of Cronbach’s α coefficient for interval-valued data in questionnaires"

Interval-valued scales have become an efficient alternative to conventional single-point scales for capturing richer information in questionnaires measuring imprecise human traits. Thus, new statistical techniques are being developed to analyze this type of data. In this respect, when items in a construct allow respondents to make use of interval-v...

The first robust central tendency measures for fuzzy number-valued data introduced in the literature were extensions of the notion of median in the real-valued settings. In particular, they were defined as the fuzzy numbers that minimize the mean distance to the sample fuzzy number-valued observations. In order to solve the minimization problem , o...

https://link.springer.com/book/9783031659928#overview

Along recent years, interval-valued rating scales have been considered as an alternative to traditional single-point psychometric tools for human evaluations, such as Likert-type or visual analogue scales. More concretely, in answering to intrinsically imprecise items in a questionnaire, interval-valued scales seem to allow capturing a richer infor...

Questionnaires are widely used in many different fields, especially in connection with human rating. Different rating scales are considered in questionnaires to base the response to their items on. The most popular scales of measurement are Likert-type ones. Other well-known rating scales to be involved in the items in a questionnaire are visual an...

In analyzing fuzzy-valued imprecise data statistically, scale measures/estimates play an important role. Scale measures/estimates of datasets are often considered, among others, to descriptively summarize them, to compare the dispersion or the spread of different datasets, to standardize data, to state rules for detecting outliers, to formulate reg...

In dealing with intrinsically imprecise-valued magnitudes, a common rating scale type is the natural language-based Likert. Along the last decades, fuzzy scales (more concretely, fuzzy linguistic scales/variables and fuzzy ratig scales) have also been considered for rating values of these magnitudes. A comparative descriptive analysis focussed on t...

For practical purposes, and to ease both the drawing and the computing processes, the fuzzy rating scale was originally introduced assuming values based on such a scale to be modeled by means of trapezoidal fuzzy numbers. In this paper, to know whether or not such an assumption is too restrictive, we are going to examine on the basis of a real-life...

This book is a tribute to Professor Pedro Gil, who created the Department of Statistics, OR and TM at the University of Oviedo, and a former President of the Spanish Society of Statistics and OR (SEIO). In more than eighty original contributions, it illustrates the extent to which Mathematics can help manage uncertainty, a factor that is inherent t...

The concept of the so-called fuzzy random variables has been introduced in the literature aiming to model random mechanisms ‘producing’ fuzzy values. However, the best known approaches (namely, the one by Kwakernaak-Kruse and Meyer and the one by Féron-Puri and Ralescu) have been thought to deal with two different situations and, to a great extent,...

In assessing fuzzy numbers to model imprecise data associated with random experiments, trapezoidal fuzzy numbers are often considered. Such an assessment is mainly due to easing both interpretation and computation. This becomes especially noticeable when those assessing fuzzy numbers to data have a weak knowledge, low background and little or no ex...

In previous papers, it has been empirically proved that descriptive (summary measures) and inferential conclusions (in particular, tests about means p-values) with imprecise-valued data are often affected by the scale considered to model such data. More concretely, conclusions from the numerical and fuzzy linguistic encodings of Likert-type data ha...

In dealing with questionnaires concerning satisfaction , quality perception , attitude, judgement , etc., the fuzzy rating scale has been introduced as a flexible way to respond to questionnaires’ items. Designs for this type of questionnaires are often based on Likert scales. This paper aims to examine three different real-life examples in which r...

In a previous paper the fuzzy characterizing function of a random fuzzy number was introduced as an extension of the moment generating function of a real-valued random variable. Properties of the fuzzy characterizing function have been examined, among them, the crucial one proving that it unequivocally determines the distribution of a random fuzzy...

This proceedings volume is a collection of peer reviewed papers presented at the 8th International Conference on Soft Methods in Probability and Statistics (SMPS 2016) held in Rome (Italy). The book is dedicated to Data science which aims at developing automated methods to analyze massive amounts of data and to extract knowledge from them. It show...

Metrics between fuzzy values are a topic with interest for different purposes. Among them, statistics with fuzzy data is growing in modelling and techniques largely through the use of suitable distances between such data. This paper introduces a generalized (actually, parameterized) L2 metric between fuzzy vectors which is based on their representa...

When Statistics deals with data which cannot be expressed in a numerical scale, the scale of fuzzy values (in particular, the scale of fuzzy numbers) often becomes a suitable tool to express such data. In this way, many ratings, opinions, judgements, etc. mostly coming from human valuations can be appropriately described in terms of fuzzy data. To...

Characterizing the distribution of random elements is valuable for different purposes. Among them, inferential conclusions about the population distri-bution can be drawn on the basis of the sample one. When one deals with real-valued random variables this characterization is usually made through the distribution function or other ones, like the mo...

Background: The fuzzy rating scale was introduced to cope with the imprecision of human thought and experience in measuring attitudes in many fields of Psychology. The flexibility and expressiveness of this scale allow us to properly describe the answers to many questions involving psychological measurement. Method: Analyzing the responses to a...

The fuzzy rating scale was introduced to cope with the imprecision of human thought and experience in measuring attitudes in many fi elds of Psychology. The fl exibility and expressiveness of this scale allow us to properly describe the answers to many questions involving psychological measurement. Method: Analyzing the responses to a fuzzy rating...

Randomness and fuzziness are often referred to as different sources to cope with uncertainty. However, albeit different, they arise jointly in many real-life situations leading to some new concepts, approaches and methods which are being explored mainly along the last two decades. This paper aims to summarize some of the most remarkable divergences...

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...

This paper means an introduction to analyze whether the choice of the shape for fuzzy data in their statistical analysis can or cannot affect the conclusions of such an analysis. More concretely, samples of fuzzy data are simulated in accordance with different assumptions (distributions) concerning four relevant points (namely, those determining th...

Often atypical observations separated from the majority or deviate from the general pattern appear in the datasets. Classical estimators such as the sample mean or the sample variance, can be substantially affected by these observations, which are referred to as outliers. Robust statistics provides methods which are not unduly influenced by atypica...

Glossary Definition of the Subject Introduction Mathematical Modeling of Imprecise Data Fuzzy Random Variables Statistical Analysis of Fuzzy Data Corresponding to Fuzzy Perceptions of Existing Real–Valued Data Statistical Analysis of Existing Fuzzy-Valued Data Future Directions Bibliography

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...

In this comment, several paragraphs from the paper “Statistical reasoning with set-valued information: Ontic vs. epistemic views” have been selected and discussed. The selection has been based, on one side, on a personal view of what can be considered the most clarifying points in the paper and, on the other side, on the aspects I am more familiar...

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'.

Random fuzzy numbers are becoming a valuable tool to model and handle fuzzy-valued data generated through a random process. Recent studies have been devoted to introduce measures of the central tendency of random fuzzy numbers showing a more robust behaviour than the so-called Aumann-type mean value. This paper aims to deepen in the (rather compara...

When handling fuzzy number data, it is a common practice to make use of a metric to quantify distances between fuzzy numbers. Several metrics have been suggested in the literature for this purpose. When statistically analyzing fuzzy number-valued data, L2L2 metrics become especially useful. This paper introduces a new family of generalized L2L2 met...

Random elements of non-Euclidean spaces have reached the forefront of statistical research with the extension of continuous process monitoring, leading to a lively interest in functional data. A fuzzy set is a generalized set for which membership degrees are identified by a [0, 1]-valued function. The aim of this review is to present random fuzzy s...

Random elements of non-Euclidean spaces have reached the forefront of statistical research with the extension of continuous process monitoring, leading to a lively interest in functional data. A fuzzy set is a generalized set for which membership degrees are identified by a [0, 1]-valued function. The aim of this review is to present random fuzzy s...

Since Bertoluzza et al.’s metric between fuzzy numbers has been introduced, several studies involving it have been developed. Some of these studies concern equivalent expressions for the metric which are useful for either theoretical, practical or simulation purposes. Other studies refer to the potentiality of Bertoluzza et al.’s metric to establis...

In dealing with data generated from a random experiment, L2 metrics are suitable for many statistical approaches and developments. To analyze fuzzy-valued experimental data a generalized L2 metric based on the mid/spread representation of fuzzy values has been stated, and a related methodology to conduct statistics with fuzzy data has been carried...

Data obtained in association with many real-life random experiments from different fields cannot be perfectly/exactly quantified. Often the underlying imprecision can be suitably described in terms of fuzzy numbers/ values. For these random experiments, the scale of fuzzy numbers/values enables to capture more variability and subjectivity than that...

In recent years there has been a growing interest to extend classical methods for data analysis. The aim is to allow a more flexible modeling of phenomena such as uncertainty, imprecision or ignorance. Such extensions of classical probability theory and statistics are useful in many real-life situations, since uncertainties in data are not only pre...

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...

The first time that I heard about fuzzy sets was my brother, Pedro Gil, who talked about. To get the position of Full Professor at the University of Oviedo he had to pass different habilitation exams, among them one in which he had to prepare presentations on challenging topics. Professor Sixto Ríos, who was my brother’s mentor and the scientific a...

The scale of fuzzy numbers have been used in the literature to measurement of many ratings/perceptions/valuations, expectations, and so on. Among the most common uses one can point out: the so-called 'fuzzy rating', which is based on a free fuzzy numbered response scheme, and the 'fuzzy conversion', which corresponds to the conversion of linguistic...

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...

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...

In quantifying the central tendency of the distribution of a random fuzzy number (or fuzzy random variable in Puri and Ralescu's sense), the most usual measure is the Aumann-type mean, which extends the mean of a real-valued random variable and preserves its main properties and behavior. Although such a behavior has very valuable and convenient imp...

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 historical evolution of Statistics and Probability in Spain can be viewed from different perspectives. In this paper three of them have been included, namely, the essentially historical perspective, a (rather personal) view of how most of the Statistics departments or groups were created in around the third quarter of the XX Century, and a conc...

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...

In real-life situations experimental data can arise which do not derive from exact measurements or observations, but they correspond to ranges, judgements, perceptions or ratings often involving imprecision and subjectivity. These data are usually formalized with (and treated as) grouped or categorical/qualitative data for which the statistical ana...

CONTENTS: Part I Advanced Methods in Statistics.- Part II Applied Mathematics.- Part III Distribution Theory and Applications.- Part IV Divergence Measures and Statistical Applications.- Part V Modelling in Engineering Problems.- Part VI Theory of Games.- Part VII Model-Based Methods for Survey Sampling.- Part VIII Probability Theory.- Part IX Robu...

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...

In dealing with real-valued random variables, the median of the distribution is the ‘central tendency’ summary measure associated with its ‘middle position’. When available random elements are interval-valued, the lack of a universal ranking of values makes it impossible to formalize the extension of the concept of median as a middle-position summa...

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...

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...

Recent developments in Soft Computing and Statistics

Selected papers from the 4th International Conference on Soft Methods in Probability and Statistics, SMPS 2008, Toulouse, France, September 8-10, 2008

Probability theory has been the only well-founded theory of uncertainty for a long time. It was viewed either as a powerful tool for modelling random phenomena, or as a rational approach to the notion of degree of belief. During the last thirty years, in areas centered around decision theory, artificial intelligence and information processing, nume...

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...

Interval-valued observations arise in several real-life situations, and it is convenient to develop statistical methods to deal with them. In the literature on Statistical Inference with single-valued observations one can find different studies on drawing conclusions about the population mean on the basis of the information supplied by the availabl...

Fuzzy representations of a real-valued random variable have been introduced with the aim of capturing relevant information on the distribution of the variable, through the corresponding fuzzy-valued mean value. In particular, characterizing fuzzy representations of a random variable allow us to capture the whole information on its distribution. One...

In this paper we consider a new asymmetry coefficient for random variables. This measure of skewness is based on a fuzzy representation of real-valued random variables which characterize the distribution of the original random variable through the expected value of the 'fuzzified' one. This representation has been recently introduced by the authors...

In previous works valuable tools in testing statistical hypotheses about the means of fuzzy random variables have been developed. In this paper we present a study about the power function of an asymptotic procedure for the one-sample test. More precisely, the behaviour of the statistic under local alternatives is analyzed. The procedure is carried...

Testing methods are introduced in order to determine whether there is some ‘linear’ relationship between imprecise predictor and response variables in a regression analysis. The variables are assumed to be interval-valued. Within this context, the variables are formalized as compact convex random sets, and an interval arithmetic-based linear model...

The notion of Fuzzy Random Variable has been introduced to model random mechanisms generating imprecisely-valued data which can be properly described by means of fuzzy sets. Probabilistic aspects of these random elements have been deeply discussed in the literature. However, statistical analysis of fuzzy random variables has not received so much at...

The notion of Fuzzy Random Variable has been introduced to model random mechanisms generating imprecisely-valued data which can be properly described by means of fuzzy sets. Probabilistic aspects of these random elements have been deeply discussed in the literature. However, statistical analysis of fuzzy random �variables has not received so much a...

For the last decades, research studies have been developed in which a coalition of Fuzzy Sets Theory and Statistics has been established with different purposes. These namely are: (i) to introduce new data analysis problems in which the objective involves either fuzzy relationships or fuzzy terms; (ii) to establish well-formalized models for elemen...

This paper presents a backward analysis on the interpretation, modelling and impact of the concept of fuzzy random variable. After some preliminaries, the situations modelled by means of fuzzy random variables as well as the main approaches to model them are explained. We also summarize briefly some of the probabilistic studies concerning this conc...

In previous studies we have stated that the well-known bootstrap techniques are a valuable tool in testing statistical hypotheses about the means of fuzzy random variables, when these variables are supposed to take on a finite number of different values and these values being fuzzy subsets of the one-dimensional Euclidean space. In this paper we sh...

In this paper we analyze the re-lationship between the regression models with fuzzy random vari-ables and the regression models with the corresponding support func-tions. This relationship will allow us to take advantage of some re-cent studies concerning regression models in functional data analysis. Special features arisen in handling fuzzy rando...

A family of fuzzy representations of random variables is presented. Each representation transforms a real-valued random variable into a fuzzy-valued one. These representations can be chosen so that they lead to fuzzy random variables whose means capture different relevant information on the probability distribution of the original real-valued rando...

A bootstrap approach to the multi-sample test of means for imprecisely valued sample data is introduced. For this purpose imprecise data are modelled in terms of fuzzy values. Populations are identified with fuzzy-valued random elements, often referred to in the literature as fuzzy random variables. An example illustrates the use of the suggested m...