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.

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 article, we study the measurement of these biases by reviewing the existing metrics, including those that can be borrowed from other disciplines. We develop a taxonomy for the classification of these metrics, providing a practical guide for the selection of appropriate metrics. To illustrate the utility of our framework, and to further understand the practical characteristics of the metrics, we conduct a case study of 20 datasets used in Facial Emotion Recognition (FER), analyzing the biases present in them. Our experimental results show that many metrics are redundant and that a reduced subset of metrics may be sufficient to measure the amount of demographic bias. The article provides valuable insights for researchers in AI and related fields to mitigate dataset bias and improve the fairness and accuracy of AI models.

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 classifiers has shown its advantage. The learning of the fuzzy measure can be done either in a supervised or unsupervised manner. This paper focuses on supervised approaches. Existing supervised approaches are designed to minimize the mean squared error cost function, even for classification problems. We propose a new fuzzy measure learning algorithm for combining classifiers that can optimize any cost function. To do so, advancements from deep learning frameworks are considered such as automatic gradient computation. Therefore, a gradient-based method is presented together with three new update policies that are required to preserve the monotonicity constraints of the fuzzy measures. The usefulness of the proposal and the optimization of cross-entropy cost are shown in an extensive experimental study with 58 datasets corresponding to both binary and multi-class classification problems. In this framework, the proposed method is compared with other state-of-the-art methods for fuzzy measure learning.

This study 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 propose three weights allocation methods that are specifically designed for the proposed GnIOWA operators. For each of the proposed weights allocation methods, a numerical example is also attached accordingly. With the use of convex/concave Regular Increasing Monotone quantifiers, we further discuss some mathematical properties of these weights allocation methods.

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 choice of aggregation function is sometimes restricted to a desired value of orness (orness-directed aggregation). In 1988, Yager presented a particular example of orness measure for ordered weighted averaging (OWA) functions and initiated a series of contributions aiming at proposing an axiomatic definition of orness measure for OWA functions. In this paper, we go much further and present an axiomatic definition of orness measure for the whole family of aggregation functions. We end by proposing two natural construction methods for an orness measure for aggregation functions. The particular examples of the (discrete) Choquet integral and uninorms are studied in detail.

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 explores and proposes four novel preference involved aggregation techniques by using RIM quantifiers and OWA operators. The first two models are both with two steps to carry out the aggregation processes, with one using two times of OWA operators and another considering evaluation matrix as a vector lattice. The last two models come from a whole perspective to direct the aggregation processes, with one arising from a global magnitude view and another based on staggered ordering using two specially defined collections of permutations. Illustrative examples and remarks are also spotted immediately following the proposed models or at suitable positions.

In the last years we have seen huge advancements in the area of Machine Learning, specially with the use of Deep Neural Networks. One of the most relevant examples is in image classification, where convolutional neural networks have shown to be a vital tool, hard to replace with any other techniques. Although aggregation functions, such as OWA operators, have been previously used on top of neural networks, usually to aggregate the outputs of different networks or systems (ensembles), in this paper we propose and explore a new way of using OWA aggregations in deep learning. We implement OWA aggregations as a new layer inside a convolutional neural network. These layers are used to learn additional order-based information from the feature maps of a certain layer, and then the newly generated information is used as a complement input for the following layers. We carry out several tests introducing the new layer in a VGG13-based reference network and show that this layer introduces new knowledge into the network without substantially increasing training times.

The design of an ensemble of classifiers involves the definition of an aggregation mechanism that produces a single response obtained from the information provided by the classifiers. A specific aggregation methodology that has been studied in the literature is the use of fuzzy integrals, such as the Choquet or the Sugeno integral, where the associated fuzzy measure tries to represent the interaction existing between the classifiers of the ensemble. However, defining the big number of coefficients of a fuzzy measure is not a trivial task and therefore, many different algorithms have been proposed. These can be split into supervised and unsupervised, each class having different learning mechanisms and particularities. Since there is no clear knowledge about the correct method to be used, in this work we propose an experimental study for comparing the performance of eight different learning algorithms under the same framework of imbalanced dataset. Moreover, we also compare the specific fuzzy integral (Choquet or Sugeno) and their synergies with the different fuzzy measure construction methods.

In this work we propose a new OWA operator defined on bounded convex posets of a vector-lattice. In order to overcome the non-existence of a total order, which is necessary to obtain a non-decreasing arrangement of the input data, we use the concept of admissible permutation. Based on it, our proposal calculates the different ways in which the input vector could be arranged, always respecting the partial order. For each admissible arrangement, we calculate an intermediate value which is finally collected and averaged by means of the arithmetic mean. We analyze several properties of this operator and we give some counterexamples of those properties of aggregation functions which are not satisfied.

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 recent evolutionary changes in OWA operators, we propose formulation paradigms for induced OWA aggregation and a related weight function with self-contained properties that make it possible to model such complex preference-involved evaluation problems in a systematic way. The new formulations have some recursive forms that provide more ways to apply OWA aggregation and deserve further study from a mathematical perspective. In addition, the new proposal generalizes almost all of the well-known extensions to the original OWA operators. We provide an example showing the representative use of such paradigms in decision-making and evaluation problems.

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, 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.

In this work we study the possibility of learning fuzzy measures from classifiers' performance for improving the standard aggregation methods in classifier ensembles. Fuzzy measures are set-valued functions, which are not necessarily additive, and they are the basis for constructing non-linear fuzzy integrals, such as Choquet or Sugeno integral. These integrals have shown to be very useful in the aggregation of interacting criteria, since this interaction can be well modeled by a fuzzy measure. Classifier ensembles are composed of several classifiers and are aimed at improving the performance of every one of their counterparts. There are two main aspects about ensembles, first, how to build them, and second, how to combine the outputs of all their members. In this work, we focus on the second part, which is a key factor to obtain a successful ensemble. More specifically, we focus on the usage of fuzzy measures for the aggregation phase aiming at taking into account the coalitions and interactions among the members of the ensemble. Our hypothesis is that taking such information into account can lead to better performance. Moreover, we propose to directly obtain the fuzzy measure from data by considering the performance of each subset of classifiers in the ensemble. This way, one needs not include any additional learning for the fuzzy measure that can easily lead to overfitting. In order to test the usefulness of the proposed fuzzy measure, we will consider a set of 33 highly imbalanced datasets and we will develop a complete experimental study comparing the proposed combination scheme with other approaches commonly considered in the literature.

In this paper, 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 theoretical study of internal fusion functions and, furthermore, we propose three different construction methods, which are based on 1) an arbitrary fusion function and a partition of the domain; 2) a linear order; and 3) a minimization mechanism using penalty functions. Finally, we illustrate this paper with the application of internal fusion functions in two image processing algorithms where a set of images must be fused, namely multifocus image and denoised image fusion, as well as in an example of multiclass problem, where we fuse a set of score matrices obtained by several classification algorithms.

In this work we investigate a new family of fusion functions called internal fusion functions. The main characteristic of these functions is the fact that the output always corresponds to some of the given inputs. We propose a construction method and we study whether internal functions constructed in this way also satisfy properties of aggregation functions Finally, we apply internal functions in an example of a multi-class problem, where a set of matrices must be combine into a single representative collective matrix in order to obtain better classification rates.

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 these characterizations when OWA operators are defined on a complete lattice. In addition, the set of all n-ary OWA operators is studied as a sublattice of the lattice of all the n-ary aggregation functions defined on a distributive lattice.

n-dimensional fuzzy sets are an extension of fuzzy sets where the membership values are n-truples of real numbers in the unit interval [0, 1] ordered in increasing order, called n-dimensional intervals. The set of n-dimensional intervals is denoted by Ln([0, 1]). This paper aims to investigate the class of functions on Ln([0, 1]) which are continuous and strictly decreasing, called n-dimensional strict fuzzy negations. In particular, investigate the class of representable n-dimensional strict fuzzy negations, i.e., n-dimensional strict fuzzy negation which are determined by strict fuzzy negation. The main properties of strict fuzzy negations on [0, 1] are preserved by representable strict fuzzy negations on Ln([0, 1]). In addition, the conjugate obtained by action of an n-dimensional automorphism on an n-dimensional strict fuzzy negation provides a method to obtain other n-dimensional strict fuzzy negations, in which the properties of the original one are preserved, as well as the Fodor's characterization theorem.

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 single membership value; since for hesitant sets, membership values are given by a whole set of values. On the other hand, since fuzzy negations have an important role in applications as well as in the theoretical approach to of fuzzy logics, it is important to study an extension of the concept of fuzzy negation for hesitant fuzzy degrees (elements). In this paper, we propose such a definition and we study some of the main properties of this new concept.

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 functions applied to the problem of image segmentation.

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 arithmetic mean and the median can be obtained by minimizing specific penalty functions. Moreover, we study other penalty functions and we show that, in general, aggregation functions on product lattices do not coincide with the cartesian product of the corresponding aggregation functions. Finally, we make an experimental study where we test our reduction algorithm and we analyze the stability of the penalty functions in images affected by noise.

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 discuss which of them coincide with the Cartesian product of the standard mean and the median. We apply these functions in image processing. We present three algorithms for color image reduction based on minimizing penalty functions on discrete product lattices.

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 of robust estimators of location, and then introduce a new estimator based on penalty minimisation.

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. We proof that global segmentation performs better results than local segmentation and improves the results obtained by other thresholding algorithm.

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 analyze these results over natural images and noisy images.

In this work an ignorance-based fuzzy clustering algorithm is presented. The algorithm is based on the entropy-based clustering algorithm proposed by Yao et al.. In our proposal, we calculate the total ignorance instead of using the entropy at each data point to select the data point as the first cluster center. The experimental results show that the ignorance-based clustering improves the data classification made by the EFC in image segmentation.