Browsing by Author "Miguel Turullols, Laura de"
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Publication Open Access An algorithm for group decision making using n -dimensional fuzzy sets, admissible orders and OWA operators(Elsevier, 2017) Miguel Turullols, Laura de; Sesma Sara, Mikel; Elkano Ilintxeta, Mikel; Asiain Ollo, María José; Bustince Sola, Humberto; Automatika eta Konputazioa; Matematika; Institute of Smart Cities - ISC; Automática y Computación; Matemáticas; Universidad Pública de Navarra / Nafarroako Unibertsitate PublikoaIn this paper we propose an algorithm to solve group decision making problems using n-dimensional fuzzy sets, namely, sets in which the membership degree of each element to the set is given by an in- creasing tuple of n elements. The use of these sets has naturally led us to define admissible orders for n-dimensional fuzzy sets, to present a construction method for those orders and to study OWA operators for aggregating the tuples used to represent the membership degrees of the elements. In these condi- tions, we present an algorithm and apply it to a case study, in which we show that the exploitation phase which appears in many decision making methods can be omitted by just considering linear orders between tuples.Publication Open Access Application of two different methods for extending lattice-valued restricted equivalence functions used for constructing similarity measures on L-fuzzy sets(Elsevier, 2018) Palmeira, Eduardo S.; Bedregal, Benjamin; Bustince Sola, Humberto; Paternain Dallo, Daniel; Miguel Turullols, Laura de; Automatika eta Konputazioa; Institute of Smart Cities - ISC; Automática y Computación; Universidad Pública de Navarra / Nafarroako Unibertsitate PublikoaBased 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 face of fuzzy operators related to image processing, we have applied these methods so as to extend restricted equivalence functions, restricted dissimilarity functions and Ee,N-normal functions. We also generalize the concepts of similarity measure, distance measure and entropy measure for L-fuzzy sets constructing them via restricted equivalence functions, restricted dissimilarity functions and Ee,N-normal functionsPublication Embargo Binary relations coming from solutions of functional equations: orderings and fuzzy subsets(World Scientific Publishing Company, 2017) Campión Arrastia, María Jesús; Miguel Turullols, Laura de; García Catalán, Olga Raquel; Induráin Eraso, Esteban; Abrísqueta Usaola, Francisco Javier; Automatika eta Konputazioa; Matematika; Institute of Smart Cities - ISC; Institute for Advanced Research in Business and Economics - INARBE; Institute for Advanced Materials and Mathematics - INAMAT2; Automática y Computación; Matemáticas; Universidad Pública de Navarra / Nafarroako Unibertsitate PublikoaWe analyze the main properties of binary relations, defined on a nonempty set, that arise in a natural way when dealing with real-valued functions that satisfy certain classical functional equations on two variables. We also consider the converse setting, namely, given binary relations that accomplish some typical properties, we study whether or not they come from solutions of some functional equation. Applications to the numerical representability theory of ordered structures are also furnished as a by-product. Further interpretations of this approach as well as possible generalizations to the fuzzy setting are also commented. In particular, we discuss how the values taken for bivariate functions that are bounded solutions of some classical functional equations define, in a natural way, fuzzy binary relations on a set.Publication Open Access Computing with uncertainty truth degrees: a convolution-based degrees(2017) Miguel Turullols, Laura de; Bustince Sola, Humberto; Baets, Bernard de; Induráin Eraso, Esteban; Automática y Computación; Automatika eta KonputazioaLa teoría de los conjuntos difusos puede contemplarse como un conjunto de herramientas matemáticas excepcionalmente adaptadas para trabajar con información incompleta, falta de nitidez e incertidumbre no aleatoria. De hecho, como herramienta en ingeniería, para traducir el lenguaje natural humano impreciso en un objeto matemático, los conjuntos difusos juegan un papel decisivo para superar la brecha entre el hombre y los ordenadores. Sin embargo, es ampliamente conocido que la asignación de un valor preciso como pertenencia no es una tarea sencilla. En la literatura, se han propuesto y estudiado varias generalizaciones de los conjuntos difusos para resolver esta dificultad. Más aún, estas generalizaciones han demostrado ser una herramienta útil, al mejorar los resultados en diferentes aplicaciones. Las generalizaciones difieren de los conjuntos difusos en el objeto matemático que se utiliza para modelar la imprecisión y/o incertidumbre. Especifícamente, los conjuntos difusos toman elementos en el intervalo unidad [0, 1] mientras que las generalizaciones toman objetos matemáticos más complejos como intervalos (conjuntos difusos intervalo-valorados), subconjuntos del intervalo unidad (conjuntos difusos "conjunto-valorados") o funciones (conjuntos difusos tipo-2), entre otros. No obstante, el uso de las generalizaciones de los conjuntos difusos tiene un gran inconveniente. Antes de aplicar las generalizaciones de los conjuntos difusos es necesario adaptar ad hoc cada noción teórica al correspondiente objeto matemático que modela la incertidumbre en la aplicación, es decir, es necesario redefinir cada noción teórica reemplazando el intervalo unidad [0, 1] por objetos matemáticos más complejos. En la historia de los conjuntos difusos quedó claro relativamente pronto que la relación natural entre la teoría de conjuntos y la lógica clásica podía ser imitada generando una relación entre la teoría de los conjuntos difusos y la lógica multi-valuada. Hoy en día esta lógica multivaluada recibe el nombre de lógica difusa. Del mismo modo, cada generalización de los conjuntos difusos genera un nuevo sistema lógico. Todos estos sistemas lógicos coinciden en que intentan modelar incertidumbre, pero difieren en el objeto matemático que representa esta incertidumbre. Es fácil comprobar que el mismo problema entre conjuntos difusos y sus generalizaciones puede encontrarse en los distintos sistemas lógicos, es decir, aunque todos ellos son similares, cada noción teórica tiene que ser redefinida para cada lógica. Este problema, junto con el gran número de lógicas que modelan incertidumbre, nos ha llevado a estudiar si es o no posible encontrar un sistema que englobe estas lógicas y nos ha motivado a proponer un sistema lógico que permita modelar la incertidumbre de manera más flexible. Centrándonos especialmente en sistemas lógicos provenientes de la lógica difusa, en esta tesis doctoral proponemos un nuevo sistema lógico que recupera varias de las lógicas de la literatura. La principales ventajas de nuestra propuesta son: evitará la excesiva repetición de las nociones teóricas; permitirá adaptar la aplicación a la generalización de los conjuntos difusos más adecuada de una manera mucho más sencilla. En esta tesis doctoral presentamos la semántica del modelo lógico propuesto junto con un estudio en profundidad de la operación de convolución que se utiliza para definir las conectivas disyunción y conjunción del sistema.Publication Open Access Construction of admissible linear orders for interval-valued Atanassov intuitionistic fuzzy sets with an application to decision making(Elsevier, 2015) Miguel Turullols, Laura de; Bustince Sola, Humberto; Fernández Fernández, Francisco Javier; Induráin Eraso, Esteban; Kolesárová, Anna; Mesiar, Radko; Matemáticas; Matematika; Automática y Computación; Automatika eta Konputazioa; Universidad Pública de Navarra / Nafarroako Unibertsitate PublikoaIn this work we introduce a method for constructing linear orders between pairs of intervals by using aggregation functions. We adapt this method to the case of interval-valued Atanassov intuitionistic fuzzy sets and we apply these sets and the considered orders to a decision making problem.Publication Open Access Convolution lattices(Elsevier, 2018) Miguel Turullols, Laura de; Bustince Sola, Humberto; Baets, Bernard de; Automatika eta Konputazioa; Institute of Smart Cities - ISC; Automática y ComputaciónWe propose two convolution operations on the set of functions between two bounded lattices and investigate the algebraic structure they constitute, in particular the lattice laws they satisfy. Each of these laws requires the restriction to a specific subset of functions, such as normal, idempotent or convex functions. Combining all individual results, we identify the maximal subsets of functions resulting in a bounded lattice, and show this result to be equivalent to the distributivity of the lattice acting as domain of the functions. Furthermore, these lattices turn out to be distributive as well. Additionally, we show that for the larger subset of idempotent functions, although not satisfying the absorption laws, the convolution operations satisfy the Birkhoff equation.Publication Open Access Description and properties of curve-based monotone functions(Springer, 2019) Sesma Sara, Mikel; Miguel Turullols, Laura de; Roldán López de Hierro, Antonio Francisco; Špirková, Jana; Mesiar, Radko; Bustince Sola, Humberto; Institute of Smart Cities - ISCCurve-based monotonicity is one of the lately introduced relaxations of monotonicity. As directional monotonicity regards monotonicity along fixed rays, which are given by real vectors, curve-based monotonicity studies the increase of functions with respect to a general curve. In this work we study some theoretical properties of this type of monotonicity and we relate this concept with previous relaxations of monotonicity.Publication Open Access Distance transformations based on ordered weighted averaging operators(University of Hawaii Press, 2021) López Molina, Carlos; Miguel Turullols, Laura de; Iglesias Rey, Sara; Bustince Sola, Humberto; Baets, Bernard de; Estadística, Informática y Matemáticas; Estatistika, Informatika eta MatematikaBinary image comparison has been a study subject for a long time, often rendering in context-specific solutions that depend upon the type of visual contents in the binary images. Distance transformations have been a recurrent tool in many of such solutions. The literature contains works on the generation and definition of distance transformations, but also on how to make a sensible use of their results. In this work, we attempt to solve one of the most critical problems in the application of distance transformations to real problems: their oversensitivity to certain spurious pixels which, even if having a minimal visual impact in the binary images to be compared, may have a severe impact on their distance transforms. With this aim, we combine distance transformations with Ordered Weighted Averaging (OWA) operators, a well-known information fusion tool from Fuzzy Set Theory.Publication Open Access Estudio de representaciones granulares para segmentación de imagen(2024) Alonso Martínez, Ander; López Molina, Carlos; Miguel Turullols, Laura de; Escuela Técnica Superior de Ingeniería Industrial, Informática y de Telecomunicación; Industria, Informatika eta Telekomunikazio Ingeniaritzako Goi Mailako Eskola TeknikoaLa tecnología es algo que está en auge en estos últimos años y que está teniendo un desarrollo que incluso da hasta miedo. Esto se debe a diversos factores que se juntan en el mismo intervalo de tiempo, como por ejemplo el uso de grandes cantidades de datos. Un concepto que no puede faltar si hablamos de la tecnología de la actualidad es la inteligencia artificial. La inteligencia artificial se divide en distintas ramas, pero dentro de todas estas se encuentra una que nos interesa especialmente, la visión artificial. La visión artificial se centra en el procesado de imágenes para distintos ámbitos de nuestra vida, ayudando así por ejemplo con la detección de objetos. Esta es capaz de detectar objetos mediante el ensayo y el error, donde el objetivo final es que nos de como resultado el objeto en cuestión mejor o por lo menos parecido a como lo haría un humano. Para ello, se introduce la idea del color. Necesitamos que nuestra maquina hable el mismo idioma que los humanos para poder comunicarnos, por lo cual no nos sirve que para una región aparentemente de un solo color este nos diga que hay quince colores distintos. Aquí entra el concepto de granularidad. La granularidad aplicada al mundo de la imagen se refiere al nivel de detalle que queremos, así pues si una imagen tiene una granularidad alta tiene un mayor número de detalles y traducido al color, tendrá un mayor número de colores. El trabajo realizado se centra en estos puntos, en usar un numero de colores parecido al que usaría un humano para describir la misma imagen. El proceso es sencillo, primero creamos dentro de la propia imagen regiones que tienen características similares, para esto hacemos uso de los superpixeles, más concretamente de los denominados SLIC. Una vez tenemos esas regiones definidas, sustituimos todos los píxeles por un único color, haciendo alusión a que regiones con características parecidas pueden ser definidas únicamente con un color y así acercarnos más a la visión humana. Por último segmentamos esta imagen haciendo un proceso similar, vamos juntando las regiones que tienen características de color más similares hasta quedarnos con un numero de colores optimo, más parecido a el número de colores que podría usar un humano para describir la imagen.Publication Open Access Evaluación de distintas arquitecturas de redes neuronales aplicadas a la clasificación de datos tabulares(2022) Rodríguez Villar, Izaskun; Rodríguez Martínez, Iosu; Miguel Turullols, Laura de; Escuela Técnica Superior de Ingeniería Industrial, Informática y de Telecomunicación; Industria, Informatika eta Telekomunikazio Ingeniaritzako Goi Mailako Eskola TeknikoaEn este trabajo se va a estudiar la aplicabilidad de distintos modelos de redes neuronales artificiales a la clasificación de datos tabulares. Recientemente, la transformación de problemas de “machine learning” entre dominios, con el fin de poder aplicar arquitecturas muy potentes, han ofrecido resultados muy prometedores [1][2]. Nuestro objetivo en este trabajo es comparar el rendimiento en modelos distintos: así como perceptrones multicapa (MLP) y redes convolucionales (CNN), combinando todos ellos con técnicas de ingeniería de características (“Feature engineering”) y la búsqueda de hiperparémetros para abordar el problema de clasificación de datos tabulares.Publication Open Access Extension of restricted equivalence functions and similarity measures for type-2 fuzzy sets(IEEE, 2021) Miguel Turullols, Laura de; Santiago, Regivan; Wagner, Christian; Garibaldi, Jonathan M.; Takáč, Zdenko; Roldán López de Hierro, Antonio Francisco; Bustince Sola, Humberto; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC; Estadística, Informática y Matemáticas; Universidad Pública de Navarra / Nafarroako Unibertsitate PublikoaIn this work we generalize the notion of restricted equivalence function for type-2 fuzzy sets, leading to the notion of extended restricted equivalence functions. We also study how under suitable conditions, these new functions recover the standard axioms for restricted equivalence functions in the real setting. Extended restricted equivalence functions allow us to compare any two general type-2 fuzzy sets and to generate a similarity measure for type-2 fuzzy sets. The result of this similarity is a fuzzy set on the same referential set (i.e., domain) as the considered type-2 fuzzy set. The latter is crucial for applications such as explainable AI and decision making, as it enables an intuitive interpretation of the similarity within the domain-specific context of the fuzzy sets. We show how this measure can be used to compare type-2 fuzzy sets with different membership functions in such a way that the uncertainty linked to type-2 fuzzy sets is not lost. This is achieved by generating a fuzzy set rather than a single numerical value. Furthermore, we also show how to obtain a numerical value for discrete referential sets.Publication Open Access A framework for radial data comparison and its application to fingerprint analysis(Elsevier, 2016) Marco Detchart, Cedric; Cerrón González, Juan; Miguel Turullols, Laura de; López Molina, Carlos; Bustince Sola, Humberto; Galar Idoate, Mikel; Automatika eta Konputazioa; Institute of Smart Cities - ISC; Automática y Computación; Universidad Pública de Navarra / Nafarroako Unibertsitate PublikoaThis work tackles the comparison of radial data, and proposes comparison measures that are further applied to fingerprint analysis. First, we study the similarity of scalar and non-scalar radial data, elaborated on previous works in fuzzy set theory. This study leads to the concepts of restricted radial equivalence function and Radial Similarity Measure, which model the perceived similarity between scalar and vectorial pieces of radial data, respectively. Second, the utility of these functions is tested in the context of fingerprint analysis, and more specifically, in the singular point detection. With this aim, a novel Template-based Singular Point Detection method is proposed, which takes advantage of these functions. Finally, their suitability is tested in different fingerprint databases. Different Similarity Measures are considered to show the flexibility offered by these measures and the behaviour of the new method is compared with well-known singular point detection methods.Publication Open Access General overlap functions(Elsevier, 2019) Miguel Turullols, Laura de; Gómez, Daniel; Tinguaro, Javier; Montero, Javier; Bustince Sola, Humberto; Pereira Dimuro, Graçaliz; Sanz, Jose Antonio; Automatika eta Konputazioa; Institute of Smart Cities - ISC; Automática y Computación; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa.As a generalization of bivariate overlap functions, which measure the degree of overlapping (intersection for non-crisp sets) of n different classes, in this paper we introduce the concept of general overlap functions. We characterize the class of general overlap functions and include some construction methods by means of different aggregation and bivariate overlap functions. Finally, we apply general overlap functions to define a new matching degree in a classification problem. We deduce that the global behavior of these functions is slightly better than some other methods in the literature.Publication Open Access Hyperspectral imaging using notions from type-2 fuzzy sets(Springer, 2019) López Maestresalas, Ainara; Miguel Turullols, Laura de; López Molina, Carlos; Arazuri Garín, Silvia; Bustince Sola, Humberto; Jarén Ceballos, Carmen; Ingeniería; Ingeniaritza; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Universidad Pública de Navarra / Nafarroako Unibertsitate PublikoaFuzzy set theory has developed a prolific armamentarium of mathematical tools for each of the topics that has fallen within its scope. One of such topics is data comparison, for which a range of operators has been presented in the past. These operators can be used within the fuzzy set theory, but can also be ported to other scenarios in which data are provided in various representations. In this work, we elaborate on notions for type-2 fuzzy sets, specifically for the comparison of type-2 fuzzy membership degrees, to create function comparison operators. We further apply these operators to hyperspectral imaging, in which pixelwise data are provided as functions over a certain energy spectra. The performance of the functional comparison operators is put to the test in the context of in-laboratory hyperspectral image segmentation.Publication Open Access Interval-valued Atanassov intuitionistic OWA aggregations using admissible linear orders and their application to decision making(IEEE, 2016) Miguel Turullols, Laura de; Bustince Sola, Humberto; Pekala, Barbara; Bentkowska, Urszula; Silva, Ivanoska da; Bedregal, Benjamin; Mesiar, Radko; Ochoa Lezaun, Gustavo; Automatika eta Konputazioa; Matematika; Institute of Smart Cities - ISC; Automática y Computación; MatemáticasBased on the definition of admissible order for interval-valued Atanassov intuitionistic fuzzy sets, we study OWA operators in these sets distinguishing between the weights associated to the membership and those associated to the nonmembership degree which may differ from the latter. We also study Choquet integrals for aggregating information which is represented using interval-valued Atanassov intuitionistic fuzzy sets. We conclude with two algorithms to choose the best alternative in a decision making problem when we use this kind of sets to represent information.Publication Open Access The interval-valued Choquet integral based on admissible permutations(IEEE, 2018) Paternain Dallo, Daniel; Miguel Turullols, Laura de; Ochoa Lezaun, Gustavo; Lizasoain Iriso, María Inmaculada; Mesiar, Radko; Bustince Sola, Humberto; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC; Institute for Advanced Materials and Mathematics - INAMAT2; Estadística, Informática y Matemáticas; Universidad Pública de Navarra / Nafarroako Unibertsitate PublikoaAggregation 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 the concept of an admissible permutation of intervals. Based on this concept, which avoids any parameter selection, we propose a new approach for the interval-valued Choquet integral that takes into account every possible permutation fitting to the considered ordinal structure of data. Finally, a consensus among all the permutations is constructed.Publication Open Access Local properties of strengthened ordered directional and other forms of monotonicity(Springer, 2019) Sesma Sara, Mikel; Miguel Turullols, Laura de; Mesiar, Radko; Fernández Fernández, Francisco Javier; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa, PJUPNA13In this study we discuss some of the recent generalized forms of monotonicity, introduced in the attempt of relaxing the monotonicity condition of aggregation functions. Specifically, we deal with weak, directional, ordered directional and strengthened ordered directional monotonicity. We present some of the most relevant properties of the functions that satisfy each of these monotonicity conditions and, using the concept of pointwise directional monotonicity, we carry out a local study of the discussed relaxations of monotonicity. This local study enables to highlight the differences between each notion of monotonicity. We illustrate such differences with an example of a restricted equivalence function.Publication Open Access Neuro-inspired edge feature fusion using Choquet integrals(Elsevier, 2021) Marco Detchart, Cedric; Lucca, Giancarlo; López Molina, Carlos; Miguel Turullols, Laura de; Pereira Dimuro, Graçaliz; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Universidad Pública de Navarra / Nafarroako Unibertsitate PublikoaIt is known that the human visual system performs a hierarchical information process in which early vision cues (or primitives) are fused in the visual cortex to compose complex shapes and descriptors. While different aspects of the process have been extensively studied, such as lens adaptation or feature detection, some other aspects, such as feature fusion, have been mostly left aside. In this work, we elaborate on the fusion of early vision primitives using generalizations of the Choquet integral, and novel aggregation operators that have been extensively studied in recent years. We propose to use generalizations of the Choquet integral to sensibly fuse elementary edge cues, in an attempt to model the behaviour of neurons in the early visual cortex. Our proposal leads to a fully-framed edge detection algorithm whose performance is put to the test in state-of-the-art edge detection datasets.Publication Open Access New measures for comparing matrices and their application to image processing(Elsevier, 2018) Sesma Sara, Mikel; Miguel Turullols, Laura de; Pagola Barrio, Miguel; Burusco Juandeaburre, Ana; Mesiar, Radko; Bustince Sola, Humberto; Automatika eta Konputazioa; Institute of Smart Cities - ISC; Automática y Computación; Universidad Pública de Navarra / Nafarroako Unibertsitate PublikoaIn this work we present the class of matrix resemblance functions, i.e., functions that measure the difference between two matrices. We present two construction methods and study the properties that matrix resemblance functions satisfy, which suggest that this class of functions is an appropriate tool for comparing images. Hence, we present a comparison method for grayscale images whose result is a new image, which enables to locate the areas where both images are equally similar or dissimilar. Additionally, we propose some applications in which this comparison method can be used, such as defect detection in industrial manufacturing processes and video motion detection and object tracking.Publication Embargo Non-symmetric over-time pooling using pseudo-grouping functions for convolutional neural networks(Elsevier, 2024) Ferrero Jaurrieta, Mikel; Paiva, Rui; Cruz, Anderson; Bedregal, Benjamin; Miguel Turullols, Laura de; Takáč, Zdenko; López Molina, Carlos; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISCConvolutional Neural Networks (CNNs) are a family of networks that have become state-of-the-art in several fields of artificial intelligence due to their ability to extract spatial features. In the context of natural language processing, they can be used to build text classification models based on textual features between words. These networks fuse local features to generate global features in their over-time pooling layers. These layers have been traditionally built using the maximum function or other symmetric functions such as the arithmetic mean. It is important to note that the order of input local features is significant (i.e. the symmetry is not an inherent characteristic of the model). While this characteristic is appropriate for image-oriented CNNs, where symmetry might make the network robust to image rigid transformations, it seems counter-productive for text processing, where the order of the words is certainly important. Our proposal is, hence, to use non-symmetric pooling operators to replace the maximum or average functions. Specifically, we propose to perform over-time pooling using pseudo-grouping functions, a family of non-symmetric aggregation operators that generalize the maximum function. We present a construction method for pseudo-grouping functions and apply different examples of this family to over-time pooling layers in text-oriented CNNs. Our proposal is tested on seven different models and six different datasets in the context of engineering applications, e.g. text classification. The results show an overall improvement of the models when using non-symmetric pseudo-grouping functions over the traditional pooling function.