Inés Couso

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

Este trabajo de investigación analiza la actividad internacional de las empresas del Principado de Asturias desde una perspectiva de género, estudiando la implicación de las mujeres en las estrategias, decisiones y actividades internacionales de las empresas. El estudio evidencia la existencia de una notable brecha de género: no solo la mayor parte...

During the pandemic, most of the teaching has been done online. The lack of face-to-face interaction has many undesirable effects, including students being less focused, not receiving feedback on how they are approaching the current topic/task, and an increased risk of cheating. It is expected that those students with similarly graded assignments/e...

Learning the deterioration of a battery from charge and discharge data is associated with different non-random uncertainties. A specific methodology is developed, capable of integrating expert knowledge about the problem and of handling the epistemic uncertainty associated with conflicts in the available information. It is shown that the simple con...

We consider the set-valued variance of random sets (Kruse variance) in those cases where the outcomes of the random set are closed subsets of a (finite dimensional) Euclidean space. We prove necessary and sufficient conditions for the existence and uniqueness of a random selection with minimum variance (minimal selection). In addition, we character...

In this work we propose a semi-supervised framework to visually assess the progression of time series. To this end, we present a recurrent version of the VAE to exploit the generative properties that lead it to learn in an unsupervised way a continuous compressed representation of the data. We introduce a classifier in the VAE training process to c...

An intelligent model of the incremental capacity (IC) curve of an automotive lithium-ferrophosphate battery is presented. The relative heights of the two major peaks of the IC curve can be acquired from high-current discharges, thus enabling the state of health estimation of the battery while the vehicle is being operated and in certain cases, agin...

Pacemaker logs are used to predict the progression of paroxysmal cardiac arrhythmia to permanent atrial fibrillation by means of different deep learning algorithms. Recurrent Neural Networks are trained on data produced by a generative model. The activations of the different nets are displayed in a graphical map that helps the specialist to gain in...

A method for monitoring the condition of lithium iron phosphate (LFP) rechargeable automotive batteries under fast-charging conditions is proposed. A learning fuzzy dynamic model is used for expressing the battery voltage as a sum of the open circuit voltage and the overpotential. The open circuit voltage term depends on a fuzzy rule-based model of...

Monotone transformation models are extended to inaccurate data and are combined with recurrent neural networks in a new battery model that is able to ascertain the health of rechargeable batteries for automotive applications. The presented method exploits the information contained in the vehicle’s operational records better than other cutting-edge...

A fuzzy model is presented for detecting changes in the incremental capacity curve of an automotive lithium-ferrophosphate battery through analysis of the data collected while the vehicle is being operated. By means of the proposed model, the state of health of the energy storage system can be estimated on-vehicle. The fuzzy model is derived throug...

Some formal relationships between the different axiomatic definitions of inclusion measure are analysed. In particular, the links between the different proposals about the null-space (the collection of pairs associated with a null degree of inclusion) are studied. Taking as starting point the well-known axiomatics of Kitainik and Sinha-Dougherty, w...

The problem of learning from imprecise data has recently attracted increasing attention, and various methods to tackle this problem have been proposed. In this paper, we discuss and compare two quite opposite approaches, an “optimistic” one that interprets imprecise data in a way that is most favourable for a candidate model, and a “pessimistic” on...

A recurrent neural network with fractional order dynamics is used for assessing the health of LFP rechargeable automotive batteries through incremental capacity analysis. The proposed algorithm learns a dynamical model of the battery voltage from samples of current and voltage taken on a vehicle. The output of this dynamical model is the sum of two...

The recent literature contains a multitude of extensions of (axiomatic) notions from the context of ordinary fuzzy sets to more general contexts. Using the language of lattices, we provide a general and compact formulation encompassing a large number of those notions and their potential extensions to even more complex frameworks. The new formulatio...

We revisit the relational study between different axiomatic definitions of similarity and dissimilarity of fuzzy sets developed in two previous articles. We observe that every axiomatic definition admits two variants, depending on whether we assume that the measure fulfills the corresponding properties when we restrict ourselves to a fixed finite c...

Basic ideas and formal concepts from fuzzy sets and fuzzy logic have been used successfully in various branches of science and engineering. This paper elaborates on the use of fuzzy sets in the broad field of data analysis and statistical sciences, including modern manifestations such as data mining and machine learning. In the fuzzy logic communit...

In this study, we discuss a new class of fuzzy subsethood measures between fuzzy sets. We propose a new definition of fuzzy subsethood measure as an intersection of other axiomatizations and provide two construction methods to obtain them. The advantage of this new approach is that we can construct fuzzy subsethood measures by aggregating fuzzy imp...

In this paper, we study distance measures between interval-valued fuzzy sets and entropies of interval-valued fuzzy sets. These are well-known and widely used notions in the fuzzy sets theory. The novelty of our approach is twofold: on one hand, it considers the width of intervals in order to connect the uncertainty of the output with the uncertain...

Logs of arrhythmia episodes in patients with pacemakers are used to estimate the temporal progression of atrial arrhythmia. In order to attain an early detection, a stream of dates and episode lengths are fed to an array of detectors, each of which is responsive to a narrow range of arrhythmias. The outputs of these detectors are organized on a pro...

An empirical comparison of different intelligent soft sensors for obtaining the state of health of automotive rechargeable batteries is presented. Data streamed from on-vehicle sensors of current, voltage and temperature is processed through a selection of model-based observers of the state of health, including data-driven statistical models, first...

We examine a broad collection of axiomatic definitions from various and diverse contexts, within the domain of fuzzy sets. We evaluate their respective extensions to the case of interval-valued fuzzy sets and intuitionistic fuzzy sets, from a purely formal point of view. We conclude that a large number of such extensions follow similar formal proce...

Graphical exploratory analysis for fuzzy data allows us to represent sets of individuals whose attributes are perceived with imprecision on a map so that the degree of dissimilarity between two objects is somehow compatible with the distances between their respective representations. This study will discuss the use of this tool to jointly analyze t...

We consider the problem of statistical inference for ranking data, namely the problem of estimating a probability distribution on the permutation space. Since observed rankings could be incomplete in the sense of not comprising all choice alternatives, we propose to tackle the problem as one of learning from imprecise or coarse data. To this end, w...

A framework is proposed for learning fuzzy rule-based systems from low quality data where the differences between observed and true values may introduce systematic bias in the model. It is argued that there are problems where aggregating imprecise losses into numerical or fuzzy-valued risk functions discards useful information, thus generalizing th...

Many different notions included in the fuzzy set literature can be expressed in terms of functionals defined over collections of tuples of fuzzy sets. During the last decades, different authors have independently generalised those definitions to more general contexts, like interval-valued fuzzy sets and Atanassov intuitionistic fuzzy sets. These ge...

A soft sensor is presented that approximates certain health parameters of automotive rechargeable batteries from on-vehicle measurements of current and voltage. The sensor is based on a model of the open circuit voltage curve. This last model is implemented through monotonic neural networks and estimate over-potentials arising from the evolution in...

We consider the problem of statistical inference for ranking data, specifically rank aggregation, under the assumption that samples are incomplete in the sense of not comprising all choice alternatives. In contrast to most existing methods, we explicitly model the process of turning a full ranking into an incomplete one, which we call the coarsenin...

Maximum likelihood is a standard approach to computing a probability distribution that best fits a given dataset. However, when datasets are incomplete or contain imprecise data, a major issue is to properly define the likelihood function to be maximized. This paper highlights the fact that there are several possible likelihood functions to be cons...

A model-based virtual sensor for assessing the health of rechargeable batteries for cyber-physical vehicle systems (CPVSs) is presented that can exploit coarse data streamed from on-vehicle sensors of current, voltage, and temperature. First-principle-based models are combined with knowledge acquired from data in a semiphysical arrangement. The dyn...

The term coarse data encompasses different types of incomplete data where the (partial) information about the outcomes of a random experiment can be expressed in terms of subsets of the sample space. We consider situations where the coarsening process is stochastic, and illustrate with examples how ignoring this process may produce misleading estim...

This paper presents an approach to applying stochastic orderings to evaluate classification algorithms for low quality data. It discusses some known stochastic orderings along with practical notes about their application to classifier evaluation. Finally, a new approach based on fuzzy cost function is presented. The new method allows comparing any...

A class of Fuzzy rule-based Monotone Wiener Models (FMWMs) is introduced. These are transformation models comprising a linear dynamical block and a memoryless nonlinearity. The smoothest dynamical block that has an output which is comonotonic with the training data is sought. The dependence between the output of the linear block and the output of t...

Kendall's rank correlation coefficient, also called Kendall's τ, is an efficient and robust way for identifying monotone relationships between two data sequences. However, when applied to digital data, the high number of ties yields inconsistent results due to quantization. Here, we propose an extension of Kendall's τ that considers an epistemic vi...

Maximum likelihood is a standard approach to computing a probability distribution that best fits a given dataset. However, when datasets are incomplete or contain imprecise data, depending on the purpose, a major issue is to properly define the likelihood function to be maximized. This paper compares several proposals in terms of their intuitive ap...

A method is proposed for predicting the pass rate of a Computer Science course. Input data comprises different software metrics that are evaluated on a set of programs, comprising students’ answers to a list of computing challenges proposed by the course instructor. Different kinds of uncertainty are accepted, including missing answers and multiple...

We develop a detailed formal study of the different variants of the notions of similarity and dissimilarity between fuzzy sets under the assumption of “additivity”. A measure of (dis)similarity is said to be additive when it can be decomposed as the sum of the particular (dis)similarities of the compared memberships over the different elements of t...

This paper provides a natural interpretation of the EM algorithm as a succession of revision steps that try to find a probability distribution in a parametric family of models in agreement with frequentist observations over a partition of a domain. Each step of the algorithm corresponds to a revision operation that respects a form of minimal change...

In the last decade, numerous proposals have been made to deal with imprecision in estimation problems. Those approaches, many of which involve dealing with interval-valued outputs, deal with the subtle difference between uncertainty and imprecision. One of the crucial points − which to our knowledge has never been addressed − is “how to compare an...

We study those problems where the goal is to find “optimal” models with respect to some specific criterion, in regression and supervised classification problems. Alternatives to the usual expected loss minimization criterion are proposed, and a general framework where this criterion can be seen as a particular instance of a general family of criter...

Numerical algorithms that can assess Engine Health Monitoring (EHM) data in aeroengines are influenced by the high level of uncertainty inherent to gas path measurements and engine-to-engine variability. Among them, fuzzy rule-based techniques have been successfully used due to their robustness towards noisy signals and their capability to learn hu...

An early detection and reeducation of dyslexic children is critical for their integration in the classroom. Parents and instructors can help the psychologist to detect potential cases of dyslexia before the children's writing age. Artificial intelligence tools can also assist in this task. Dyslexia symptoms are detected with tests whose results may...

We extend the notion of statistical preference to the general framework of imprecise probabilities, by proposing a new notion of desirability of gambles called “sign-desirability”, different from the usual desirability notion in Walley’s framework. We axiomatically characterize coherent families of sign-desirable gambles. We furthermore prove that...

In this paper we study how to make joint extensions of stochastic orderings and interval orderings so as to extend methods for comparing random variables, from the point of view of their respective location or magnitude, to fuzzy random variables. The main idea is that the way fuzzy random variables are interpreted affects the choice of the compari...

This note replies to comments made on our contribution to the Low Quality Data debate.

•This issue contains five position papers, nine discussion papers and five rejoinders.•Position papers propose different techniques to deal with uncertainty in statistics.•Each position paper is commented by two or more discussants.•A rejoinder to the discussions was written for each position paper.

In information processing tasks, sets may have a conjunctive or a disjunctive reading. In the conjunctive reading, a set represents an object of interest and its elements are subparts of the object, forming a composite description. In the disjunctive reading, a set contains mutually exclusive elements and refers to the representation of incomplete...

A new method for State of Charge estimation of LiFePO4 batteries through recursive filtering is presented. A fuzzy rule-based system is used to compute the nonlinear gain of the filter, and computational intelligence techniques are used to evolve the definition of the rule base. The estimation of the charge is based on a novel battery model that ac...

During the last decades, many papers on statistics with (fuzzy) set-valued data have been written. Successive editions of the SMPS conference have significantly contributed to the dissemination of these works. They cover some generalisations of different notions and methods in probability and statistics, ranging from the concepts of expectation or...

The roughness of a set (according to the notion introduced by Pawlak in 1991) can be regarded as the MZ-distance between its upper and the lower approximations. With this idea in mind, we have generalized Pawlak's definition, by replacing the MZ-distance by a general “distance” measure. We also generalize the notion of roughness of fuzzy sets intro...

Here we propose an adaption of Wilcoxon's two-sample rank-sum test to interval data. This adaption is interval-valued: it computes the minimum and maximum values of the statistic when we rank the set of all feasible samples (all joint samples compatible with the initial set-valued information). We prove that these bounds can be explicitly computed...

The concept of fuzzy random variable, that extends the classical definition of random variable, was introduced by Féron [37] in 1976. Later on, several authors, and especially Kwakernaak [54], Puri and Ralescu [62], Kruse and Meyer [53], Diamond and Kloeden [26], proposed other variants. More recently Krätschmer [51] surveyed all of these definitio...

The modern theory of random sets was initiated in the seventies, independently by Kendall [30] and Matheron [37] and it has been fruitfully applied in different fields such as economy, stochastic geometry and ill-observed random objects. Roughly speaking, a random set is a random element in a family of subsets of a certain universe. In particular,...

The notion of preference is reviewed from different perspectives, including the Imprecise Probabilities’ approach. Formal connections between different streams of the literature are provided, and new definitions are proposed.

Sorting a set of inputs for relevance in modeling problems may be ambiguous if the data is vague. A general extension procedure is proposed in this paper that allows applying different deterministic or random feature selection algorithms to fuzzy data. This extension is based on a model of the relevance of a feature as a possibility distribution. T...

When selecting relevant inputs in modeling problems with low quality data, the ranking of the most informative inputs is also uncertain. In this paper, this issue is addressed through a new procedure that allows the extending of different crisp feature selection algorithms to vague data. The partial knowledge about the ordinal of each feature is mo...

Genetic Fuzzy Systems have been successfully applied to assess Engine Health Monitoring (EHM) data from aeroengines, not only due to their robustness towards noisy gas path measurements and engine-to-engine variability, but also because of their capability to produce human-readable expressions. These techniques can detect the presence of certain ty...

A new bootstrap test is introduced that allows for assessing the significance of the differences between stochastic algorithms in a cross-validation with repeated folds experimental setup. Intervals are used for modeling the variability of the data that can be attributed to the repetition of learning and testing stages over the same folds in cross...

A methodology for designing semi-physical fuzzy models is proposed. Prior physical knowledge about the dynamics of the system is modeled with continuous time differential equations. Fuzzy knowledge bases are embedded in these equations as nonlinear constructive blocks. Rules comprising the knowledge bases are fitted to interval-valued data with met...

The design of user-friendly plots of Equipment Health Management (EHM) data for prognostic fault detection of aircraft engines is addressed. EHM plots link trend shift signatures, originated in cruise data of the engine being diagnosed, either with prototypes of specific known events or abnormal signatures derived from service data. Abnormalities a...

The notion of preference is reviewed from different perspectives, including the Imprecise Probabilities' approach. Formal connections between different streams of the literature are provided, and new definitions are proposed. © Springer International Publishing Switzerland 2014.

Within the fuzzy literature, the issue of ranking fuzzy intervals has been addressed by many authors, who proposed various solutions to the problem. Most of these solutions intend to find a total order on a given collection of fuzzy intervals. However, if one sees fuzzy intervals as descriptions of uncertain quantities, an alternative to rank them...

The classification algorithm FURIA (Fuzzy Unordered Rule Induction Algorithm) is extended in this paper to low quality data. An epistemic view of fuzzy memberships is adopted for modeling the incomplete knowledge about training and test sets. The proposed algorithm is validated in different real-world problems and compared to alternative fuzzy rule...

The software tool CI-LQD (Computational Intelligence for Low Quality Data) is introduced in this paper. CI-LQD is an ongoing project that includes a lightweight open source software that has been designed with scientific and teaching purposes in mind. The main usefulness of the software is to automate the calculations involved in the statistical co...

Existing extensions of AdaBoost-based fuzzy rule learning to low quality databases yield suboptimal results in multi-class problems. A new procedure is proposed where the original multi-class database is transformed into several multi-label problems that can be tackled with binary AdaBoost. The performance of this proposal is assessed in comparison...

A new algorithm for assessment of Engine Health Monitoring (EHM) data in aircraft is proposed. The diagnostic tool quantifies step changes, shifts and trends in EHM data by means of a transformation that aggregates concurrent readings of EHM data into a single fuzzy state. A Genetic Fuzzy System is used to detect the occurance of a specific trend o...

We introduce the notion of mode-desirability of a gamble, that generalizes the idea of non-negativeness of the mode of a random variable. The lower and upper previsions derived from this new definition coincide with the minimum and maximum values of the set of modes of a gamble, when the credal set is a singleton, but they only bound them in the ge...

The paper deals with the well-known notion of (dis)similarity measures between fuzzy sets. We provide three separate lists of axioms that fit with the respective notions of “general comparison measure”, “similarity measure” and “dissimilarity measure”. Then we review some of the most important axiomatic definitions of (dis)similarity measures in th...

An extension of the Adaboost algorithm is proposed for obtain-ing fuzzy rule based classifiers from imprecisely perceived data. Isolated fuzzy rules are regarded as weak learners, and knowl-edge bases as ensembles. Rules are iteratively added to a base, and the search of the best rule at each iteration is carried out by a genetic algorithm driven b...

Determining whether an imprecise dataset is imbalanced is not immediate. The vagueness in the data causes that the prior probabilities of the classes are not precisely known, and therefore the degree of imbalance can also be uncertain. In this paper we propose suitable extensions of different resampling algorithms that can be applied to interval va...

An extension of the Adaboost algorithm for obtaining fuzzy rule-based systems from low quality data is combined with preprocessing algorithms for equalizing imbalanced datasets. With the help of synthetic and real-world problems, it is shown that the performance of the Adaboost algorithm is degraded in presence of a moderate uncertainty in either t...

This paper deals with methods for ranking uncertain quantities in the setting of imprecise probabilities. It is shown that many techniques for comparing random variables or intervals can be generalized by means of upper and lower expectations of sets of gambles, so as to compare more general kinds of uncertain quantities. We show that many comparis...

Using a statistical model in a diagnosis task generally requires a large amount of labeled data. When ground truth information is not available, too expensive or difficult to collect, one has to rely on expert knowledge. In this paper, it is proposed ...

We extend the notion of confidence region to fuzzy data, by defining a pair of fuzzy inner and outer confidence regions. We show the connection with previous proposals, as well as with recent studies on hypothesis testing with low quality data.

The usual procedure to compare metaheuristics or evolutionary algorithms using cross validation is repeating the training stage several times for each train/test pair. In general, the results of the different repetitions are not independent and this practice is questionable. In this work, it is suggested to represent the results of each train/test...

Fuzzy memberships can be understood as coverage functions of random sets. This interpretation makes sense in the context of fuzzy rule learning: a random-sets-based semantic of the linguistic labels is compatible with the use of fuzzy statistics for obtaining knowledge bases from data. In particular, in this paper we formulate the learning of a fuz...

The theory of sets of desirable gambles is a very general model which covers most of the existing theories for imprecise probability as special cases; it has a clear and simple axiomatic justification; and mathematical definitions are natural and intuitive. However, much work remains to be done until the theory of desirable gambles can be considere...

Cost-sensitive classification is based on a set of weights defining the expected cost of misclassifying an object. In this paper, a Genetic Fuzzy Classifier, which is able to extract fuzzy rules from interval or fuzzy valued data, is extended to this type of classification. This extension consists in enclosing the estimation of the expected misclas...

When the Adaboost algorithm is used for extracting fuzzy rules from data, each rule is regarded as a weak learner, and knowledge bases as assimilated to ensembles. In this paper we propose an extension of this framework for obtaining fuzzy rule-based classifiers from imprecise data. In the new approach, the mentioned search of the best rule at each...

The usual procedure to compare metaheuristics or evolutionary algorithms using cross validation is repeating the training stage several times for each train/test pair. In general, the results of the different repetitions are not independent and this practice is questionable. In this work, it is suggested to represent the results of each train/test...

A generalization of the singular spectral anal-ysis (SSA) technique to ill-defined data is introduced in this paper. The proposed algorithm achieves tight estimates of the energy of irregular or aperiodic oscillations from records of interval or fuzzy-valued signals. Fuzzy signals are given a possibilistic interpretation as families of nested confi...