@article {COUSO201735,
	title = {Additive similarity and dissimilarity measures},
	journal = {Fuzzy Sets and Systems},
	volume = {322},
	year = {2017},
	note = {Theme: Preference and Similarity},
	pages = {35 - 53},
	abstract = {We develop a detailed formal study of the different variants of the notions of similarity and dissimilarity between fuzzy sets under the assumption of {\textquotedblleft}additivity{\textquotedblright}. 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 the universe. Some formal relations between existing formalizations of the notions of {\textquotedblleft}similarity{\textquotedblright} and {\textquotedblleft}dissimilarity{\textquotedblright} arise under this additional assumption. We conclude that, in this particular setting, one may basically distinguish between two main categories of comparison measures in the literature: those that depend on both the intersection and the difference of the compared items and those that only depend on their difference.},
	keywords = {Comparison measure, Dissimilarity measure, Divergence measure, Measure of resemblance, Measure of similitude, Similarity measure},
	issn = {0165-0114},
	doi = {https://doi.org/10.1016/j.fss.2016.12.013},
	url = {http://www.sciencedirect.com/science/article/pii/S0165011416304547},
	author = {In{\'e}s Couso and Luciano S{\'a}nchez}
}
@article {PALACIOS201660,
	title = {An extension of the FURIA classification algorithm to low quality data through fuzzy rankings and its application to the early diagnosis of dyslexia},
	journal = {Neurocomputing},
	volume = {176},
	year = {2016},
	note = {Recent Advancements in Hybrid Artificial Intelligence Systems and its Application to Real-World Problems},
	pages = {60 - 71},
	abstract = {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 be vague or ambiguous, thus machine learning techniques for low quality data are advised. In particular, in this paper it is suggested that a new extension to vague datasets of the classification algorithm FURIA (Fuzzy Unordered Rule Induction Algorithm) has advantages over other approaches in both the computational effort during the learning stage and the linguistic quality of the induced classification rules. The new approach is benchmarked with different test problems and compared to other artificial intelligence tools for dyslexia diagnosis in the literature.},
	keywords = {Dyslexia, FURIA, Fuzzy rule based classifiers, Low Quality Data},
	issn = {0925-2312},
	doi = {https://doi.org/10.1016/j.neucom.2014.11.088},
	url = {http://www.sciencedirect.com/science/article/pii/S0925231215005706},
	author = {Ana Palacios and Luciano S{\'a}nchez and In{\'e}s Couso and S{\'e}bastien Destercke}
}
@article {OTERO201642,
	title = {Finding informative code metrics under uncertainty for predicting the pass rate of online courses},
	journal = {Information Sciences},
	volume = {373},
	year = {2016},
	pages = {42 - 56},
	abstract = {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{\textquoteright} answers to a list of computing challenges proposed by the course instructor. Different kinds of uncertainty are accepted, including missing answers and multiple responses to the same challenge. The most informative metrics are selected according to an extension to vague data of the observed Fisher information. The proposed method was tested on experimental data collected during two years at Oviedo University. Yearly changes in the pass rate of two groups were accurately predicted on the basis of 7 software metrics. 73 volunteer students and 1500 source files were involved in the experimentation.},
	keywords = {Automatic grading, feature selection, Genetic Fuzzy Systems, Low Quality Data, vague data},
	issn = {0020-0255},
	doi = {https://doi.org/10.1016/j.ins.2016.08.090},
	url = {http://www.sciencedirect.com/science/article/pii/S0020025516306715},
	author = {Jos{\'e} Otero and Luis Junco and Rosario Su{\'a}rez and Ana Palacios and In{\'e}s Couso and Luciano S{\'a}nchez}
}
@article {COUSO2016129,
	title = {Machine learning models, epistemic set-valued data and generalized loss functions: An encompassing approach},
	journal = {Information Sciences},
	volume = {358-359},
	year = {2016},
	pages = {129 - 150},
	abstract = {We study those problems where the goal is to find {\textquotedblleft}optimal{\textquotedblright} 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 criteria is provided. In the new setting, each model is formally identified with a random variable that associates a loss value to each individual in the population. Based on this identification, different stochastic orderings between random variables lead to different criteria to compare pairs of models. Our general setting encompasses the classical criterion based on the minimization of the expected loss, but also other criteria where a numerical loss function is not available, and therefore the computation of its expectation does not make sense. The presentation of the new framework is divided into two stages. First, we consider the new framework under standard situations about the sample information, where both the collection of attributes and the response variables are observed with precision. Then, we assume that just incomplete information about them (expressed in terms of set-valued data sets) is provided. We cast some comparison criteria from the recent literature on learning methods from low-quality data as particular instances of our general approach.},
	keywords = {classification, Generalized stochastic ordering, Loss function, Low-quality data, Regression, Set-valued data},
	issn = {0020-0255},
	doi = {https://doi.org/10.1016/j.ins.2016.04.016},
	url = {http://www.sciencedirect.com/science/article/pii/S0020025516302511},
	author = {In{\'e}s Couso and Luciano S{\'a}nchez}
}
@article {PALACIOS201510,
	title = {Sequential pattern mining applied to aeroengine condition monitoring with uncertain health data},
	journal = {Engineering Applications of Artificial Intelligence},
	volume = {44},
	year = {2015},
	pages = {10 - 24},
	abstract = {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 human-readable rules from data. These techniques are useful in detecting the presence of certain types of abnormal events or general engine deterioration, through the identification of specific combinations of EHM signals associated with these specific cases. However, there are also other types of engine events that manifest themselves as an ordered sequence of otherwise normal combinations of the EHM signals. These combinations are dismissed when considered in isolation as the current existing techniques cannot assess them. In this paper it is proposed to use sequence mining techniques in order to obtain fuzzy rules from uncertain EHM data which can in turn be used to identify the cases where an engine event is determined as a sequence of otherwise normal combinations of EHM signals. The results are subsequently tested on a representative sample of aeroengine data.},
	keywords = {engine health monitoring, Fuzzy rule-based systems, Fuzzy sequence mining, Uncertain data},
	issn = {0952-1976},
	doi = {https://doi.org/10.1016/j.engappai.2015.05.003},
	url = {http://www.sciencedirect.com/science/article/pii/S0952197615001062},
	author = {Ana Palacios and Alvaro Mart{\'\i}nez and Luciano S{\'a}nchez and In{\'e}s Couso}
}
@article {COUSO2015127,
	title = {The behavioral meaning of the median},
	journal = {Information Sciences},
	volume = {294},
	year = {2015},
	note = {Innovative Applications of Artificial Neural Networks in Engineering},
	pages = {127 - 138},
	abstract = {We extend the notion of statistical preference to the general framework of imprecise probabilities, by proposing a new notion of desirability of gambles called {\textquotedblleft}sign-desirability{\textquotedblright}, different from the usual desirability notion in Walley{\textquoteright}s framework. We axiomatically characterize coherent families of sign-desirable gambles. We furthermore prove that the pair of lower and upper previsions of a gamble, according to this new desirability notion, coincides with the pair of bounds (infimum and supremum) of the set of medians associated to a coherent family of linear previsions. Thus, a general notion of median is naturally derived, and provided with a behavioral meaning. As a consequence of these results, the connection between statistical preference in classical Probability Theory, and the sign of the median of the difference of two random variables is laid bare.},
	keywords = {Desirable gamble, Imprecise Probability, Median, Statistical preference, Stochastic ordering},
	issn = {0020-0255},
	doi = {https://doi.org/10.1016/j.ins.2014.08.049},
	url = {http://www.sciencedirect.com/science/article/pii/S0020025514008548},
	author = {In{\'e}s Couso and Seraf{\'\i}n Moral and Luciano S{\'a}nchez}
}
@article {SANCHEZ2014269,
	title = {A design methodology for semi-physical fuzzy models applied to the dynamic characterization of LiFePO4 batteries},
	journal = {Applied Soft Computing},
	volume = {14},
	year = {2014},
	note = {Evolving Soft Computing Techniques and Applications},
	pages = {269 - 288},
	abstract = {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 metaheuristics. A possibilistic filter is proposed that is able to gradually evolve an initial estimation of the latent variables of the model on the basis of successive prediction errors. This methodology has been applied to the prediction of voltage and state of charge of LiFePO4 batteries. An empirical study has been carried over data gathered in experiments at the Battery Laboratory at Oviedo University. Fitting between the proposed model and actual measurements is studied for four different manufacturers and different charge{\textendash}discharge patterns. Predictions of the evolution of the voltage during charge, discharge and inactivity compare favorably to different models in the literature. The possibilistic filter allows to estimate the state of charge of batteries after an arbitrary path that may include partial charges and discharges. It is shown that the accuracy of the open loop model improves that of other approaches in the literature, and at the same time the observer-based online model is able to approximate the effective remnant charge of the battery after a reasonably short time.},
	keywords = {fuzzy models, Imprecise data, LiFePO batteries, Online identification, Semi-physical modeling},
	issn = {1568-4946},
	doi = {https://doi.org/10.1016/j.asoc.2013.03.020},
	url = {http://www.sciencedirect.com/science/article/pii/S156849461300135X},
	author = {Luciano S{\'a}nchez and In{\'e}s Couso and Manuela Gonz{\'a}lez}
}
@conference {Otero2014APF,
	title = {A Procedure for Extending Input Selection Algorithms to Low Quality Data in Modelling Problems with Application to the Automatic Grading of Uploaded Assignments},
	booktitle = {TheScientificWorldJournal},
	year = {2014},
	author = {Jos{\'e} Varela Otero and Ana M. Palacios and Rosario Su{\'a}rez and Luis Junco and In{\'e}s Couso and Luciano S{\'a}nchez}
}
@article {OTERO201488,
	title = {Bootstrap analysis of multiple repetitions of experiments using an interval-valued multiple comparison procedure},
	journal = {Journal of Computer and System Sciences},
	volume = {80},
	number = {1},
	year = {2014},
	pages = {88 - 100},
	abstract = {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 validation. Numerical experiments are provided that support the following three claims: (1) Bootstrap tests can be more powerful than ANOVA or Friedman test for comparing multiple classifiers. (2) In the presence of outliers, interval-valued bootstrap tests achieve a better discrimination between stochastic algorithms than nonparametric tests. (3) Choosing ANOVA, Friedman or Bootstrap can produce different conclusions in experiments involving actual data from machine learning tasks.},
	keywords = {Cross validation, Statistical comparisons of algorithms, Tests for interval-valued data},
	issn = {0022-0000},
	doi = {https://doi.org/10.1016/j.jcss.2013.03.009},
	url = {http://www.sciencedirect.com/science/article/pii/S0022000013000731},
	author = {Jos{\'e} Otero and Luciano S{\'a}nchez and In{\'e}s Couso and Ana Palacios}
}
@article {Couso2014HarnessingTI,
	title = {Harnessing the information contained in low-quality data sources},
	journal = {Int. J. Approx. Reasoning},
	volume = {55},
	year = {2014},
	pages = {1485-1486},
	author = {In{\'e}s Couso and Luciano S{\'a}nchez}
}
@article {COUSO2014114,
	title = {The notion of roughness of a fuzzy set},
	journal = {Fuzzy Sets and Systems},
	volume = {249},
	year = {2014},
	note = {Theme: Automata Theory and Algebra},
	pages = {114 - 127},
	abstract = {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{\textquoteright}s definition, by replacing the MZ-distance by a general {\textquotedblleft}distance{\textquotedblright} measure. We also generalize the notion of roughness of fuzzy sets introduced by Huyhn and Nakamori in 2005.},
	keywords = {Dissimilarity measure, Divergence measure, fuzzy set, Rough set, Roughness},
	issn = {0165-0114},
	doi = {https://doi.org/10.1016/j.fss.2014.02.013},
	url = {http://www.sciencedirect.com/science/article/pii/S0165011414000657},
	author = {In{\'e}s Couso and Laura Garrido and Luciano S{\'a}nchez}
}
@article {Couso2013SimilarityAD,
	title = {Similarity and dissimilarity measures between fuzzy sets: A formal relational study},
	journal = {Inf. Sci.},
	volume = {229},
	year = {2013},
	pages = {122-141},
	author = {In{\'e}s Couso and Laura Garrido and Luciano S{\'a}nchez}
}
@article {COUSO201168,
	title = {Inner and outer fuzzy approximations of confidence intervals},
	journal = {Fuzzy Sets and Systems},
	volume = {184},
	number = {1},
	year = {2011},
	note = {Preference Modelling and Decision Analysis (Selected Papers from EUROFUSE 2009)},
	pages = {68 - 83},
	abstract = {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.},
	keywords = {Confidence region, Hypothesis testing, Possibility measure},
	issn = {0165-0114},
	doi = {https://doi.org/10.1016/j.fss.2010.11.004},
	url = {http://www.sciencedirect.com/science/article/pii/S0165011410004550},
	author = {In{\'e}s Couso and Luciano S{\'a}nchez}
}
@article {PALACIOS2011841,
	title = {Linguistic cost-sensitive learning of genetic fuzzy classifiers for imprecise data},
	journal = {International Journal of Approximate Reasoning},
	volume = {52},
	number = {6},
	year = {2011},
	pages = {841 - 862},
	abstract = {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 misclassification risk of a classifier, when assessed on low quality data, in an interval or a fuzzy number. A cooperative-competitive genetic algorithm searches for the knowledge base whose fitness is primal with respect to a precedence relation between the values of this interval or fuzzy valued risk. In addition to this, the numerical estimation of this risk depends on the entrywise product of cost and confusion matrices. These have been, in turn, generalized to vague data. The flexible assignment of values to the cost function is also tackled, owing to the fact that the use of linguistic terms in the definition of the misclassification cost is allowed.},
	keywords = {Cost sensitive classification, genetic fuzzy system, Low Quality Data},
	issn = {0888-613X},
	doi = {https://doi.org/10.1016/j.ijar.2011.02.007},
	url = {http://www.sciencedirect.com/science/article/pii/S0888613X11000545},
	author = {Ana M. Palacios and Luciano S{\'a}nchez and In{\'e}s Couso}
}
@article {COUSO2011240,
	title = {Mark-recapture techniques in statistical tests for imprecise data},
	journal = {International Journal of Approximate Reasoning},
	volume = {52},
	number = {2},
	year = {2011},
	note = {Philosophy of Probability},
	pages = {240 - 260},
	abstract = {We aim to construct suitable tests when we have imprecise information about a sample. More specifically, we assume that we get a collection of n sets of values, each one characterizing an imprecise measurement. Each set specifies where the true sample value is (and where it is not) with full confidence, but it does not provide any additional information. Our main objectives are twofold: first we will review different kinds of tests in the literature about inferential statistics with random sets and discuss the approach that best suits our definition of imprecise data. Secondly, we will show that we can take advantage from mark and recapture techniques to improve the accuracy of our decisions. These techniques will be specially important when the population is small enough (with respect to the sample size) that recaptures are common. They also seem to be useful when resampling techniques are involved in the decision process.},
	keywords = {Hypothesis testing, Imprecise data analysis, Multi-valued mappings, Multi-valued test function, Probability bounds},
	issn = {0888-613X},
	doi = {https://doi.org/10.1016/j.ijar.2010.07.009},
	url = {http://www.sciencedirect.com/science/article/pii/S0888613X10000952},
	author = {In{\'e}s Couso and Luciano S{\'a}nchez}
}
@conference {Snchez2010AssessingTE,
	title = {Assessing the evolution of learning capabilities and disorders with graphical exploratory analysis of surveys containing missing and conflicting answers},
	year = {2010},
	author = {Luciano S{\'a}nchez and In{\'e}s Couso and Jos{\'e} Varela Otero and Ana M. Palacios}
}
@article {COUSO2008237,
	title = {Higher order models for fuzzy random variables},
	journal = {Fuzzy Sets and Systems},
	volume = {159},
	number = {3},
	year = {2008},
	note = {Theme: Probability and Statistics},
	pages = {237 - 258},
	abstract = {A fuzzy random variable is viewed as the imprecise observation of the outcomes in a random experiment. Since randomness and vagueness coexist in the same framework, it seems reasonable to integrate fuzzy random variables into imprecise probabilities theory. Nevertheless, fuzzy random variables are commonly presented in the literature as classical measurable functions associated to a classical probability measure. We present here a higher order possibility model that represents the imprecise information provided by a fuzzy random variable. We compare it with previous classical models in the literature. First, some aspects about the acceptability function associated to a fuzzy random variable are investigated. Secondly, we present three different higher order possibility models, all of them arising in a natural way. We investigate their similarities and differences, and observe that the first one (the fuzzy probability envelope) is the most informative. Finally we compare the fuzzy probability envelope with the (classical) probability measure induced by the fuzzy random variable. We conclude that the classical probability measure does not always contain all relevant information provided by a fuzzy random variable.},
	keywords = {Fuzzy random variable, Imprecise probabilities, Random set, Second order possibility measure},
	issn = {0165-0114},
	doi = {https://doi.org/10.1016/j.fss.2007.09.004},
	url = {http://www.sciencedirect.com/science/article/pii/S0165011407003971},
	author = {In{\'e}s Couso and Luciano S{\'a}nchez}
}
@article {SANCHEZ2008607,
	title = {Mutual information-based feature selection and partition design in fuzzy rule-based classifiers from vague data},
	journal = {International Journal of Approximate Reasoning},
	volume = {49},
	number = {3},
	year = {2008},
	pages = {607 - 622},
	abstract = {Algorithms for preprocessing databases with incomplete and imprecise data are seldom studied. For the most part, we lack numerical tools to quantify the mutual information between fuzzy random variables. Therefore, these algorithms (discretization, instance selection, feature selection, etc.) have to use crisp estimations of the interdependency between continuous variables, whose application to vague datasets is arguable. In particular, when we select features for being used in fuzzy rule-based classifiers, we often use a mutual information-based ranking of the relevance of inputs. But, either with crisp or fuzzy data, fuzzy rule-based systems route the input through a fuzzification interface. The fuzzification process may alter this ranking, as the partition of the input data does not need to be optimal. In our opinion, to discover the most important variables for a fuzzy rule-based system, we want to compute the mutual information between the fuzzified variables, and we should not assume that the ranking between the crisp variables is the best one. In this paper we address these problems, and propose an extended definition of the mutual information between two fuzzified continuous variables. We also introduce a numerical algorithm for estimating the mutual information from a sample of vague data. We will show that this estimation can be included in a feature selection algorithm, and also that, in combination with a genetic optimization, the same definition can be used to obtain the most informative fuzzy partition for the data. Both applications will be exemplified with the help of some benchmark problems.},
	keywords = {feature selection, Fuzzy fitness, Genetic Fuzzy Systems, vague data},
	issn = {0888-613X},
	doi = {https://doi.org/10.1016/j.ijar.2008.06.005},
	url = {http://www.sciencedirect.com/science/article/pii/S0888613X08001102},
	author = {Luciano S{\'a}nchez and M. Rosario Su{\'a}rez and J.R. Villar and In{\'e}s Couso}
}
@article {SANCHEZ2001175,
	title = {Combining GP operators with SA search to evolve fuzzy rule based classifiers},
	journal = {Information Sciences},
	volume = {136},
	number = {1},
	year = {2001},
	note = {Recent Advances in Genetic Fuzzy Systems},
	pages = {175 - 191},
	abstract = {The genotype{\textendash}phenotype encoding of fuzzy rule bases in GA, along with their corresponding crossover and mutation operators, can be used by other search schemes, improving the behavior of these last ones. As a practical consequence of this, a simulated annealing-based method for inducting both parameters and structure of a fuzzy classifier has been developed. The adjacency operator in SA has been replaced with a macromutation taken from tree-shaped genotype GAs. We will show that results of SA search are similar to those of GP in both the efficiency of the learned classifiers and in its linguistic interpretability, while the memory consumption of the learning process is lower.},
	keywords = {Fuzzy classification, genetic algorithms, Genetic programming, Simulated annealing},
	issn = {0020-0255},
	doi = {https://doi.org/10.1016/S0020-0255(01)00146-3},
	url = {http://www.sciencedirect.com/science/article/pii/S0020025501001463},
	author = {Luciano S{\'a}nchez and In{\'e}s Couso and J.A. Corrales}
}
