title: Automatic Detection of Symmetry in Dermoscopic Images Based on Shape and Texture

text: In this paper we present computational methods to detect the symmetry in dermoscopic images of skin lesions. Skin lesions are assessed by dermatologists based on a number of factors. In the literature, the asymmetry of lesions appears recurrently since it may indicate irregular growth. We aim at developing an automatic algorithm that can detect symmetry in skin lesions, as well as indicating the axes of symmetry. We tackle this task based on skin lesions’ shape, based on their color and texture, and based on their combination. To do so, we consider symmetry axes through the center of mass, random forests classifiers to aggregate across different orientations, and a purposely-built dataset to compare textures that are specific of dermoscopic imagery. We obtain 84–88% accuracy in comparison with samples manually labeled as having either 1-axis symmetry, 2-axes symmetry or as being asymmetric. Besides its diagnostic value, the symmetry of a lesion also explains the reasons that might support such diagnosis. Our algorithm does so by indicating how many axes of symmetry were found, and by explicitly computing them.


title: Softening the Robustness of Optimization Problems: A New Budgeted Uncertainty Approach

text: In this paper an optimization problem with uncertain parameters is discussed. In the traditional robust approach a pessimistic point of view is assumed. Namely, a solution is computed under the worst possible parameter realizations, which can lead to large deterioration of the objective function value. In this paper a new approach is proposed, which assumes a less pessimistic point of view. The complexity of the resulting problem is explored and some methods of solving its special cases are presented.


title: Electrical Power Grid Frequency Estimation with Fuzzy Boolean Nets

text: Power quality analysis involves the measurement of quantities that characterize a power supply waveform such as its frequency. The measurement of those quantities are regulated by internationally accepted standards from IEEE or IEC. Monitoring the delivered power quality is even more important due to recent advances in power electronics and also due to the increasing penetration of renewable energies in the electrical power grid. The primary suggested method by IEC to measure the power grid frequency is to count the number of zero crossings in the voltage waveform that occur during 0.2 s. The standard zero crossing method is usually applied to a filtered signal that has a non deterministic and frequency dependent delay. For monitoring the power grid a range between 42.5 and 57.5 Hz should be considered which means that the filter must be designed in order to attenuate the delay compensation error. Fuzzy Boolean Nets can be considered a neural fuzzy model where the fuzziness is an inherent emerging property that can ignore some outliers acting as a filter. This property can be useful to apply zero crossing without false crossing detection and estimate the real timestamp without the non deterministic delay concern. This paper presents a comparison between the standard frequency estimation, a Goertzel interpolation method, and the standard method applied after a FBN network instead of a filtered signal.


title: Automatic Truecasing of Video Subtitles Using BERT: A Multilingual Adaptable Approach

text: This paper describes an approach for automatic capitalization of text without case information, such as spoken transcripts of video subtitles, produced by automatic speech recognition systems. Our approach is based on pre-trained contextualized word embeddings, requires only a small portion of data for training when compared with traditional approaches, and is able to achieve state-of-the-art results. The paper reports experiments both on general written data from the European Parliament, and on video subtitles, revealing that the proposed approach is suitable for performing capitalization, not only in each one of the domains, but also in a cross-domain scenario. We have also created a versatile multilingual model, and the conducted experiments show that good results can be achieved both for monolingual and multilingual data. Finally, we applied domain adaptation by finetuning models, initially trained on general written data, on video subtitles, revealing gains over other approaches not only in performance but also in terms of computational cost.


title: Concept Membership Modeling Using a Choquet Integral

text: Imprecise and subjective concepts, as e.g. promising students, may be used within data mining tasks or database queries to faithfully describe data properties of interest. However, defining these concepts is a demanding task for the end-user. We thus provide a strategy, called CHOCOLATE, that only requires the user to give a tiny subset of data points that are representative of the concept he/she has in mind, and that infers a membership function from them. This function may then be used to retrieve, from the whole dataset, a ranked list of points that satisfy the concept of interest. CHOCOLATE relies on a Choquet integral to aggregate the relevance of individual attribute values among all the representative points as well as the representativity of sets of such attribute values. As a consequence, a valuable property of the proposed approach is that it is able to both capture properties shared by most of the user-selected representative data points as well as specific properties possessed by only one specific representative data point.


title: Graphical Causal Models and Imputing Missing Data: A Preliminary Study

text: Real-world datasets often contain many missing values due to several reasons. This is usually an issue since many learning algorithms require complete datasets. In certain cases, there are constraints in the real world problem that create difficulties in continuously observing all data. In this paper, we investigate if graphical causal models can be used to impute missing values and derive additional information on the uncertainty of the imputed values. Our goal is to use the information from a complete dataset in the form of graphical causal models to impute missing values in an incomplete dataset. This assumes that the datasets have the same data generating process. Furthermore, we calculate the probability of each missing data value belonging to a specified percentile. We present a preliminary study on the proposed method using synthetic data, where we can control the causal relations and missing values.


title: On Ruspini’s Models of Similarity-Based Approximate Reasoning

text: In his 1991 seminal paper, Enrique H. Ruspini proposed a similarity-based semantics for fuzzy sets and approximate reasoning which has been extensively used by many other authors in various contexts. This brief note, which is our humble contribution to honor Ruspini’s great legacy, describes some of the main developments in the field of logic that essentially rely on his ideas.


title: Deep Conformal Prediction for Robust Models

text: Deep networks, like some other learning models, can associate high trust to unreliable predictions. Making these models robust and reliable is therefore essential, especially for critical decisions. This experimental paper shows that the conformal prediction approach brings a convincing solution to this challenge. Conformal prediction consists in predicting a set of classes covering the real class with a user-defined frequency. In the case of atypical examples, the conformal prediction will predict the empty set. Experiments show the good behavior of the conformal approach, especially when the data is noisy.


title: Sufficient Solvability Conditions for Systems of Partial Fuzzy Relational Equations

text: This paper focuses on searching sufficient conditions for the solvability of systems of partial fuzzy relational equations. In the case of solvable systems, we provide solutions of the systems. Two standard systems of fuzzy relational equations – namely the systems built on the basic composition and on the Bandler-Kohout subproduct – are considered under the assumption of partiality. Such an extension requires to employ partial algebras of operations for dealing with undefined values. In this investigation, we consider seven most-known algebras of undefined values in partial fuzzy set theory such as the Bochvar, Bochvar external, Sobociński, McCarthy, Nelson, Kleene, and the Łukasiewicz algebra. Conditions that are sufficient for the solvability of the systems are provided. The crucial role will be played by the so-called boundary condition.


title: Thin Structures Segmentation Using Anisotropic Neighborhoods

text: Bayesian and probabilistic models are widely used in image processing to handle noise due to various alteration phenomena. To benefit from the spatial information in a tractable way, Markov Random Fields (MRF) are often assumed with isotropic neighborhoods, that is however at the detriment of the preservation of thin structures. In this study, we aim at relaxing this assumption on stationarity and isotropy of the neighborhood shape in order to get a prior probability term that is relevant not only within the homogeneous areas but also close to object borders and within thin structures. To tackle the issue of neighborhood shape estimation, we propose to use tensor voting, that allows for the estimation of structure direction and saliency at various scales. We propose three main ways to derive anisotropic neighborhoods, namely shape-based, target-based and cardinal-based neighborhood. Then, having defined the neighborhood field, we introduce an energy that will be minimized using graph cuts, and illustrate the benefits of our approach against the use of isotropic neighborhoods in the applicative context of crack detection. First results on such a challenging problem are very encouraging.


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title: Le confinement généralisé pendant l’épidémie de Coronavirus: Conséquences médico-psychologiques en populations générales, soignantes, et de sujets souffrant antérieurement de troubles psychiques

text: Background. – The situation we are currently experiencing is unprecedented. Declaring a state of health emergency in order to curb a frightening epidemic, the authorities have decreed the home confinement of the majority of the population of our country for several weeks. In a few days, innumerable questions arise for very diverse spaces: epidemiological, immunological, sociological, information scientists, medical, administrative, political, etc. Objective. – We propose a reflection intended to describe the psychological risks, to clarify the disorders found and, to discuss the means to take care of them in the duration. Material and methods. – We base our thinking on a review of the literature confronted with our current clinical experience, including concerning the possibilities of dematerialized medico-psychological monitoring. Results. – We recall the collective repercussions of emerging lethal mass risks, and in particular viral infectious agents, before approaching the existing scientific models of collective confinement according to military operations in hostile zones, polar wintering missions and aerospace conquest. It appears that for the study of a global containment, somewhat studied during previous pandemics, the conceptions of stress reaction and psychodynamic adaptation prove to be relevant. We detail the psychological consequences of confinement on individual mental health and their countermeasures according to three population typologies: general population, population of caregivers on the front line against the epidemic, and population of subjects already suffering from mental illness or seeing their disorders reappear. We also refer to works in social cognitive psychology explaining how, in an anxiety-provoking situation, reasoning can be biased and lead to choices that ultimately prove to be not very rational, in the opinion of those who made them. The current situation in the health sector is favorable in this, as evidenced by the "debate on chloroquine" widely reported in the media and on social networks, opposing conclusions most often decided on the basis of beliefs on contrary to evidence based medicine. Discussion. – The psychological repercussions of confinement appear conditioned by the multiple forms that it can take: voluntary or suffered, more or less prolonged, spent at home or in another place, lived in individual isolation or in a small community, associated other stressors and/or traumatic factors, etc. The home confinement of a population across a country has never been assessed. This experience seems to us to confront our society as a whole with the taboo of death which is imposed, death more and more evaded as the "Western man" tries to move away from his terrestrial origins. In this sense, psychotraumatic type repercussions are to be prevented. In order to face multiple challenges, the healthcare system has adapted with, in particular, the development of the use of the Internet for the provision of information intended to better experience confinement, or even the generalization of psychotherapy remotely asking as many questions as it provides answers. These intricacies of computer techniques in the area of psychotherapy, techniques with which we had some mistrust, became established as quickly as the virus: the task of clinicians and researchers to measure the issues and the consequences. Conclusion. – Public health programs could emerge on the model of those already existing in order to manage well-known chronic endemic disorders: protection against the effects of an unbalanced diet associated with a sedentary lifestyle, fight against smoking and alcoholism, prevention of self-aggressive behavior, etc. We will also need to support the caregivers who have been on the front line and who will emerge tested from this pandemic: will depend on the sustainability of the action capacities of our healthcare system to return to its nominal state and also perhaps, so that it can face other crises, especially social ones.


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How to deal with misinformation and disinformation during public health emergencies. A new EACH course.


title: Evidential Group Spammers Detection

text: Online reviews are considered as one of the most prevalent reference indicators for people to evaluate the quality of different products or services before purchasing. Since these reviews affect the buying decision of customers and control the success of the different e-commerce websites, the activity of fake reviews posting is more and more increasing. These fraudulent reviews are posted by a large number of spammers who try to promote or demote target products or companies. The reviewers spammers generally work collaboratively under group of spammers to take control of reviews given to some products, which seriously damage the review system. To deal with this issue, we propose a novel method aim to detect group spammers while relying on various group spamming behavioral indicators. Our approach is based on the K-nearest neighbors algorithm under the belief function theory to treat the uncertainty in the used behavioral indicators. Our method succeeds in distinguishing between genuine and fraudulent group of reviewers. It was tested on two large real datasets extracted from yelp.com.


title: Gold Price: Trend-Cycle Analysis Using Fuzzy Techniques

text: In this paper, we apply special fuzzy techniques to analyze the gold price historical data. The main tools are the higher degree fuzzy transform and specific methods of fuzzy natural logic. First, we show how to apply the former for the estimation of the trend-cycle. Then, we provide methodologies for identifying monotonous periods in the trend-cycle and describe them by sentences in natural language.


title: Statistical Methods for Processing Neuroimaging Data from Two Different Sites with a Down Syndrome Population Application

text: Harmonization of magnetic resonance imaging (MRI) and positron emission tomography (PET) scans from multi-scanner and multi-site studies presents a challenging problem. We applied the Removal of Artificial Voxel Effect by Linear regression (RAVEL) method to normalize T1-MRI intensities collected on two different scanners across two different sites as part of the Neurodegeneration in Aging Down syndrome (NiAD) study. The effects on FreeSurfer regional cortical thickness and volume outcome measures, in addition to FreeSurfer-based regional quantification of amyloid PET standardized uptake value ratio (SUVR) outcomes, were evaluated. A neuroradiologist visually assessed the accuracy of FreeSurfer hippocampus segmentations with and without the application of RAVEL. Quantitative results demonstrated that the application of RAVEL intensity normalization prior to running FreeSurfer significantly impacted both FreeSurfer volume and cortical thickness outcome measures. Visual assessment demonstrated that the application of RAVEL significantly improved FreeSurfer hippocampal segmentation accuracy. The RAVEL intensity normalization had little impact on PET SUVR measures.


title: Imprecise Approaches to Analysis of Insurance Portfolio with Catastrophe Bond

text: In this paper, imprecise approaches to model the risk reserve process of an insurer’s portfolio, which consists of a catastrophe bond and external help, and with a special penalty function in the case of a bankruptcy event, are presented. Apart from the general framework, two special cases, when parameters of the portfolio are described by L-R fuzzy numbers or shadowed sets, are discussed and compared. In a few examples based on the real-life data for these two types of impreciseness, some important characteristics of the portfolio, like the expected value and the probability of the ruin, are estimated, analysed and compared using the Monte Carlo simulations.


title: Robust Predictive-Reactive Scheduling: An Information-Based Decision Tree Model

text: In this paper we introduce a proactive-reactive approach to deal with uncertain scheduling problems. The method constructs a robust decision tree for a decision maker that is reusable as long as the problem parameters remain in the uncertainty set. At each node of the tree we assume that the scheduler has access to some knowledge about the ongoing scenario, reducing the level of uncertainty and allowing the computation of less conservative solutions with robustness guarantees. However, obtaining information on the uncertain parameters can be costly and frequent rescheduling can be disturbing. We first formally define the robust decision tree and the information refining concepts in the context of uncertainty scenarios. Then we propose algorithms to build such a tree. Finally, focusing on a simple single machine scheduling problem, we provide experimental comparisons highlighting the potential of the decision tree approach compared with reactive algorithms for obtaining more robust solutions with fewer information updates and schedule changes.


title: Enhancing the Efficiency of the Interval-Valued Fuzzy Rule-Based Classifier with Tuning and Rule Selection

text: Interval-Valued fuzzy rule-based classifier with TUning and Rule Selection, IVTURS, is a state-of-the-art fuzzy classifier. One of the key point of this method is the usage of interval-valued restricted equivalence functions because their parametrization allows one to tune them to each problem, which leads to obtaining accurate results. However, they require the application of the exponentiation several times to obtain a result, which is a time demanding operation implying an extra charge to the computational burden of the method. In this contribution, we propose to reduce the number of exponentiation operations executed by the system, so that the efficiency of the method is enhanced with no alteration of the obtained results. Moreover, the new approach also allows for a reduction on the search space of the evolutionary method carried out in IVTURS. Consequently, we also propose four different approaches to take advantage of this reduction on the search space to study if it can imply an enhancement of the accuracy of the classifier. The experimental results prove: 1) the enhancement of the efficiency of IVTURS and 2) the accuracy of IVTURS is competitive versus that of the approaches using the reduced search space.


title: Optimal Control Under Fuzzy Conditions for Dynamical Systems Associated with the Second Order Linear Differential Equations

text: This paper is devoted to an optimal trajectory planning problem with uncertainty in location conditions considered as a problem of constrained optimal control for dynamical systems. Fuzzy numbers are used to incorporate uncertainty of constraints into the classical setting of the problem under consideration. The proposed approach applied to dynamical systems associated with the second order linear differential equations allows to find an optimal control law at each [Formula: see text]-level using spline-based methods developed in the framework of the theory of splines in convex sets. The solution technique is illustrated by numerical examples.


title: On Compatibility of Two Approaches to Generalization of the Lovász Extension Formula

text: We present a method of generalization of the Lovász extension formula combining two known approaches - the first of them based on the replacement of the product operator by some suitable binary function F and the second one based on the replacement of the minimum operator by a suitable aggregation function A. We propose generalization by simultaneous replacement of both product and minimum operators and investigate pairs (F, A) yielding an aggregation function for all capacities.


title: A Fuzzy Model for Interval-Valued Time Series Modeling and Application in Exchange Rate Forecasting

text: Financial interval time series (ITS) is a time series whose value at each time step is an interval composed by the low and the high price of an asset. The low-high price range is related to the concept of volatility because it inherits intraday price variability. Accurate forecasting of price ranges is essential for derivative pricing, trading strategies, risk management, and portfolio allocation. This paper suggests a fuzzy rule-based approach to model and to forecast interval-valued time series. The model is a collection of functional fuzzy rules with affine consequents capable to express the nonlinear relationships encountered in interval-valued data. An application concerning one-step-ahead forecast of interval-valued EUR/USD exchange rate using actual data is also addressed. The forecast performance of the fuzzy rule-based model is compared to that of traditional econometric time series methods and alternative interval models employing statistical criteria for both, low and high exchange rate prices. The results show that fuzzy rule-based modeling approach developed in this paper outperforms the random walk, and other competitive approaches in out-of-sample interval-valued exchange rate forecasting.


title: Converting Possibilistic Networks by Using Uncertain Gates

text: The purpose of this paper is to define a general frame to convert the Conditional Possibility Tables (CPT) of an existing possibilistic network into uncertain gates. In possibilistic networks, CPT parameters must be elicited by an expert but when the number of parents of a variable grows, the number of parameters to elicit grows exponentially. This problem generates difficulties for experts to elicit all parameters because it is time-consuming. One solution consists in using uncertain gates to compute automatically CPTs. This is useful in knowledge engineering. When possibilistic networks already exist, it can be interesting to transform them by using uncertain gates because we can highlight the combination behaviour of the variables. To illustrate our approach, we will present at first a simple example of the estimation for 3 test CPTs with behaviours MIN, MAX and weighted average. Then, we will perform a more significant experimentation which will consist in converting a set of Bayesian networks into possibilistic networks to perform the estimation of CPTs by uncertain gates.


title: Mining Text Patterns over Fake and Real Tweets

text: With the exponential growth of users and user-generated content present on online social networks, fake news and its detection have become a major problem. Through these, smear campaigns can be generated, aimed for example at trying to change the political orientation of some people. Twitter has become one of the main spreaders of fake news in the network. Therefore, in this paper, we present a solution based on Text Mining that tries to find which text patterns are related to tweets that refer to fake news and which patterns in the tweets are related to true news. To test and validate the results, the system faces a pre-labelled dataset of fake and real tweets during the U.S. presidential election in 2016. In terms of results interesting patterns are obtained that relate the size and subtle changes of the real news to create fake news. Finally, different ways to visualize the results are provided.


title: Handling Mixture Optimisation Problem Using Cautious Predictions and Belief Functions

text: Predictions from classification models are most often used as final decisions. Yet, there are situations where the prediction serves as an input for another constrained decision problem. In this paper, we consider such an issue where the classifier provides imprecise and/or uncertain predictions that need to be managed within the decision problem. More precisely, we consider the optimisation of a mix of material pieces of different types in different containers. Information about those pieces is modelled by a mass function provided by a cautious classifier. Our proposal concerns the statement of the optimisation problem within the framework of belief function. Finally, we give an illustration of this problem in the case of plastic sorting for recycling purposes.


title: Measure of Lattice-Valued Direct F-transforms and Its Topological Interpretations

text: The goal is to introduce and study the measure of quality of approximation of a given fuzzy set by its lattice-valued F-transform. Further, we show that this measure is connected with an Alexandroff LM-fuzzy topological (co-topological) spaces. Finally, we discuss the categorical relationship between the defined structures.


title: Isotone [Formula: see text]-Fuzzy Formal Concept Analysis and [Formula: see text]-Valued Fuzzy Measures and Integrals

text: The main idea of the paper is to generalize the concept of lattice valued fuzzy measures and integrals for data from complete residuated lattice where double negation law holds and then to show their relationship to isotone [Formula: see text]-fuzzy concept forming operators.


title: Network of Fuzzy Comparators for Ovulation Window Prediction

text: This paper presents the problem and the solution of ovulation date prediction based on simple data acquired by a woman in home environment. It describes a method of processing collected data as a multivariate time series. The novelty of this algorithm lies in its ability to predict the ovulation date and not only to retrospectively detect it. This is achieved by applying the fuzzy network of comparators (NoC) to compare the menstrual cycle being analyzed with the reference set of historical cycles.


title: Two-Sample Dispersion Problem for Fuzzy Data

text: The problem of comparing variability of two populations with fuzzy data is considered. A new permutation two-sample test for dispersion based on fuzzy random variables is proposed. A case-study illustrating the applicability of the suggested testing procedure is also presented.


title: Binary Credal Classification Under Sparsity Constraints

text: Binary classification is a well known problem in statistics. Besides classical methods, several techniques such as the naive credal classifier (for categorical data) and imprecise logistic regression (for continuous data) have been proposed to handle sparse data. However, a convincing approach to the classification problem in high dimensional problems (i.e., when the number of attributes is larger than the number of observations) is yet to be explored in the context of imprecise probability. In this article, we propose a sensitivity analysis based on penalised logistic regression scheme that works as binary classifier for high dimensional cases. We use an approach based on a set of likelihood functions (i.e. an imprecise likelihood, if you like), that assigns a set of weights to the attributes, to ensure a robust selection of the important attributes, whilst training the model at the same time, all in one fell swoop. We do a sensitivity analysis on the weights of the penalty term resulting in a set of sparse constraints which helps to identify imprecision in the dataset.


title: Random Steinhaus Distances for Robust Syntax-Based Classification of Partially Inconsistent Linguistic Data

text: We use the Steinhaus transform of metric distances to deal with inconsistency in linguistic classification. We focus on data due to G. Longobardi’s school: languages are represented through yes-no strings of length 53, each string position corresponding to a syntactic feature which can be present or absent. However, due to a complex network of logical implications which constrain features, some positions might be undefined (logically inconsistent). To take into account linguistic inconsistency, the distances we use are Steinhaus metric distances generalizing the normalized Hamming distance. To validate the robustness of classifications based on Longobardi’s data we resort to randomized transforms. Experimental results are provided and commented upon.


title: Measuring Polarization: A Fuzzy Set Theoretical Approach

text: The measurement of polarization has been studied over the last thirty years. Despite the different applied approaches, since polarization concept is complex, we find a lack of consensus about how it should be measured. This paper proposes a new approach to the measurement of the polarization phenomenon based on fuzzy set. Fuzzy approach provides a new perspective whose elements admit degrees of membership. Since reality is not black and white, a polarization measure should include this key characteristic. For this purpose we analyze polarization metric properties and develop a new risk of polarization measure using aggregation operators and overlapping functions. We simulate a sample of [Formula: see text] cases across a 5-likert-scale with different distributions to test our measure. Other polarization measures were applied to compare situations where fuzzy set approach offers different results, where membership functions have proved to play an essential role in the measurement. Finally, we want to highlight the new and potential contribution of fuzzy set approach to the polarization measurement which opens a new field to research on.


title: General-Purpose Automated Machine Learning for Transportation: A Case Study of Auto-sklearn for Traffic Forecasting

text: Currently, there are no guidelines to determine what are the most suitable machine learning pipelines (i.e. the workflow from data preprocessing to model selection and validation) to approach Traffic Forecasting (TF) problems. Although automated machine learning (AutoML) has proved to be successful dealing with the model selection problem in other applications areas, only a few papers have explored the performance of general-purpose AutoML methods, purely based on optimisation, when tackling TF. In this paper, we provide a thorough exploration of the benefits of Auto-sklearn for TF, as a general-purpose AutoML method that follows a hybrid search strategy combining optimisation with meta-learning and ensemble learning. Particularly, we focus on how well Auto-sklearn is able to recommend competitive machine learning pipelines to forecast traffic, modelled as a TF multi-class imbalanced classification problem, along different time horizons at two spatial scales (point and road segment) and two environments (freeway and urban). Concretely, we test the following scenarios: I) a hybrid search strategy with the three components (optimisation, meta-learning, ensemble learning), II) a strategy based on meta-learning and ensemble learning, and III) a strategy based on the estimation of the best performing pipeline from those suggested by the meta-learning. Experimental results show that the meta-learning component of Auto-sklearn does not work properly on TF problems, and on the other hand, that the optimisation does not contribute too much to the final performance of predictions.


title: Planning Wi-Fi Access Points Activation in Havana City: A Proposal and Preliminary Results

text: The availability of Wi-Fi connection points or hotspots in places such as parks, transport stations, libraries, and so on is one of the key aspects to allow people the usage of Internet resources (to study, work or meet). This is even more important in Central America and Caribbean countries where the deployment of huge cost infrastructure (like optical fiber) to provide Internet access at home is not envisaged neither in the short or mid term. And this is clearly the case in Havana, Cuba. This contribution presents the problem of planning the Wi-Fi access points activation, where each point can have different signal power levels and availability along the time. Due to power consumption constraints, it is impossible to have all the points activated simultaneously with maximum signal strength. The problem is modelled as a dynamic maximal covering location one with facility types and time dependant availability. A metaheuristic approach is used to solve the problem by using an Algorithm portfolio and examples on how solutions can be analyzed (beyond the coverage provided) are shown.


title: New Results in the Calculus of Fuzzy-Valued Functions Using Mid-Point Representations

text: We present new results in the calculus for fuzzy-valued functions of a single real variable. We adopt extensively the midpoint-radius representation of intervals in the real half-plane and show its usefulness in fuzzy calculus. Concepts related to convergence and limits, continuity, level-wise gH-differentiability of first and second orders have nice and useful midpoint expressions. Using mid-point representation of fuzzy-valued functions, partial orders and properties of monotonicity and convexity are discussed and analysed in detail. Periodicity is easy to represent and identify. Graphical examples and pictures accompany the presentation.


title: A Bidirectional Subsethood Based Fuzzy Measure for Aggregation of Interval-Valued Data

text: Recent advances in the literature have leveraged the fuzzy integral (FI), a powerful multi-source aggregation operator, where a fuzzy measure (FM) is used to capture the worth of all combinations of subsets of sources. While in most applications, the FM is defined either by experts or numerically derived through optimization, these approaches are only viable if additional information on the sources is available. When such information is unavailable, as is commonly the case when sources are unknown a priori (e.g., in crowdsourcing), prior work has proposed the extraction of valuable insight (captured within FMs) directly from the evidence or input data by analyzing properties such as specificity or agreement amongst sources. Here, existing agreement-based FMs use established measures of similarity such as Jaccard and Dice to estimate the source agreement. Recently, a new similarity measure based on bidirectional subsethood was put forward to compare evidence, minimizing limitations such as aliasing (where different inputs result in the same similarity output) present in traditional similarity measures. In this paper, we build on this new similarity measure to develop a new instance of the agreement-based FM for interval-valued data. The proposed FM is purposely designed to support aggregation, and unlike previous agreement FMs, it degrades gracefully to an average operator for cases where no overlap between sources exists. We validate that it respects all requirements of a FM and explore its impact when used in conjunction with the Choquet FI for data fusion as part of both synthetic and real-world datasets, showing empirically that it generates robust and qualitatively superior outputs for the cases considered.


title: A Computational Study on the Entropy of Interval-Valued Datasets from the Stock Market

text: Using interval-valued data and computing, researchers have reported significant quality improvements of the stock market annual variability forecasts recently. Through studying the entropy of interval-valued datasets, this work provides both information theoretic and empirical evidences on that the significant quality improvements are very likely come from interval-valued datasets. Therefore, using interval-valued samples rather than point-valued ones is preferable in making variability forecasts. This study also computationally investigates the impacts of data aggregation methods and probability distributions on the entropy of interval-valued datasets. Computational results suggest that both min-max and confidence intervals can work well in aggregating point-valued data into intervals. However, assuming uniform probability distribution should be a good practical choice in calculating the entropy of an interval-valued dataset in some applications at least.


title: On Solutions of Marginal Problem in Evidence Theory

text: Recently introduced marginal problem – which addresses the question of whether or not a common extension exists for a given set of marginal basic assignments – in the framework of evidence theory is recalled. Sets of solutions are studied in more detail and it is shown, by a simple example, that their structure is much more complicated (i.e. the number of extreme vertices of the convex set of solutions is substantially greater) than that in an analogous problem in probabilistic framework. The concept of product extension of two basic assignments is generalized (via operator of composition) to a finite sequence of basic assignments. This makes possible not only to express the extension, if it exists, in a closed form, but also enables us to find the sufficient condition for the existence of an extension of evidential marginal problem. Presented approach is illustrated by a simple example.


title: An Interval-Valued Divergence for Interval-Valued Fuzzy Sets

text: Characterizing the degree of similarity or difference between two sets is a very important topic, since it has many applications in different areas, including image processing or decision making. Several studies have been done about the comparison of fuzzy sets and its extensions, in particular for interval-valued fuzzy sets. However, in most of the cases, the results of the comparison is just a number. In order to avoid this reduction of the information, we have introduced a measure for comparing two interval-valued fuzzy sets such that it is an interval itself, which can be reduced to a number if it is necessary. Thus, a richer class of measures is now considered.


title: Construction of Nullnorms Based on Closure and Interior Operators on Bounded Lattices

text: In this paper, we introduce two rather effective methods for constructing new families of nullnorms with a zero element on the basis of the closure operators and interior operators on a bounded lattice under some additional conditions. Our constructions can be seen as a generalization of the ones in [28]. As a by-product, two types of idempotent nullnorms on bounded lattices are obtained. Several interesting examples are included to get a better understanding of the structure of new families of nullnorms.


title: Possibilistic Bounds for Granular Counting

text: Uncertain data are observations that cannot be uniquely mapped to a referent. In the case of uncertainty due to incompleteness, possibility theory can be used as an appropriate model for processing such data. In particular, granular counting is a way to count data in presence of uncertainty represented by possibility distributions. Two algorithms were proposed in literature to compute granular counting: exact granular counting, with quadratic time complexity, and approximate granular counting, with linear time complexity. This paper extends approximate granular counting by computing bounds for exact granular count. In this way, the efficiency of approximate granular count is combined with certified bounds whose width can be adjusted in accordance to user needs.


title: On the Sum of Generalized Hukuhara Differentiable Fuzzy Functions

text: In this article we present new results on the sum of gH-differentiable fuzzy functions . We give conditions so that the sum of two gH-differentiable fuzzy functions become gH-differentiable. We present also practical rules for obtaining the gH-derivative of the sum of fuzzy functions.


title: Graded Cube of Opposition with Intermediate Quantifiers in Fuzzy Natural Logic

text: In our previous papers, we formally analyzed the generalized Aristotle’s square of opposition using tools of higher-order fuzzy logic. Namely, we introduced general definitions of selected intermediate quantifiers, constructed a generalized square of opposition consisting of them and syntactically analyzed the emerged properties. The main objective of this paper is to extend the graded Peterson’s square of opposition into the graded cube of opposition with intermediate quantifiers.


title: Combining Absolute and Relative Information with Frequency Distributions for Ordinal Classification

text: A large amount of labelled data (absolute information) is usually needed for an ordinal classifier to attain a good performance. As shown in a recent paper by the present authors, the lack of a large amount of absolute information can be overcome by additionally considering some side information in the form of relative information, thus augmenting the method of nearest neighbors. In this paper, we adapt the method of nearest neighbors for dealing with a specific type of relative information: frequency distributions of pairwise comparisons (rather than a single pairwise comparison). We test the proposed method on some classical machine learning datasets and demonstrate its effectiveness.


title: Predicting S&P500 Monthly Direction with Informed Machine Learning

text: We propose a systematic framework based on a dynamic functional causal graph in order to capture complexity and uncertainty on the financial markets, and then to predict the monthly direction of the S&P500 index. Our results highlight the relevance of (i) using the hierarchical causal graph model instead of modelling directly the S&P500 with its causal drivers (ii) taking into account different types of contexts (short and medium term) through latent variables (iii) using unstructured forward looking data from the Beige Book. The small size of our training data is compensated by the a priori knowledge on financial market. We obtain accuracy and F1-score of 70.9% and 67% compared to 64.1% and 50% for the industry benchmark on a period of over 25 years. By introducing a hierarchical interaction between drivers through a latent context variable, we improve performance of two recent works on same inputs.


title: On Uncertain Discontinuous Functions and Quasi-equilibrium in Some Economic Models

text: In the paper is studied some properties of uncertain discontinuous mappings, the so-called w-discontinuous mappings. Based on them, the existence of a quasi-equilibrium for a new economic model is proved.


title: On the Logic of Left-Continuous t-Norms and Right-Continuous t-Conorms

text: Double residuated lattices are expansions of residuated lattices with an extra monoidal operator, playing the role of a strong disjunction operation, together with its dual residuum. They were introduced by Orłowska and Radzikowska. In this paper we consider the subclass of double residuated structures that are expansions of MTL-algebras, that is, prelinear, bounded, commutative and integral residuated lattices. MTL-algebras constitute the algebraic semantics for the MTL logic, the system of mathematical fuzzy logic that is complete w.r.t. the class of residuated lattices on the real unit interval [0, 1] induced by left-continuous t-norms. Our aim is to axiomatise the logic whose intended semantics are commutative and integral double residuated structures on [0, 1], that are induced by an arbitrary left-continuous t-norm, an arbitrary right-continuous t-conorm, and their corresponding residual operations.


title: Limit Behaviour of Upper and Lower Expected Time Averages in Discrete-Time Imprecise Markov Chains

text: We study the limit behaviour of upper and lower bounds on expected time averages in imprecise Markov chains; a generalised type of Markov chain where the local dynamics, traditionally characterised by transition probabilities, are now represented by sets of ‘plausible’ transition probabilities. Our main result is a necessary and sufficient condition under which these upper and lower bounds, called upper and lower expected time averages, will converge as time progresses towards infinity to limit values that do not depend on the process’ initial state. Remarkably, our condition is considerably weaker than those needed to establish similar results for so-called limit—or steady state—upper and lower expectations, which are often used to provide approximate information about the limit behaviour of time averages as well. We show that such an approximation is sub-optimal and that it can be significantly improved by directly using upper and lower expected time averages.


title: High Dimensional Bayesian Regularization in Regressions Involving Symmetric Tensors

text: This article develops a regression framework with a symmetric tensor response and vector predictors. The existing literature involving symmetric tensor response and vector predictors proceeds by vectorizing the tensor response to a multivariate vector, thus ignoring the structural information in the tensor. A few recent approaches have proposed novel regression frameworks exploiting the structure of the symmetric tensor and assume symmetric tensor coefficients corresponding to scalar predictors to be low-rank. Although low-rank constraint on coefficient tensors are computationally efficient, they might appear to be restrictive in some real data applications. Motivated by this, we propose a novel class of regularization or shrinkage priors for the symmetric tensor coefficients. Our modeling framework a-priori expresses a symmetric tensor coefficient as sum of low rank and sparse structures, with both these structures being suitably regularized using Bayesian regularization techniques. The proposed framework allows identification of tensor nodes significantly influenced by each scalar predictor. Our framework is implemented using an efficient Markov Chain Monte Carlo algorithm. Empirical results in simulation studies show competitive performance of the proposed approach over its competitors.


title: Hybrid Model for Parkinson’s Disease Prediction

text: Parkinson’s is a chronic, progressive neurological disease with no known cause that affects the central nervous system of older people and compromises their movement. This disorder can impair daily aspects of people and therefore identify their existence early, helps in choosing treatments that can reduce the impact of the disease on the patient’s routine. This work aims to identify Parkinson’s traces through a voice recording replications database applied to a fuzzy neural network to identify their patterns and enable the extraction of knowledge about situations present in the data collected in patients. The results obtained by the hybrid model were superior to state of the art for the theme, proving that it is possible to perform hybrid models in the extraction of knowledge and the classification of behavioral patterns of high accuracy Parkinson’s.


title: Bayesian Image Analysis in Fourier Space Using Data-Driven Priors (DD-BIFS)

text: Statistical image analysis is an extensive field that includes problems such as noise-reduction, de-blurring, feature enhancement, and object detection/identification, to name a few. Bayesian image analysis can improve image quality, by balancing a priori expectations of image characteristics, with a model for the noise process via Bayes Theorem. We have previously given a reformulation of the conventional Bayesian image analysis paradigm in Fourier space, i.e. the prior distribution (the prior) and likelihood are given in terms of spatial frequency signals. By specifying the Bayesian model in Fourier space, spatially correlated priors, that are relatively difficult to model and compute in conventional image space, can be efficiently modeled as a set of independent processes across Fourier space. The originally inter-correlated and high-dimensional problem in image space is thereby broken down into a series of (trivially parallelizable) independent one-dimensional problems. In this paper we adapt this Fourier space process into a data-driven framework in which the Fourier space priors are built empirically from a database of images and then used to enhance future images. We will describe the data-driven Bayesian image analysis in Fourier space (DD-BIFS) modeling approach, illustrate it’s computational efficiency and speed. Finally, we give specific applications of DD-BIFS to improve the quality of arterial-spin-labeling (ASL) perfusion images via a database of human brain positron emission tomography (PET) images.


title: Fuzzy Relational Mathematical Morphology: Erosion and Dilation

text: In the recent years, the subject if fuzzy mathematical morphology entered the field of interest of many researchers. In our recent paper [23], we have developed the basis of the (unstructured) L-fuzzy relation mathematical morphology where L is a quantale. In this paper we extend it to the structured case. We introduce structured L-fuzzy relational erosion and dilation operators, study their basic properties, show that under some conditions these operators are dual and form an adjunction pair. Basing on the topological interpretation of these operators, we introduce the category of L-fuzzy relational morphological spaces and their continuous transformations.


title: Classification of Hyperbolic Singularities in Interval 3-Dimensional Linear Differential Systems

text: We study the classification of the hyperbolic singularities to 3-dimensional interval linear differential equations as an application of interval eigenvalues using the Constraint Interval Arithmetic (CIA). We also present the ideas to calculate the interval eigenvalues using the standard interval arithmetic.


title: Improvements on the Convergence and Stability of Fuzzy Grey Cognitive Maps

text: Fuzzy grey cognitive maps (FGCMs) are extensions of fuzzy cognitive maps (FCMs), where the causal connections between the concepts are represented by so-called grey numbers. Just like in classical FCMs, the inference is determined by an iteration process, which may converge to an equilibrium point, but limit cycles or chaotic behaviour may also show up. In this paper, based on network measures like in-degree, out-degree and connectivity, we provide new sufficient conditions for the existence and uniqueness of fixed points for FGCMs. Moreover, a tighter convergence condition is presented using the spectral radius of the modified weight matrix.


title: Galois Connections Between Unbalanced Structures in a Fuzzy Framework

text: The construction of Galois connections between unbalanced structures has received considerable attention in the recent years. In a nutshell, the problem is to find a right adjoint of a mapping defined between sets with unbalanced structure; in this paper we survey recent results obtained in this framework, focusing specially on the fuzzy structures that have been considered so far in this context: fuzzy preposets, fuzzy preordered structures, and fuzzy T-digraphs.


title: Information Fusion-2-Text: Explainable Aggregation via Linguistic Protoforms

text: Recent advancements and applications in artificial intelligence (AI) and machine learning (ML) have highlighted the need for explainable, interpretable, and actionable AI-ML. Most work is focused on explaining deep artificial neural networks, e.g., visual and image captioning. In recent work, we established a set of indices and processes for explainable AI (XAI) relative to information fusion. While informative, the result is information overload and domain expertise is required to understand the results. Herein, we explore the extraction of a reduced set of higher-level linguistic summaries to inform and improve communication with non-fusion experts. Our contribution is a proposed structure of a fusion summary and method to extract this information from a given set of indices. In order to demonstrate the usefulness of the proposed methodology, we provide a case study for using the fuzzy integral to combine a heterogeneous set of deep learners in remote sensing for object detection and land cover classification. This case study shows the potential of our approach to inform users about important trends and anomalies in the models, data and fusion results. This information is critical with respect to transparency, trustworthiness, and identifying limitations of fusion techniques, which may motivate future research and innovation.


title: Fuzzy Set Based Models Comparative Study for the TD TSP with Rush Hours and Traffic Regions

text: This study compares three fuzzy based model approaches for solving a realistic extension of the Time Dependent Traveling Salesman Problem. First, the triple Fuzzy (3FTD TSP) model, where the uncertain costs between the nodes depend on time are expressed by fuzzy sets. Second, the intuitionistic fuzzy (IFTD TSP) approach, where including hesitation was suitable for quantifying the jam regions and the bimodal rush hour periods during the day. Third, the interval-valued intuitionistic fuzzy sets model, that calculates the interval-valued intuitionistic fuzzy weighted arithmetic average (IIFWAA) of the edges’ confirmability degrees and non-confirmability degrees, was contributing in minimizing the information loss in cost (delay) calculation between nodes.


title: BIOWA Operators

text: Based on bi-capacities and related Choquet integral introduced by Grabisch and Labreuche, a new generalization of OWA operators, namely BIOWA operators are introduced. Our approach is exemplified by several examples. Bi-capacities leading to the standard Yager’s OWA operators on real line are completely characterized.


title: Analyzing Non-deterministic Computable Aggregations

text: Traditionally, the term aggregation is associated with an aggregation function, implicitly assuming that any aggregation process can be represented by a function. However, the concept of computable aggregation considers that the core of the aggregation processes is the program that enables it. This new concept of aggregation introduces the scenario where the aggregation can even be non-deterministic. In this work, this new class of aggregation is formally defined, and some desirable properties related with consistency, robustness and monotonicity are proposed.


title: Two Dualities for Weakly Pseudo-complemented quasi-Kleene Algebras

text: Quasi-Nelson algebras are a non-involutive generalisation of Nelson algebras that can be characterised in several ways, e.g. as (i) the variety of bounded commutative integral (not necessarily involutive) residuated lattices that satisfy the Nelson identity; (ii) the class of (0, 1)-congruence orderable commutative integral residuated lattices; (iii) the algebraic counterpart of quasi-Nelson logic, i.e. the (algebraisable) extension of the substructural logic [Formula: see text] by the Nelson axiom. In the present paper we focus on the subreducts of quasi-Nelson algebras obtained by eliding the implication while keeping the two term-definable negations. These form a variety that (following A. Sendlewski, who studied the corresponding fragment of Nelson algebras) we dub weakly pseudo-complemented quasi-Kleene algebras. We develop a Priestley-style duality for these algebras (in two different guises) which is essentially an application of the general approach proposed in the paper A duality for two-sorted lattices by A. Jung and U. Rivieccio.


title: Fuzzy k-NN Based Classifiers for Time Series with Soft Labels

text: Time series are temporal ordered data available in many fields of science such as medicine, physics, astronomy, audio, etc. Various methods have been proposed to analyze time series. Amongst them, time series classification consists in predicting the class of a time series according to a set of already classified data. However, the performance of a time series classification algorithm depends on the quality of the known labels. In real applications, time series are often labeled by an expert or by an imprecise process, leading to noisy classes. Several algorithms have been developed to handle uncertain labels in case of non-temporal data sets. As an example, the fuzzy k-NN introduces for labeled objects a degree of membership to belong to classes. In this paper, we combine two popular time series classification algorithms, Bag of SFA Symbols (BOSS) and the Dynamic Time Warping (DTW) with the fuzzy k-NN. The new algorithms are called Fuzzy DTW and Fuzzy BOSS. Results show that our fuzzy time series classification algorithms outperform the non-soft algorithms especially when the level of noise is high.


title: Dynamic Portfolio Selection Under Ambiguity in the [Formula: see text]-Contaminated Binomial Model

text: Investors often need to look for an optimal portfolio acting under ambiguity, as they may not be able to single out a unique real-world probability measure. In this paper a discrete-time dynamic portfolio selection problem is studied, referring to an [Formula: see text]-contaminated binomial market model and assuming investors’ preferences are consistent with the Choquet expected utility theory. We formulate the portfolio selection problem for a CRRA utility function in terms of the terminal wealth, and provide a characterization of the optimal solution in the case stock price returns are uniformly distributed. In this case, we further investigate the effect of the contamination parameter [Formula: see text] on the optimal portfolio.


title: Dempster-Shafer Theory: Ηow Constraint Programming Can Help

text: Dealing with uncertainty has always been a challenging topic in the area of knowledge representation. Nowadays, as the internet provides a vast platform for knowledge exploitation, the need becomes even more imminent. The kind of uncertainty encountered in most of these cases as well as its distributed nature make Dempster-Shafer (D-S) Theory to be an appropriate framework for its representation. However, we have to face the drawback of the computation burden of Dempster’s rule of combination due to its combinatorial behavior. Constraint Programming (CP) has proved to be an efficient tool in cases where results have to satisfy some specified properties and pruning of the computation space can be achieved. As D-S theory measures’ computation fulfills this requirement, CP seems a promising framework to employ for this purpose. In this paper, we present our approach to use CP to compute the belief and plausibility measures of D-S Theory and Dempster’s rule of combination as well as the results of the effort. As it was expected, the results are quite promising and in many cases impressive.


title: An Introduction to Differential Algebraic Equations Under Interval Uncertainty: A First Step Toward Generalized Uncertainty DAEs

text: This presentation introduces the theory leading to solution methods for differential algebraic equations (DAEs) under interval uncertainty in which the uncertainty is in the initial conditions of the differential equation and/or the entries of the coefficients of the differential equation and algebraic restrictions. While we restrict these uncertainties to be intervals, other types of uncertains like generalized uncertainties such as fuzzy intervals are done in a similar manner albeit leading to more complex analyses. Linear constant coefficient DAEs and then interval linear constant coefficient problems will illustrate both the theoretically challenges and solution approaches. The way the interval uncertainty is handled is novel and serves as a basis for more general uncertainty analysis.


title: The Fuzzy Processing of Metaphors

text: The question under investigation about verbal metaphor is what kind of thinking and reasoning can help catching the metaphorical target category (e.g., octopus meaning citrus press, child meaning son or daughter, pizzas meaning people) from a source category (children, pizzas or octopuses); knowing that this kind of “logically false” way of talking/understanding and of reasoning appears to be the most prominent kind of human of thinking. We are reviewing some of the prominent work of Bernadette Bouchon-Meunier with her team to evaluate how much the fuzzy logic computation of metaphorical reasoning and schemes can be used to model the human computation of metaphors.


title: Impact of Local Congruences in Attribute Reduction

text: Local congruences are equivalence relations whose equivalence classes are convex sublattices of the original lattice. In this paper, we present a study that relates local congruences to attribute reduction in FCA. Specifically, we will analyze the impact in the context of the use of local congruences, when they are used for complementing an attribute reduction.


title: Interactive Fuzzy Fractional Differential Equation: Application on HIV Dynamics

text: This work presents an application of interactive fuzzy fractional differential equation, with Caputo derivative, to an HIV model for seropositive individuals under antiretroviral treatment. The initial condition of the model is given by a fuzzy number and the differentiability is given by a fuzzy interactive derivative. A discussion about the model considering these notions are presented. Finally, a numerical solution to the problem is provided, in order to illustrate the results.


title: Dealing with Inconsistent Measurements in Inverse Problems: An Approach Based on Sets and Intervals

text: We consider the (inverse) problem of finding back the parameter values of a physical model given a set of measurements. As the deterministic solution to this problem is sensitive to measurement error in the data, one way to resolve this issue is to take into account uncertainties in the data. In this paper, we explore how interval-based approaches can be used to obtain a solution to the inverse problem, in particular when measurements are inconsistent with one another. We show on a set of experiments, in which we compare the set-based approach with the Bayesian one, that this is particularly interesting when some measurements can be suspected of being outliers.


title: A Belief Classification Approach Based on Artificial Immune Recognition System

text: Artificial Immune Recognition Systems (AIRS) are supervised classification methods inspired by the immune system metaphors. They enjoy a great popularity in the filed of machine learning by achieving good and competitive classification results. Nonetheless, while these approaches work properly under a certain framework, they present some weaknesses basically related to their inability to deal with uncertainty. This is considered as an important challenge in real-world classification problems. Furthermore, using traditional AIRS approaches, all memory cells are considered with the same importance during the classification process which may affect the final generated results. To tackle these issues, we propose in this paper a new AIRS approach under the belief function framework. Our approach tends to handle the uncertainty pervaded in the classification stage while taking into account the number of training antigens represented by each memory cell. The performance of the proposed evidential AIRS approach is validated on real-world data sets and compared to state of the art AIRS under certain and uncertain frameworks.


title: On Categories of L-Fuzzifying Approximation Spaces, L-Fuzzifying Pretopological Spaces and L-Fuzzifying Closure Spaces

text: This paper investigates the essential connections among several categories with a weaker structure than that of L-fuzzifying topology, namely category of L-fuzzifying approximation spaces based on reflexive L-fuzzy relations, category of L-fuzzifying pretopological spaces and category of L-fuzzifying interior (closure) spaces. The interrelations among these structures are established in categorical setup.


title: New Methods for Comparing Interval-Valued Fuzzy Cardinal Numbers

text: In this contribution the concept how to solve the problem of comparability in the interval-valued fuzzy setting and its application in medical diagnosis is presented. Especially, we consider comparability of interval-valued fuzzy sets cardinality, where order of its elements is most important. We propose an algorithm for comparing interval-valued fuzzy cardinal numbers (IVFCNs) and we evaluate it in a medical diagnosis decision support system.


title: A Measurement Theory Characterization of a Class of Dissimilarity Measures for Fuzzy Description Profiles

text: We consider objects associated with a fuzzy set-based representation. By using a classic method of measurement theory, we characterize dissimilarity relations agreeing with a particular class of fuzzy dissimilarity measures. Dissimilarity measures in the considered class are those only depending on the attribute-wise distance of fuzzy description profiles. In particular, we analyze the subclass of weighted Manhattan dissimilarity measures.


title: Transparency of Classification Systems for Clinical Decision Support

text: In collaboration with the Civil Hospitals of Lyon, we aim to develop a “transparent” classification system for medical purposes. To do so, we need clear definitions and operational criteria to determine what is a “transparent” classification system in our context. However, the term “transparency” is often left undefined in the literature, and there is a lack of operational criteria allowing to check whether a given algorithm deserves to be called “transparent” or not. Therefore, in this paper, we propose a definition of “transparency” for classification systems in medical contexts. We also propose several operational criteria to evaluate whether a classification system can be considered “transparent”. We apply these operational criteria to evaluate the “transparency” of several well-known classification systems.


title: Cautious Label-Wise Ranking with Constraint Satisfaction

text: Ranking problems are difficult to solve due to their combinatorial nature. One way to solve this issue is to adopt a decomposition scheme, splitting the initial difficult problem in many simpler problems. The predictions obtained from these simplified settings must then be combined into one single output, possibly resolving inconsistencies between the outputs. In this paper, we consider such an approach for the label ranking problem, where in addition we allow the predictive model to produce cautious inferences in the form of sets of rankings when it lacks information to produce reliable, precise predictions. More specifically, we propose to combine a rank-wise decomposition, in which every sub-problem becomes an ordinal classification one, with a constraint satisfaction problem (CSP) approach to verify the consistency of the predictions. Our experimental results indicate that our approach produces predictions with appropriately balanced reliability and precision, while remaining competitive with classical, precise approaches.


title: A Comparison of Explanatory Measures in Abductive Inference

text: Computer simulations have been carried out to investigate the performance of two measures for abductive inference, Maximum Likelihood (ML), and Product Coherence Measure (PCM), by comparing them with a third approach, Most Probable Explanation (MPE). These have been realized through experiments that compare outcomes from a specified model (the correct model) with those from incorrect models which assume that the hypotheses are mutually exclusive or independent. The results show that PCM tracks the results of MPE more closely than ML when the degree of competition is greater than 0 and hence is able to infer explanations that are more likely to be true under such a condition. Experiments on the robustness of the measures with respect to incorrect model assumptions show that ML is more robust in general, but that MPE and PCM are more robust when the degree of competition is positive. The results also show that in general it is more reasonable to assume the hypotheses in question are independent than to assume they are mutually exclusive.


title: On the Relationship Among Relational Categories of Fuzzy Topological Structures

text: Relational variants of categories of Čech closure or interior L-valued operators, categories of L-fuzzy pretopological and L-fuzzy co-pretopological operators, category of L-valued fuzzy relation, categories of upper and lower F-transforms and the category of spaces with fuzzy partitions are introduced. The existence of relationships defined by functors among these categories are investigated and a key role of a relational category of spaces with fuzzy partitions is described.


title: An Initial Study on Typical Hesitant (T,N)-Implication Functions

text: In the theory of Hesitant Fuzzy Sets (HFS), the membership degree of an element is characterized by a membership function which always returns a fuzzy set. This approach enables one to express, for example, the hesitance of several experts in the process of decision making based on multiple attributes and multiple criteria. In this work, we focus on the study of a class of implication functions for typical hesitant fuzzy sets (THFS). The novelty of our proposal lies on the fact that it is the first time that an admissible order is used to define operators on hesitant fuzzy setting. Thus, we introduce typical hesitant fuzzy negations, typical hesitant t-norms and typical hesitant implication functions considering an admissible order, which allows the comparison of typical hesitant fuzzy elements with different cardinalities.


title: Orders Preserving Convexity Under Intersections for Interval-Valued Fuzzy Sets

text: Convexity is a very important property in many areas and the studies of this property are frequent. In this paper, we have extended the notion of convexity for interval-valued fuzzy sets based on different order between intervals. The considered orders are related and their behavior analyzed. In particular, we study the preservation of the convexity under intersections, where again the chosen order is essential. After this study, we can conclude the appropriate behavior of the admissible orders for this purpose.


title: SK-MOEFS: A Library in Python for Designing Accurate and Explainable Fuzzy Models

text: Recently, the explainability of Artificial Intelligence (AI) models and algorithms is becoming an important requirement in real-world applications. Indeed, although AI allows us to address and solve very difficult and complicated problems, AI-based tools act as a black box and, usually, do not explain how/why/when a specific decision has been taken. Among AI models, Fuzzy Rule-Based Systems (FRBSs) are recognized world-wide as transparent and interpretable tools: they can provide explanations in terms of linguistic rules. Moreover, FRBSs may achieve accuracy comparable to those achieved by less transparent models, such as neural networks and statistical models. In this work, we introduce SK-MOEFS (acronym of SciKit-Multi Objective Evolutionary Fuzzy System), a new Python library that allows the user to easily and quickly design FRBSs, employing Multi-Objective Evolutionary Algorithms. Indeed, a set of FRBSs, characterized by different trade-offs between their accuracy and their explainability, can be generated by SK-MOEFS. The user, then, will be able to select the most suitable model for his/her specific application.


title: A S-QFD Approach with Bipolar Fuzzy Hamacher Aggregation Operators and Its Application on E-Commerce

text: In a global competitive environment, companies’ ability to develop products and respond to customer demands is crucial to their success. Quality Function Deployment is an approach that companies use to meet customer needs and expectations in the product design process. It provides competitive advantage to the firm by shortening the development period of products that meet customer expectations. The purpose of this research is to explore the feasibility of the QFD approach in the design of an e-commerce web site. In this context, the QFD application has been implemented to meet customer expectations and increase competitive power of the site to be designed. Bipolar fuzzy numbers are used to express customers’ decisions. This research contributes to the literature with a new QFD approach with bipolar fuzzy numbers and practice by expanding QFD’s application field in software sector.


title: Is the Invariance with Respect to Powers of a t-norm a Restrictive Property on Fuzzy Implication Functions? The Case of Strict t-norms

text: The invariance with respect to powers of a t-norm has emerged as an important property for fuzzy implication functions in approximate reasoning. Recently, those fuzzy implication functions satisfying this property where fully characterized leading to seemingly new families of these operators. In this paper, the additional properties of the family of fuzzy implication functions which are invariant with respect to powers of a strict t-norm are analyzed. In particular, properties such as the exchange principle, the law of importation with respect to a t-norm or the left neutrality principle, among others, can be fulfilled by some members of this family. This study allows to characterize the intersection of these operators with the most important families of fuzzy implication functions.


title: On Statistics, Probability, and Entropy of Interval-Valued Datasets

text: Applying interval-valued data and methods, researchers have made solid accomplishments in information processing and uncertainty management. Although interval-valued statistics and probability are available for interval-valued data, current inferential decision making schemes rely on point-valued statistic and probabilistic measures mostly. To enable direct applications of these point-valued schemes on interval-valued datasets, we present point-valued variational statistics, probability, and entropy for interval-valued datasets. Related algorithms are reported with illustrative examples.


title: Learning Tversky Similarity

text: In this paper, we advocate Tversky’s ratio model as an appropriate basis for computational approaches to semantic similarity, that is, the comparison of objects such as images in a semantically meaningful way. We consider the problem of learning Tversky similarity measures from suitable training data indicating whether two objects tend to be similar or dissimilar. Experimentally, we evaluate our approach to similarity learning on two image datasets, showing that is performs very well compared to existing methods.


title: Group Definition Based on Flow in Community Detection

text: Community detection problems are one of the hottest disciplines in social network analysis. Nevertheless, most of the related algorithms are specific for non-directed networks, or are based on a density concept of group. In this paper, we deal with a new concept of community for directed networks that is based on the classical flow concept. A community is strong and cohesive if their members can communicate among them. With the aim of dealing with the identification of this new class of groups, in this work, we propose the use of fuzzy measures to represent the flow capacity of a group. We also provide a competitive community detection algorithm that focus on the identification of these new class of flow-based community.


title: Evaluation of Probabilistic Transformations for Evidential Data Association

text: Data association is one of the main tasks to achieve in perception applications. Its aim is to match the sensor detections to the known objects. To treat such issue, recent research focus on the evidential approach using belief functions, which are interpreted as an extension of the probabilistic model for reasoning about uncertainty. The data fusion process begins by quantifying sensor data by belief masses. Thereafter, these masses are combined in order to provide more accurate information. Finally, a probabilistic approximation of these combined masses is done to make-decision on associations. Several probabilistic transformations have been proposed in the literature. However, to the best of our knowledge, these transformations have been evaluated only on simulated examples. For this reason, the objective of this paper is to benchmark most of interesting probabilistic transformations on real-data in order to evaluate their performances for the autonomous vehicle perception problematic.


title: On Semantic Properties of Fuzzy Quantifiers over Fuzzy Universes: Restriction and Living on

text: The article investigates important semantic properties of fuzzy quantifiers, namely restriction and living on a (fuzzy) set. These properties are introduced in the novel frame of fuzzy quantifiers over fuzzy universes.


title: Contextualizing Naive Bayes Predictions

text: A classification process can be seen as a set of actions by which several objects are evaluated in order to predict the class(es) those objects belong to. In situations where transparency is a necessary condition, predictions resulting from a classification process are needed to be interpretable. In this paper, we propose a novel variant of a naive Bayes (NB) classification process that yields such interpretable predictions. In the proposed variant, augmented appraisal degrees (AADs) are used for the contextualization of the evaluations carried out to make the predictions. Since an AAD has been conceived as a mathematical representation of the connotative meaning in an experience-based evaluation, the incorporation of AADs into a NB classification process helps to put the resulting predictions in context. An illustrative example, in which the proposed version of NB classification is used for the categorization of newswire articles, shows how such contextualized predictions can favor their interpretability.


title: Correction of Belief Function to Improve the Performances of a Fusion System

text: Our application concerns the fusion of classifiers for the recognition of trees from their leaves, in the framework of belief functions theory. In order to improve the rate of good classification it is necessary to correct Bayesian mass functions. This correction will be done from the meta-knowledge which is estimated from the confusion matrix. The corrected mass functions considerably improve the recognition rate based on the decisions provided by the classifiers.


title: An Undesirable Behaviour of a Recent Extension of OWA Operators to the Setting of Multidimensional Data

text: OWA operators have been ubiquitous in many disciplines since they were introduced by Yager in 1988. Aside of some other intuitive properties (e.g. monotonicity and idempotence), OWA operators are known to be continuous and, for some carefully constructed weighing vectors, very robust in the presence of outliers. In a recent paper, a natural extension of OWA operators to the setting of multidimensional data has been proposed based on the use of a linear extension of the product order by means of several weighted arithmetic means. Unfortunately, OWA operators constructed in such a way focus too strongly on the level sets of one of the weighted arithmetic means. It is here shown that this focus ultimately results in a forfeit of the properties of continuity and robustness in the presence of outliers.


title: Necessary and Possible Interaction Between Criteria in a General Choquet Integral Model

text: This paper deals with interaction between criteria in a general Choquet integral model. When the preference of the Decision Maker (DM) contains no indifference, we first give a necessary and sufficient condition for them to be representable by a Choquet integral model. Using this condition, we show that it is always possible to choose from the numerical representations, one relatively for which all the Shapley interaction indices are strictly positive. We illustrate our results with an example.


title: Fuzzy Temporal Graphs and Sequence Modelling in Scheduling Problem

text: Processing sequential data and time-dependent data is a problem of constructing computational graph with a certain structure. A computational graph formalizes the structure of a set of computations including mapping temporal inputs and outputs. In this paper we apply graph theory and fuzzy interval representation of uncertain variables to indicate states of the temporal scheduling system. Descriptive model for temporal reasoning on graph, sequence modelling and ordering of fuzzy inputs for scheduling problem is introduced.


title: A Method to Generate Soft Reference Data for Topic Identification

text: Text mining and topic identification models are becoming increasingly relevant to extract value from the huge amount of unstructured textual information that companies obtain from their users and clients nowadays. Soft approaches to these problems are also gaining relevance, as in some contexts it may be unrealistic to assume that any document has to be associated to a single topic without any further consideration of the involved uncertainties. However, there is an almost total lack of reference documents allowing a proper assessment of the performance of soft classifiers in such soft topic identification tasks. To address this lack, in this paper a method is proposed that generates topic identification reference documents with a soft but objective nature, and which proceeds by combining, in random but known proportions, phrases of existing documents dealing with different topics. We also provide a computational study illustrating the application of the proposed method on a well-known benchmark for topic identification, as well as showing the possibility of carrying out an informative evaluation of soft classifiers in the context of soft topic identification.


title: HIV Dynamics Under Antiretroviral Treatment with Interactivity

text: This manuscript presents a model for HIV dynamics of seropositive individuals under antiretroviral treatment described from fuzzy set theory by two different approaches considering interactivity: differential equation with interactive derivative and differential equation with Fréchet derivative. It also establishes an identity between interactive derivative and fuzzy Fréchet derivative. With this identity, we establish when the solutions of the two differential equations coincide. Lastly, we present biological interpretations for both cases.


title: The Necessary and Possible Importance Relation Among Criteria in a 2-Additive Choquet Integral Model

text: In the context of the representation of a preference information by a 2-additive Choquet integral, we introduce the necessary and possible importance relations allowing to compare the Shapley values of two criteria. We present some sufficient conditions, using a set of binary alternatives, to get a necessary importance relation among two criteria.


title: Unification in Łukasiewicz Logic with a Finite Number of Variables

text: We prove that the unification type of Łukasiewicz logic with a finite number of variables is either infinitary or nullary. To achieve this result we use Ghilardi’s categorical characterisation of unification types in terms of projective objects, the categorical duality between finitely presented MV-algebras and rational polyhedra, and a homotopy-theoretic argument.


title: A Fuzzy Goal Programming Approach to Fully Fuzzy Linear Regression

text: Traditional linear regression analysis aims at finding a linear functional relationship between predictor and response variables based on available data of a given system, and, when this relationship is found, it is used to predict the future behaviour of the system. The difference between the observed and predicted data is supposed to be due to measurement errors. In fuzzy linear regression, on the other hand, this difference is supposed to be mainly due to the indefiniteness of the system. In this paper, we assume that predictor and response variables are LR-type fuzzy numbers, and so are all regression coefficients; this is known as fully fuzzy linear regression (FFLR) problem. We transform the FFLR problem into a fully fuzzy multiobjective linear programming (FFMOLP) problem. Two fuzzy goal programming methods based on linear and Chebyshev scalarisations are proposed to solve the FFMOLP problem. The proposed methods are compared with a recently published method and show promising results.


title: Towards a Logic-Based View of Some Approaches to Classification Tasks

text: This paper is a plea for revisiting various existing approaches to the handling of data, for classification purposes, based on a set-theoretic view, such as version space learning, formal concept analysis, or analogical proportion-based inference, which rely on different paradigms and motivations and have been developed separately. The paper also exploits the notion of conditional object as a proper tool for modeling if-then rules. It also advocates possibility theory for handling uncertainty in such settings. It is a first, and preliminary, step towards a unified view of what these approaches contribute to machine learning.


title: Towards a Classification of Rough Set Bireducts

text: Size reduction mechanisms are very important in several mathematical fields. In rough set theory, bireducts arose to reduce simultaneously the set of attributes and the set of objects of the considered dataset, providing subsystems with the minimal sets of attributes that connect the maximum number of objects preserving the information of the original dataset. This paper presents the main properties of bireducts and how they can be used for removing inconsistencies.


title: On PSO-Based Approximation of Zadeh’s Extension Principle

text: Zadeh’s extension is a powerful principle in fuzzy set theory which allows to extend a real-valued continuous map to a map having fuzzy sets as its arguments. In our previous work we introduced an algorithm which can compute Zadeh’s extension of given continuous piecewise linear functions and then to simulate fuzzy dynamical systems given by them. The purpose of this work is to present results which generalize our previous approach to a more complex class of maps. For that purpose we present an adaptation on optimization algorithm called particle swarm optimization and demonstrate its use for simulation of fuzzy dynamical systems.


title: Dissimilarity Based Choquet Integrals

text: In this paper, in order to generalize the Choquet integral, we replace the difference between inputs in its definition by a restricted dissimilarity function and refer to the obtained function as d-Choquet integral. For some particular restricted dissimilarity function the corresponding d-Choquet integral with respect to a fuzzy measure is just the ‘standard’ Choquet integral with respect to the same fuzzy measure. Hence, the class of all d-Choquet integrals encompasses the class of all ‘standard’ Choquet integrals. This approach allows us to construct a wide class of new functions, d-Choquet integrals, that are possibly, unlike the ’standard’ Choquet integral, outside of the scope of aggregation functions since the monotonicity is, for some restricted dissimilarity function, violated and also the range of such functions can be wider than [0, 1], in particular it can be [0, n].


title: Intelligent Detection of Information Outliers Using Linguistic Summaries with Non-monotonic Quantifiers

text: In the processing of imprecise information, principally in big data analysis, it is very advantageous to transform numerical values into the standard form of linguistic statements. This paper deals with a novel method of outlier detection using linguistic summaries. Particular attention is devoted to examining the usefulness of non-monotonic quantifiers, which represent a fuzzy determination of the amount of analyzed data. The answer is positive. The use of non-monotonic quantifiers in the detection of outliers can provide a more significant value of the degree of truth of a linguistic summary. At the end, this paper provides a computational example of practical importance.


title: A Study of the Set of Probability Measures Compatible with Comparative Judgements

text: We consider a set of comparative probability judgements over a finite possibility space and study the structure of the set of probability measures that are compatible with them. We relate the existence of some compatible probability measure to Walley’s behavioural theory of imprecise probabilities, and introduce a graphical representation that allows us to bound, and in some cases determine, the extreme points of the set of compatible measures. In doing this, we generalise some earlier work by Miranda and Destercke on elementary comparisons.


title: Imprecise Classification with Non-parametric Predictive Inference

text: In many situations, classifiers predict a set of states of a class variable because there is no information enough to point only one state. In the data mining area, this task is known as Imprecise Classification. Decision Trees that use imprecise probabilities, also known as Credal Decision Trees (CDTs), have been adapted to this field. The adaptation proposed so far uses the Imprecise Dirichlet Model (IDM), a mathematical model of imprecise probabilities that assumes prior knowledge about the data, depending strongly on a hyperparameter. This strong dependence is solved with the Non-Parametric Predictive Inference Model (NPI-M), also based on imprecise probabilities. This model does not make any prior assumption of the data and does not have parameters. In this work, we propose a new adaptation of CDTs to Imprecise Classification based on the NPI-M. An experimental study carried out in this research shows that the adaptation with NPI-M has an equivalent performance than the one obtained with the adaptation based on the IDM with the best choice of the hyperparameter. Consequently, since the NPI-M is a non-parametric approach, it is concluded that the NPI-M is more appropriated than the IDM to be applied to the adaptation of CDTs to Imprecise Classification.


title: Covariate-Adjusted Hybrid Principal Components Analysis

text: Electroencephalography (EEG) studies produce region-referenced functional data in the form of EEG signals recorded across electrodes on the scalp. The high-dimensional data capture underlying neural dynamics and it is of clinical interest to model differences in neurodevelopmental trajectories between diagnostic groups, for example typically developing (TD) children and children with autism spectrum disorder (ASD). In such cases, valid group-level inference requires characterization of the complex EEG dependency structure as well as covariate-dependent heteroscedasticity, such as changes in variation over developmental age. In our motivating study, resting state EEG is collected on both TD and ASD children aged two to twelve years old. The peak alpha frequency (PAF), defined as the location of a prominent peak in the alpha frequency band of the spectral density, is an important biomarker linked to neurodevelopment and is known to shift from lower to higher frequencies as children age. To retain the most amount of information from the data, we model patterns of alpha spectral variation, rather than just the peak location, regionally across the scalp and chronologically across development for both the TD and ASD diagnostic groups. We propose a covariate-adjusted hybrid principal components analysis (CA-HPCA) for region-referenced functional EEG data, which utilizes both vector and functional principal components analysis while simultaneously adjusting for covariate-dependent heteroscedasticity. CA-HPCA assumes the covariance process is weakly separable conditional on observed covariates, allowing for covariate-adjustments to be made on the marginal covariances rather than the full covariance leading to stable and computationally efficient estimation. A mixed effects framework is proposed to estimate the model components coupled with a bootstrap test for group-level inference. The proposed methodology provides novel insights into neurodevelopmental differences between TD and ASD children.


title: Tolerance and Control Solutions of Two-Sided Interval Linear System and Their Applications

text: This work investigates tolerance and control solutions to a two-sided interval linear system. Their semantics are different, even though, we would be able to interchange the role of the interval information algebraically. We present necessary and sufficient conditions of their solvabilities as the inequalities depending on center and radius of coefficient interval matrices on both sides of the system. In a situation when the vector of variables is nonnegative, the conditions can simply be modified as the inequalities depending on boundaries of the interval matrices. This result helps to find out the feasible solutions of a quadratic programming problem with two-sided interval linear equation constraints.


title: Modus Ponens Tollens for RU-Implications

text: In fuzzy rules based systems, fuzzy implication functions are usually considered to model fuzzy conditionals and to perform forward and backward inferences. These processes are guaranteed by the fulfilment of the Modus Ponens and Modus Tollens properties by the fuzzy implication function with respect to the considered conjunction and fuzzy negation. In this paper, we investigate which residual implications derived from uninorms satisfy both Modus Ponens and Modus Tollens properties with respect to the same t-norm and a fuzzy negation simultaneously. The most usual classes of uninorms are considered and many solutions are obtained which allow to model the fuzzy conditionals in a fuzzy rules based systems (and perform backward and forward inferences) with a unique residual implication derived from a uninorm.


title: On Integral Transforms for Residuated Lattice-Valued Functions

text: The article aims to introduce four types of integral transforms for functions whose function values belong to a complete residuated lattice. The integral transforms are defined using so-called qualitative residuum based fuzzy integrals and integral kernels in the form of binary fuzzy relations. We present some of the basic properties of proposed integral transforms including a linearity property that is satisfied under specific conditions for comonotonic functions.


title: A Genetic Approach to the Job Shop Scheduling Problem with Interval Uncertainty

text: In this paper we tackle a variant of the job shop scheduling problem where task durations are uncertain and only an interval of possible values for each task duration is known. We propose a genetic algorithm to minimise the schedule’s makespan that takes into account the problem’s uncertainty during the search process. The behaviour of the algorithm is experimentally evaluated and compared with other state-of-the-art algorithms. Further analysis in terms of solution robustness proves the advantage of taking into account interval uncertainty during the search process with respect to considering only the expected processing times and solving the problem’s crisp counterpart. This robustness analysis also illustrates the relevance of the interval ranking method used to compare schedules during the search.


title: Nonlocal Laplace Operator in a Space with the Fuzzy Partition

text: Differential operators play an important role in the mathematical modeling of dynamic processes and the analysis of various structures. However, there are certain limitations in their use. To remove them, nonlocal differential operators have been proposed. In this work, we focus on nonlocal Laplace operator, which has become increasingly useful in image processing. We introduce the representation of F-transform based Laplace operator in a space with a fuzzy partition. Many useful properties of this operator are proposed and their proofs are also included.


title: Bayesian Smoothing of Decision Tree Soft Predictions and Evidential Evaluation

text: As for many classifiers, decision trees predictions are naturally probabilistic, with a frequentist probability distribution on labels associated to each leaf of the tree. Those probabilities have the major drawback of being potentially unreliable in the case where they have been estimated from a limited number of examples. Empirical Bayes methods enable the updating of observed probability distributions for which the parameters of the prior distribution are estimated from the data. This paper presents an approach of smoothing decision trees predictive binary probabilities with an empirical Bayes method. The update of probability distributions associated with tree leaves creates a correction concentrated on small-sized leaves, which improves the quality of probabilistic tree predictions. The amplitude of these corrections is used to generate predictive belief functions which are finally evaluated through the ensemblist extension of three evaluation indexes of predictive probabilities.


title: On the Elicitation of an Optimal Outer Approximation of a Coherent Lower Probability

text: The process of outer approximating a coherent lower probability by a more tractable model with additional properties, such as 2- or completely monotone capacities, may not have a unique solution. In this paper, we investigate whether a number of approaches may help in eliciting a unique outer approximation: minimising a number of distances with respect to the initial model, or maximising the specificity of the outer approximation. We apply these to 2- and completely monotone approximating lower probabilities, and also to possibility measures.