Papers by Maria Angeles Gil
Studies in Fuzziness and Soft Computing, 2002
Advances in Intelligent and Soft Computing, 2002
IEEE Transactions on Fuzzy Systems, 2016
The Aumann-type mean has been shown to possess valuable properties as a measure of the location o... more 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 behaviour is not appropriate. The Aumann-type mean is highly affected by slight changes in the fuzzy data or when outliers arise in the sample. Robust estimators of location, on the other hand, avoid such adverse effects. For this purpose, this paper considers the M-estimation approach and discusses conditions under which this alternative yields valid fuzzy-valued M-estimators. The resulting M-estimators are applied to a real-life example. Finally, some simulation studies show empirically the suitability of the introduced estimators.
Fuzzy Sets and Systems, 2012
In quantifying the central tendency of the distribution of a random fuzzy number (or fuzzy random... more 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 implications, 'extreme' values or changes of data entail too much influence on the Aumann-type mean of a random fuzzy number. This strong influence motivates the search for a more robust central tendency measure. In this respect, this paper aims to explore the extension of the median to random fuzzy numbers. This extension is based on the 1-norm distance and its adequacy will be shown by analyzing its properties and comparing its robustness with that of the mean both theoretically and empirically.
Computational Complexity, 2012
Fuzzy Sets and Systems, 2007
A basic problem, at the present stage of the Information society, is how to manage cognitive proc... more A basic problem, at the present stage of the Information society, is how to manage cognitive processes while taking into account their intrinsic features of uncertainty, including imprecision and vagueness. This has both theoretical and practical implications in Technology, Economics, Bio-Medicine, and so on. In fact, real-life situations are the prime source of motivation for this management to be considered. Traditional Statistics has developed tools and procedures for coping with this problem, assuming that uncertainty is basically due to random mechanisms appropriately handled by means of models from Probability Theory. Fuzzy Sets Theory and its generalization to what may be called "Fuzzy thinking'' has widened the scope of Statistics enabling us to deal with other sources of uncertainty, such as vagueness and imprecision, pervading both empirical data and/or models for data analysis. In this respect, for the last decades many research studies have been developed in which a coalition of Fuzzy Sets Theory and Statistics has been established with different purposes, namely,
For practical purposes, and to ease both the drawing and the computing processes, the fuzzy ratin... more 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 example how statistical conclusions concerning location-based scale estimates are affected by the shape chosen to model imprecise data with fuzzy numbers. The discussion will be descriptive for the considered scale estimates, but for the Frechet-type variance it will be also inferential. The study will lead us to conclude that statistical conclusions are scarcely influenced by data shape.
Random elements of non-Euclidean spaces have reached the forefront of statistical research with t... more 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 sets (also called fuzzy random variables) as a mathematical formalization of data-generating processes yielding fuzzy data. They will be contextualized as Borel measurable random elements of metric spaces endowed with a special convex cone structure. That allows one to construct notions of distribution, independence, expectation, variance, and so on, which mirror and generalize the literature of random variables and random vectors. The connections and differences between random fuzzy sets and random elements of classical function spaces (functional data) will be underlined. The paper also includes some bibliometric remarks, comments on the ...
This paper first presents cases involving different sources of fuzzy imprecision firom random exp... more This paper first presents cases involving different sources of fuzzy imprecision firom random experiments. Then, the interpretation of grades of membership in terms of probabilities in those cases is discussed
Advances in Intelligent Systems and Computing
In dealing with intrinsically imprecise-valued magnitudes, a common rating scale type is the natu... more 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 the variability/dispersion associated with the magnitude depending on the considered rating scale is performed in this study. Fuzzy rating responses are simulated and associated with Likert responses by means of a`Likertization' criterion. Then, each`Likertized' datum is encoded by means of a fuzzy linguistic scale. In this way, with the responses available in the three scales, the value of the dierent dispersion estimators is calculated and compared among the scales.
Advances in Data Analysis and Classification
In analyzing and classifying data from a statistical perspective, fuzzy sets and logic have becom... more In analyzing and classifying data from a statistical perspective, fuzzy sets and logic have become a valuable tool either to model and handle imprecise data or to establish flexible techniques to deal with precise data. From the very beginning of his 52 years-old theory, Professor Zadeh highlighted that "Probability theory/statistics and fuzzy logic should be viewed as complementary rather than competitive," and he anticipated and encouraged the materialization of such a complementarity. Nowadays, this assertion is a reality, as shown by the many related papers, specialized conferences, special sessions and tracks in general conferences, and so on. This special issue started in 2015, with the 50th anniversary of the seminal paper on fuzzy sets by Zadeh (1965), aiming to collect a sample of research papers about the current trends on the combination of fuzzy sets/logic and data analysis/classification. When this special issue was almost ready for publication, Zadeh unfortunately passed away at age 96 (February 4, 1921-September 6, 2017). We wish this special issue to be dedicated to Professor Zadeh, as a modest part of the many tributes that he will receive, and intending to show that fuzzy sets/logic and data analysis/classification can certainly work in synergy.
Advances in Intelligent Systems and Computing, 2016
In dealing with questionnaires concerning satisfaction, quality perception, attitude, judgement, ... more 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 respondents have been allowed to doubly answer: in accordance with either a fuzzy rating scale or a Likert one. By considering a minimum distance-based criterion, each of the fuzzy rating scale answers is associated with one of the Likert scale labels. The percentages of coincidences between the two responses in the double answer are computed by the criterion-based association. Some empirical conclusions are drawn from the computation of such percentages.
European Journal of Operational Research, 2015
The fuzzy rating scale was introduced as a tool to measure intrinsically ill-defined/ imprecisely... more 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 represents their valuation or measurement. The freedom inherent to the fuzzy rating scale process allows users to collect data with a high level of richness, accuracy, expressiveness, diversity and subjectivity, what is especially valuable for statistical purposes. This paper presents an inferential approach to analyze data obtained by using the fuzzy rating scale. More concretely, the paper is to be focussed on testing different hypothesis about means, on the basis of a sound methodology which has been stated during the last years. All the procedures that have been developed to this aim will be presented in an algorithmic way adapted to the usual generic fuzzy rating scale-based data, and they will be illustrated by means of a real-life example.
RAIRO - Operations Research
Revue française d'automatique, d'informatique et de recherche opérationnelle. Recherche opération... more Revue française d'automatique, d'informatique et de recherche opérationnelle. Recherche opérationnelle, tome 19, n o 1 (1985), p. 105-111. <http © AFCET, 1985, tous droits réservés. L'accès aux archives de la revue « Revue française d'automatique, d'informatique et de recherche opérationnelle. Recherche opérationnelle » implique l'accord avec les conditions générales d'utilisation (). Toute utilisation commerciale ou impression systématique est constitutive d'une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques R.A.I.R.O. Recherche opérationnelle/Opérations Research (vol. 19, n° 1, février 1985, p. 105 à 111) FUZZIFIED BLACKWELL'S METHOD TO COMPARE EXPERIMENTS O by Angeles GIL (*) and Teófilo BREZMES (*)
Fuzzy Sets and Systems, 2014
When handling fuzzy number data, it is common practice to make use of a metric to quantify distan... more When handling fuzzy number data, it is 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, L 2 metrics become especially useful. This paper introduces a new family of generalized L 2 metrics which take into account key features of the involved fuzzy numbers, namely, a measure of central location and two measures associated with the shape of the fuzzy numbers are used. A crucial property related to these three measures is that necessary and sufficient conditions can be established for them to characterize fuzzy numbers. Furthermore, the family of generalized L 2 metrics depends on one parameter. A discussion is provided regarding the interpretation of this parameter which can guide selection of its value in practice.
METRON, 2013
Since Bertoluzza et al.'s metric between fuzzy numbers has been introduced, several studies invol... more 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 establish statistical methods for the analysis of fuzzy data. This paper shortly reviews such studies and examine part of the scientific impact of the metric.
Advances in Intelligent Systems and Computing, 2016
In a previous paper the fuzzy characterizing function of a random fuzzy number was introduced as ... more 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 number in a neighborhood of 0. This property suggests to consider the empirical fuzzy characterizing function as a tool to measure the dissimilarity between the distributions of two random fuzzy numbers, and its expected descriptive potentiality is illustrated by means of a real-life example.
Information Sciences, 2016
In evaluating aspects like quality perception, satisfaction or attitude which are intrinsically i... more 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, because of the total freedom in assessing ratings, with the ability of fuzzy linguistic variables to capture the natural imprecision in evaluating such aspects. Thanks to a recent methodology, the descriptive analysis of the responses to a fuzzy rating scale-based questionnaire can be now carried out. This paper aims to illustrate such an analysis through a real-life example, as well as to show that statistical conclusions can often be rather different from the conclusions one could get from either Likert scale-based responses or their fuzzy linguistic encoding. This difference encourages the use of the fuzzy rating scale when statistical conclusions are important, similarly to the use of exact real-valued data instead of grouping them.
Uploads
Papers by Maria Angeles Gil