Daniel Paternain

Universidad Pública de Navarra | UPNA · Department of Statistic Computer Science and Mathematics

Machine learning models can inherit biases from their training data, leading to discriminatory or inaccurate predictions. This is particularly concerning with the increasing use of large, unsupervised datasets for training foundational models. Traditionally, demographic biases within these datasets have not been well-understood, limiting our abilit...

Machine learning models can inherit biases from their training data, leading to discriminatory or inaccurate predictions. This is particularly concerning with the increasing use of large, unsupervised datasets for training foundational models. Traditionally, demographic biases within these datasets have not been well-understood, limiting our abilit...

Demographic biases in source datasets have been shown as one of the causes of unfairness and discrimination in the predictions of Machine Learning models. One of the most prominent types of demographic bias are statistical imbalances in the representation of demographic groups in the datasets. In this paper, we study the measurement of these biases...

Demographic biases in source datasets have been shown as one of the causes of unfairness and discrimination in the predictions of Machine Learning models. One of the most prominent types of demographic bias are statistical imbalances in the representation of demographic groups in the datasets. In this paper, we study the measurement of these biases...

Facial Expression Recognition (FER) uses images of faces to identify the emotional state of users, allowing for a closer interaction between humans and autonomous systems. Unfortunately, as the images naturally integrate some demographic information, such as apparent age, gender, and race of the subject, these systems are prone to demographic bias...

Fuzzy measure-based aggregations allow taking interactions among coalitions of the input sources into account. Their main drawback when applying them in real-world problems, such as combining classifier ensembles, is how to define the fuzzy measure that governs the aggregation and specifies the interactions. However, their usage for combining class...

Facial Expression Recognition (FER) uses images of faces to identify the emotional state of users, allowing for a closer interaction between humans and autonomous systems. Unfortunately, as the images naturally integrate some demographic information, such as apparent age, gender, and race of the subject, these systems are prone to demographic bias...

The increasing amount of applications of Artificial Intelligence (AI) has led researchers to study the social impact of these technologies and evaluate their fairness. Unfortunately, current fairness metrics are hard to apply in multi-class multi-demographic classification problems, such as Facial Expression Recognition (FER). We propose a new set...

In this work, we introduce the notion of dG-Choquet integral, which generalizes the discrete Choquet integral replacing, in the first place, the difference between inputs represented by closed subintervals of the unit interval [0,1] by a dissimilarity function; and we also replace the sum by more general appropriate functions. We show that particul...

Ordered Weighted Averaging (OWA) operators have been integrated in Convolutional Neural Networks (CNNs) for image classification through the OWA layer. This layer lets the CNN integrate global information about the image in the early stages, where most CNN architectures only allow for the exploitation of local information. As a side effect of this...

OWA operators and related aggregation techniques generally focus on input vector with a linear ordering. However, in commonly faced multi-criteria and multi-sources evaluation and decision making, the inputs involved form an evaluation matrix. Considering the fact that the data under evaluation are all with two dimensional meanings, this study expl...

The notion of an orness measure for aggregation functions has been a relevant study subject whose history can be traced back to the early works of Dujmović in 1973. Intuitively, an orness measure quantifies the similarity of an aggregation function to the “or” function and results in an essential tool for decision engineering, field in which the ch...

This work proposes some standard and general forms of induced ordered weighted averaging (GnIOWA) operators where the inductive information is ordered weighted averaging (OWA) weight vectors instead of real numbers. It shows the usefulness of such type of generalized induced OWA in decision making and evaluation and many other applications. We prop...

Basic Uncertain Information (BUI) as a newly introduced concept generalized a wide range of uncertain information. The well-known Ordered Weighted Averaging (OWA) operators can flexibly and effectively model bipolar preferences of decision makers over given real valued input vector. However, there are no extant methods for OWA operators to be carri...

One of the most common techniques for approaching image classification problems are Deep Neural Networks. These systems are capable of classifying images with different levels of detail at different levels of detail, with an accuracy that sometimes can surpass even manual classification by humans. Most common architectures for Deep Neural Networks...

The ordered weighted averaging (OWA) operator and its associated weight vectors have been both theoretically and practically verified to be powerful and effective in modeling the optimism/pessimism preference of decision makers. When several different OWA weight vectors are offered, it is necessary to develop certain techniques to aggregate them in...

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...

The paper introduces a new class of functions from [0,1]n to [0,n] called d-Choquet integrals. These functions are a generalization of the “standard” Choquet integral obtained by replacing the difference in the definition of the usual Choquet integral by a dissimilarity function. In particular, the class of all d-Choquet integrals encompasses the c...

In Machine Learning an ensemble refers to the combination of several classifiers with the objective of improving the performance of every one of its counterparts. To design an ensemble two main aspects must be considered: how to create a diverse set of classifiers and how to combine their outputs. This work focuses on the latter task. More specific...

Ordered Weighted Averaging (OWA) operators are a profusely applied class of averaging aggregation functions, i.e. operators that always yield a value between the minimum and the maximum of the inputs. The orness measure was introduced to classify the behavior of the OWA operators depending on the weight vectors. Defining a suitable orness measure i...

Existing extensions to Yager's ordered weighted averaging (OWA) operators enlarge the application range and to encompass more principles and properties related to OWA aggregation. However, these extensions do not provide a strict and convenient way to model evaluation scenarios with complex or grouped preferences. Based on earlier studies and recen...

It is known that when dealing with interval-valued data, there exist problems associated with the non-existence of a total order. In this work we investigate a reformulation of an interval-valued decomposition strategy for multi-class problems called IVOVO, and we analyze the effectiveness of considering different admissible orders in the aggregati...

IVOVO stands for Inverval-Valued One-Vs-One and is the combination of IVTURS fuzzy classifier and the One-Vs-One strategy. This method is designed to improve the performance of IVTURS in multi-class problems, by dividing the original problem into simpler binary ones. The key issue with IVTURS is that interval-valued confidence degrees for each clas...

Ordered weighted average (OWA) operators are commonly used to aggregate information in multiple situations, such as decision making problems or image processing tasks. The great variety of weights that can be chosen to determinate an OWA operator provides a broad family of aggregating functions, which obviously give different results in the aggrega...

Aggregation or fusion of interval data is not a trivial task, since the necessity of arranging data arises in many aggregation functions, such as OWA operators or the Choquet integral. Some arranging procedures have been given to solve this problem, but they need certain parameters to be set. In order to solve this problem, in this work we propose...

In this work we study the usage of different families of fusion functions for combining classifiers in a multiple classifier system of One-vs-One (OVO) classifiers. OVO is a decomposition strategy used to deal with multi-class classification problems, where the original multi-class problem is divided into as many problems as pair of classes. In a m...

Based on previous investigations, we have proposed two different methods to extend lattice-valued fuzzy connectives (t-norms, t-conorms, negations and implications) and other related operators, considering a generalized notion of sublattices. Taking into account the results obtained and seeking to analyze the behavior of both extension methods in f...

Ordered Weighted Averaging (OWA) operators are a family of aggregation functions for data fusion. If the data are real numbers, then OWA operators can be characterized either as a special kind of discrete Choquet integral or simply as an arithmetic mean of the given values previously ordered. This paper analyzes the possible generalizations of thes...

In this paper we replace the product of the masses in the Gravitational search algorithm introduced by [17] by other bivariate functions with specific properties. We analyze the properties of these functions to guarantee convergence in the algorithm and we discuss an application to justify our theoretical study and the need of using functions other...

In this work we propose a new algorithm for image inpainting. The proposal is patch-based, so we look for similar small regions (windows) through the whole image to inpaint the unknown area. The final goal is to obtain a complete image with no visual differences between the original part and the reconstructed one. The main novelty is the use of col...

In this work we propose an image compression algorithm based on the fuzzy transform. The algorithm tries to find the best fuzzy partition of the functions domain in order to obtain the best compressed image (in terms of quality). To solve the optimization problem we based ourselves in the Gravitational Search Algorithm, in which each agent represen...

This paper deals with OWA (ordered weighted average) operators defined on an arbitrary finite lattice endowed with a t-norm and a t-conorm. A qualitative orness measure for any OWA operator is suggested, based on its proximity to the OR operator that yields the maximum of the given data. In the particular case of a finite distributive lattice, cons...

In this work we investigate a mechanism for fusing a set of inputs (values) in such a way that the procedure does not create new information during the process. In order to do so, we introduce internal fusion functions, a family of fusion functions in which the output always corresponds to some of the given inputs. We perform an in-depth theoretica...

Implication functions are crucial operators for many fuzzy logic applications. In this work, we consider the definition of implication functions in the interval-valued setting using admissible orders and we use this interval-valued implications for building comparison measures.

In this work we investigate the use of OWA operators in color image reduction. Since the RGB color scheme can be seen as a Cartesian product of lattices, we use the generalization of OWA operators to any complete lattice. However, the behavior of lattice OWA operators in image processing is not easy to predict. Therefore, we propose an orness measu...

Implication functions are crucial operators for many fuzzy logic applications. In this work, we consider the definition of implication functions in the interval-valued setting using admissible orders and we use this interval-valued implications for building comparison measures.

We study a structural functional equation that is directly related to the pointwise aggregation of a finite number of maps from a given nonempty set into another. First we establish links between pointwise aggregation and invariance properties. Then, paying attention to the particular case of aggregation operators of a finite number of real-valued...

In this paper, we propose a generalized quasi-metric in spaces of strings, which is based on edit operations (insertion and deletions) and taking values as pairs of non-negative integers. We show that with such a generalization is possible to carry more information about similarity between strings than in the usual case where the distance between t...

In this work, we introduce a method for constructing capacities using overlap indexes between the fuzzy sets which are generated from the inputs of the considered problem. We also use these capacities to aggregate information by means of the Choquet integral in a fuzzy rule-based classifier. We observe that with these capacities the obtained result...

Lamb muscle discrimination is important for the meat industry due to the different pricing of each type of muscle. In this paper, we combine hyperspectral imaging, operating in the wavelength range 380–1028 nm, with several machine learning algorithms to deal automatically with the classification of lamb muscles. More specifically, we study the dis...

This paper deals with OWA (ordered weighted average) operators defined on any complete lattice endowed with a t-norm and a t-conorm and satisfying a certain finiteness local condition. A parametrization of these operators is suggested by introducing a quantitative orness measure for each OWA operator, based on its proximity to the OR operator. The...

Objetivos: Los sistemas de medición de gravedad son necesarios para comparar los resultados tras la asistencia al paciente traumatizado grave. Determinados índices de gravedad son muy útiles para predecir la probabilidad de supervivencia pero son de difícil realización en la práctica diaria de urgencias. Material o pacientes y método: Se analizó la...

In this work we deal with the problem of using OWA operators in color image reduction algorithms. For this reason, we study OWA operators defined on an arbitrary finite lattice endowed with a t-norm and a t-conorm. In the case of RGB color images, we apply OWA operators defined on a finite product lattice. Depending on the OWA operator considered,...

In this work we introduce the concept of a fusion operator for type-2 fuzzy sets as a mapping that takes m functions from [0, 1] to [0, 1] and brings back a new function of the same type. We study in depth the properties of pointwise fusion operators and representable fusion operators. Finally, we study the union and intersection of type-2 fuzzy se...

In this work we propose a clustering methodology model named as Mixture of Fuzzy Models (MFMs). We adopt two assumptions: the data points are generated by a membership function and the sum of the memberships to all of the clusters must be greater or equal than zero. The objective is to obtain a set of membership functions which represent the data....

In this work we present a thresholding algorithm for greyscale images. Our proposal is the use of grouping functions to find the best threshold. These functions are able to measure the belongingness of a grey intensity to the background or to the object of the image, so the best threshold is the one associated with the highest grouping value.

Since the seminal paper of fuzzy set theory by Zadeh in 1965, many extensions have been proposed to overcome the difficulty for assigning the membership degrees. In recent years, a new extension, the hesitant fuzzy sets, has attracted a lot of interest due to its usefulness to handle those problems in which it is difficult to provide accurately a s...

In this work we present an image reduction algorithm based on averaging aggregation functions. We axiomatically define the concepts of image reduction operator and local reduction operator. We study the construction of the latter by means of averaging functions and we propose an image reduction algorithm (image reduction operator). We analyze the p...

In this paper we address the problem of color image segmentation transforming it into a decision making paradigm. A set of experts is provided, so that each expert assigns a preference degree of each pixel to every object of the image considering also the ignorance associated with such assignation. We represent the objects by means of fuzzy linguis...

In this work we present the definition of strong fuzzy subsethood measure as a unifiying concept for the different notions of fuzzy subsethood that can be found in the literature. We analyze the relations of our new concept with the definitions by Kitainik ( [20]), Young ( [26]) and Sinha and Dougherty ( [23]) and we prove that the most relevant pr...

After studying several reduction algorithms that can be found in the literature, we notice that there is not an axiomatic definition of this concept. In this work we propose the definition of weak reduction operators and we propose the properties of the original image that reduced images must keep. From this definition, we study whether two methods...

In this work we address the problem of the quality assessments in the process of color images segmentation. We consider each component of a color image as a fuzzy set and therefore, we propose to use similarity measures (between fuzzy sets) to compare image segmentations. We test three segmentation algorithms, FCM [2], MAP-ML [10]and 2-TUP [19] on...

In this work we present a thresholding algorithm for greyscale images. Our proposal is based on the use of grouping functions to find the best threshold. These functions are able to measure the membership of a grey intensity to the background or to the object of the image, so the best threshold is the one associated with the highest grouping value....

In this paper we axiomatically define weak homogeneity of a fuzzy subset, which means that its membership function fulfills at least the minimum properties required to represent the homogeneity of a region. We also provide several construction methods based on the homogeneity of an interval. Besides, we show an illustrative example of these functio...

In this chapter, we present some methods to construct interval type-2 membership functions from fuzzy membership functions and their applications in image processing, classification, and decision making. First, we review some basic concepts of interval type-2 fuzzy sets (IT2FSs). Next, we analyze three different approaches to construct IT2FSs start...

In this paper we present a new fuzzy reasoning method in which the Choquet integral is used as aggregation function. In this manner, we can take into account the interaction among the rules of the system. For this reason, we consider several fuzzy measures, since it is a key point on the subsequent success of the Choquet integral, and we apply the...

In this paper we present a comparison study between different aggregation functions for the combination of RGB color channels in stereo matching problem. We introduce color information from images to the stereo matching algorithm by aggregating the similarities of the RGB channels which are calculated independently. We compare the accuracy of diffe...

This work discusses Fuzziness in Medical Image Processing. We start summarizing different techniques of medical image acquisition and their main features. Examining the specialized literature, we discuss the fuzziness present in these images, including Fuzziness in pixel information and Fuzziness in model representation. Further, we present a revie...

This work discusses Fuzziness in Medical Image Processing. We start summarizing different techniques of medical image acquisition and their main features. Examining the specialized literature, we discuss the fuzziness present in these images, including Fuzziness in pixel information and Fuzziness in model representation. Further, we present a revie...

In this work we present a construction method for Atanassov’s intuitionistic fuzzy preference relations starting from fuzzy preference relations and taking into account the ignorance of the expert in the construction of the latter. Moreover, we propose two generalizations of the weighted voting strategy to work with Atanassov’s intuitionistic fuzzy...

In image processing, particularly in image reduction, averaging aggregation functions play an important role. In this work we study the aggregation of color values (RGB) and we present an image reduction algorithm for RGB color images. For this purpose, we define and study aggregation functions and penalty functions in product lattices. We show how...

The main aim of this work is to present a generalization of Atanassov’s operators to higher dimensions. To do so, we use the concept of fuzzy set, which can be seen as a special kind of fuzzy multiset, to define a generalization of Atanassov’s operators for n-dimensional fuzzy values (called n-dimensional intervals). We prove that our generalized A...

In this work we associate an Interval-Valued Fuzzy Set with an image, so that the membership of ecah pixel represents the intensities of itself and its neighbourhood. Based on this set we propose a new simple super-resolution algorithm for color images. We show some experimental results and study how the δ parameter has influence on the results obt...

In this work we present a new image thresholding algorithm for the segmentation of MRI brain images into two classes: gray matter and white matter. The proposed algorithm is based on the concept of incomparability proposed by Fodor and Roubens for fuzzy preference relations. We test our algorithm for local and global segmentation of brain images. W...

In this work we propose an image reduction algorith based on local reduction operators. We analyze the construction of weak local reduction operators by means of aggregation functions and we analyze the effect of several aggregation functions in image reduction with original and noisy images.

We investigate the problem of averaging values on lattices and, in particular, on discrete product lattices. This problem arises in image processing when several color values given in RGB, HSL, or another coding scheme need to be combined. We show how the arithmetic mean and the median can be constructed by minimizing appropriate penalties, and we...

In this work we present a method for constructing an Atanassov’s intuitionistic fuzzy preference relation from a fuzzy preference relation that takes into account the ignorance of the expert when evaluating the preferences in the latter. Moreover, we present two algorithms that make use of this method for extending the weighted voting method to the...

We investigate the problem of combining or aggregating several color values given in coding scheme RGB. For this reason, we study the problem of averaging values on lattices, and in particular on discrete product lattices. We study the arithemtic mean and the median on product lattices. We apply these aggregation functions in image reduction and we...

We advance the theory of aggregation operators and introduce non-monotone aggregation methods based on minimization of a penalty for inputs disagreements. The application in mind is processing data sets which may contain noisy values. Our aim is to filter out noise while at the same time preserve signs of unusual values. We review various methods o...

In this work we present a new construction method of IVFSs from Fuzzy Sets. We use these IVFSs for image processing. Concretely, in this contribution we introduce a new image magnification algorithm using IVFSs. This algorithm is based on block expansion and it is characterized by its simplicity.

In this chapter we address image compression by means of two alternative algorithms. In the first algorithm, we associate to each image an interval-valued fuzzy relation, and we build an image which is n times smaller than the original one, by using two-dimensional OWA operators. The experimental results show that, in this case, best results are ob...

In this work we propose a definition of weak local reduction operators and an algorithm that uses such operators to reduce images. We show how to construct local reduction operators by means of different aggregation functions. We also present several experimental results obtained using these aggregation functions-based reduction operators. Keyword...

In this work we propose an image reduction algorithm based on weak local reduction operators. We use several averaging functions to build these operators and we analyze their properties. We present experimental results where we apply the algorithm and weak local reduction operators in procedures of reduction, and later, reconstruction of images. We...

In this work we introduce a new construction method of Atanassov's intuitionistic fuzzy sets (A-IFSs) from fuzzy sets. We use A-IFSs in image processing. We propose a new image magnification algorithm using A-IFSs. This algorithm is characterized by its simplicity and its efficiency.