Open Access
Operador de comparación de elementos multivaluados basado en funciones de equivalencia restringida
(Universidad de Málaga, 2021) Castillo López, Aitor; López Molina, Carlos; Fernández Fernández, Francisco Javier; Sesma Sara, Mikel; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
En este trabajo proponemos un nuevo enfoque del algoritmo de clustering gravitacional basado en lo que Einstein considero su 'mayor error': la constante cosmológica. De manera similar al algoritmo de clustering gravitacional, nuestro enfoque está inspirado en principios y leyes del cosmos, y al igual que ocurre con la teoría de la relatividad de Einstein y la teoría de la gravedad de Newton, nuestro enfoque puede considerarse una generalización del agrupamiento gravitacional, donde, el algoritmo de clustering gravitacional se recupera como caso límite. Además, se desarrollan e implementan algunas mejoras que tienen como objetivo optimizar la cantidad de iteraciones finales, y de esta forma, se reduce el tiempo de ejecución tanto para el algoritmo original como para nuestra versión.
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 - ISC
Curve-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.
Open Access
The law of O-conditionality for fuzzy implications constructed from overlap and grouping functions
(Elsevier, 2019) Pereira Dimuro, Graçaliz; Bedregal, Benjamin; Fernández Fernández, Francisco Javier; Sesma Sara, Mikel; Pintor Borobia, Jesús María; Bustince Sola, Humberto; Estatistika, Informatika eta Matematika; Ingeniaritza; Institute of Smart Cities - ISC; Estadística, Informática y Matemáticas; Ingeniería
Overlap and grouping functions are special kinds of non necessarily associative aggregation operators proposed for many applications, mainly when the associativity property is not strongly required. The classes of overlap and grouping functions are richer than the classes of t-norms and t-conorms, respectively, concerning some properties like idempotency, homogeneity, and, mainly, the self-closedness feature with respect to the convex sum and the aggregation by generalized composition of overlap/grouping functions. In previous works, we introduced some classes of fuzzy implications derived by overlap and/or grouping functions, namely, the residual implications R-0-implications, the strong implications (G, N)-implications and the Quantum Logic implications QL-implications, for overlap functions O, grouping functions G and fuzzy negations N. Such implications do not necessarily satisfy certain properties, but only weaker versions of these properties, e.g., the exchange principle. However, in general, such properties are not demanded for many applications. In this paper, we analyze the so-called law of O-Conditionality, O(x, 1(x, y)) <= y, for any fuzzy implication I and overlap function O, and, in particular, for Ro-implications, (G, N)-implications, QL-implications and D-implications derived from tuples (O, G, N), the latter also introduced in this paper. We also study the conditional antecedent boundary condition for such fuzzy implications, since we prove that this property, associated to the left ordering property, is important for the analysis of the O-Conditionality. We show that the use of overlap functions to implement de generalized Modus Ponens, as the scheme enabled by the law of O-Conditionality, provides more generality than the laws of T-conditionality and U-conditionality, for t-norms T and uninorms U, respectively.
Open Access
Weak and directional monotonicity of functions on Riesz spaces to fuse uncertain data
(Elsevier B.V., 2019) Sesma Sara, Mikel; Mesiar, Radko; Bustince Sola, Humberto; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC; Estadística, Informática y Matemáticas; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa
In the theory of aggregation, there is a trend towards the relaxation of the axiom of monotonicity and also towards the extension of the definition to other domains besides real numbers. In this work, we join both approaches by defining the concept of directional monotonicity for functions that take values in Riesz spaces. Additionally, we adapt this notion in order to work in certain convex sublattices of a Riesz space, which makes it possible to define the concept of directional monotonicity for functions whose purpose is to fuse uncertain data coming from type-2 fuzzy sets, fuzzy multisets, n-dimensional fuzzy sets, Atanassov intuitionistic fuzzy sets and interval-valued fuzzy sets, among others. Focusing on the latter, we characterize directional monotonicity of interval-valued representable functions in terms of standard directional monotonicity.
Open Access
Some properties and construction methods for ordered directionally monotone functions
(IEEE, 2017-08-24) Sesma Sara, Mikel; Marco Detchart, Cedric; Bustince Sola, Humberto; Barrenechea Tartas, Edurne; Lafuente López, Julio; Kolesárová, Anna; Mesiar, Radko; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC
In this work we propose a new generalization of the notion of monotonicity, the so-called ordered directionally monotonicity. With this new notion, the direction of increasingness or decreasingness at a given point depends on that specific point, so that it is not the same for every value on the domain of the considered function.
Open Access
Enhancing DreamBooth with LoRA for generating unlimited characters with stable diffusion
(IEEE, 2024-09-09) Pascual Casas, Rubén; Maiza Coupin, Adrián Mikel; Sesma Sara, Mikel; Paternain Dallo, Daniel; Galar Idoate, Mikel; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa, PJUPNA2023-11377
This paper addresses the challenge of generating unlimited new and distinct characters that encompass the style and shared visual characteristics of a limited set of human designed characters. This is a relevant problem in the audiovisual industry, as the ability to rapidly produce original characters that adhere to specific characteristics greatly increases the possibilities in the production of movies, series, or video games. Our solution is built upon DreamBooth, a widely extended fine-tuning method for text-to-image models. We propose an adaptation focusing on two main challenges: the impracticality of relying on detailed image prompts for character description and the few-shot learning scenario with a limited set of characters available for training. To solve these issues, we introduce additional character-specific tokens to DreamBooth training and remove its class-specific regularization dataset. For an unlimited generation of characters, we propose the usage of random tokens and random embeddings. This proposal is tested on two specialized datasets and the results shows our method¿s capability to produce diverse characters that adhere to a style and visual characteristics. An ablation study to analyze the contributions of the proposed modifications is also developed.
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, PJUPNA13
In 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.
Open Access
Reemplazo de la función de pooling de redes neuronales convolucionales por combinaciones lineales de funciones crecientes
(Universidad de Málaga, 2021) Rodríguez Martínez, Iosu; Lafuente López, Julio; Sesma Sara, Mikel; Herrera, Francisco; Ursúa Medrano, Pablo; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
Las redes convolucionales llevan a cabo un proceso automatico de extracción y fusión de características mediante el cual obtienen la información más relevante de una imagen dada. El proceso de submuestreo mediante el cual se fusionan características localmente próximas, conocido como ‘pooling’, se lleva a cabo tradicionalmente con funciones sencillas como el máximo o la media aritmética, ignorando otras opciones muy populares en el campo de la teoría de agregaciones. En este trabajo proponemos reemplazar dichas funciones por otra serie de ordenes estadísticos, así como por la integral de Sugeno y una nueva generalización de la misma. Además, basándonos en trabajos que emplean la combinación convexa del máximo y la media, presentamos una nueva capa que permite combinar varias de las nuevas agregaciones, mejorando sus resultados individuales.
Open Access
Strengthened ordered directionally monotone functions. Links between the different notions of monotonicity
(Elsevier, 2019) Sesma Sara, Mikel; Lafuente López, Julio; Roldán López de Hierro, Antonio Francisco; Mesiar, Radko; Bustince Sola, Humberto; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC; Estadística, Informática y Matemáticas
In this work, we propose a new notion of monotonicity: strengthened ordered directional monotonicity. This generalization of monotonicity is based on directional monotonicity and ordered directional monotonicity, two recent weaker forms of monotonicity. We discuss the relation between those different notions of monotonicity from a theoretical point of view. Additionally, along with the introduction of two families of functions and a study of their connection to the considered monotonicity notions, we define an operation between functions that generalizes the Choquet integral and the Lukasiewicz implication.
Open Access
F-homogeneous functions and a generalization of directional monotonicity
(Wiley, 2022) Santiago, Regivan; Sesma Sara, Mikel; Fernández Fernández, Francisco Javier; Takáč, Zdenko; Mesiar, Radko; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
A function that takes (Formula presented.) numbers as input and outputs one number is said to be homogeneous whenever the result of multiplying each input by a certain factor (Formula presented.) yields the original output multiplied by that same factor. This concept has been extended by the notion of abstract homogeneity, which generalizes the product in the expression of homogeneity by a general function (Formula presented.) and the effect of the factor (Formula presented.) by an automorphism. However, the effect of parameter (Formula presented.) remains unchanged for all the input values. In this study, we generalize further the condition of abstract homogeneity by introducing (Formula presented.) -homogeneity, which is defined with respect to a family of functions, enabling a different behavior for each of the inputs. Next, we study the properties that are satisfied by this family of functions and, moreover, we link this concept with the condition of directional monotonicity, which is a trendy property in the framework of aggregation functions. To achieve that, we generalize directional monotonicity by (Formula presented.) directional monotonicity, which is defined with respect to a family of functions (Formula presented.) and a family of vectors (Formula presented.). Finally, we show how the introduced concepts could be applied in two different problems of computer vision: a snow detection problem and image thresholding improvement. © 2022 The Authors. International Journal of Intelligent Systems published by Wiley Periodicals LLC.