Imbalanced classification problems pose a significant challenge in machine learning, especially when the minority class contains critical information. In this context, Fuzzy Rule-Based Classification Systems (FRBCSs) have been widely used due to their interpretability and flexibility, but typically rely on sampling techniques to address class imbalance. FARCI, a fuzzy association rule-based classifier, is specifically designed for imbalanced datasets by introducing tailored modifications to the FARC-HD fuzzy classifier, improving performance without relying on data preprocessing. However, FARCI uses fixed membership function supports, which may limit its effectiveness in small disjuncts, and the application of the additive combination may introduce bias during inference. In this paper, we propose FARCI+, an enhanced version of FARCI that addresses these limitations through two key contributions: (1) it tunes the support of the membership functions using the 3-tuples fuzzy linguistic model to better represent minority class subregions, and (2) it incorporates generalizations of the Choquet integral in the inference stage to achieve more robust aggregation in imbalanced contexts. The effectiveness of FARCI+ is assessed through extensive experimentation on 66 binary imbalanced datasets from the KEEL repository. The results demonstrate that the combination of both components in FARCI+ significantly improves classification performance, particularly for datasets with high imbalance ratios, without affecting performance in moderately imbalanced datasets.

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.

Interval-valued fuzzy sets are a generalization of classical fuzzy sets where the membership values are intervals. The epistemic interpretation of interval-valued fuzzy sets assumes that there is one real-valued membership degree of an element within the membership interval of possible membership degrees. Considering this epistemic interpretation, we propose a new measure, called IV-embedding, to compare the precision of two interval-valued fuzzy sets. An axiomatic definition for this concept as well as a construction method are provided. The construction method is based on aggregation operators and the concept of interval embedding, which is also introduced and deeply studied.

The notion of directional monotonicity emerged as a relaxation of the monotonicity condition of aggregation functions. As the extension of aggregation functions to fuse more complex information than numeric data, directional monotonicity was extended to the framework of multidimensional data, with respect to the product order, which is a partial order. In this work, we present the notion of admissible order for multidimensional data and we define the concept of directional monotonicity for multidimensional fusion functions with respect to an admissible order. Moreover, we study the main properties of directionally monotone functions in this new context. We conclude that, while some of the properties are still valid (e.g. the set of directions of increasingness is still closed under convex combinations), some of the main ones no longer hold (e.g. there does not exist a finite set of directions that characterize standard monotonicity in terms of directional monotonicity).

A function that takes n numbers as input and outputs one number is said to be homogeneous whenever the result of multiplying each input by a certain factor λ 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 g and the effect of the factor λ by an automorphism.However, the effect of parameter λ remains unchanged for all the input values.In this study, we generalize further the condition of abstract homogeneity by introducing ℱ-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 ℱ directional monotonicity, which is defined with respect to a family of functions ℱ and a family of vectors  .Finally, we show how the introduced concepts could be applied

A new concept of equivalence between intervals and the induced indistinguishability between interval-valued (IV) fuzzy sets are proposed and considered. A new notion of the degree of IV equivalence is presented where partial or linear orders and the width of intervals are involved reflecting uncertainty. Furthermore, construction methods of the considered equivalences are provided and the relation between them and other notions of IV equivalences are studied. Finally, a methodology to apply the proposed equivalences in the field of image processing is shown, along with an illustrative example.

Imbalanced classification problems are attracting the attention of the research community because they are prevalent in real-world problems and they impose extra difficulties for learning methods. Fuzzy rule-based classification systems have been applied to cope with these problems, mostly together with sampling techniques. In this paper, we define a new fuzzy association rule-based classifier, named FARCI, to tackle directly imbalanced classification problems. Our new proposal belongs to the algorithm modification category, since it is constructed on the basis of the state-of-the-art fuzzy classifier FARC–HD. Specifically, we modify its three learning stages, aiming at boosting the number of fuzzy rules of the minority class as well as simplifying them and, for the sake of handling unequal fuzzy rule lengths, we also change the matching degree computation, which is a key step of the inference process and it is also involved in the learning process. In the experimental study, we analyze the effectiveness of each one of the new components in terms of performance, F-score, and rule base size. Moreover, we also show the superiority of the new method when compared versus FARC–HD alongside sampling techniques, another algorithm modification approach, two cost-sensitive methods and an ensemble.

Two of the main research lines in the theory of aggregation functions is the extension to more general domains and the relaxation of the monotonicity conditions. In this work, we discuss the state-of-the-art of the main introduced relaxed forms of monotonicity that can be found in the literature, i.e., weak, directional, ordered directional and strengthened ordered directional monotonicity. We pay special attention to the extension of a relaxed form of monotonicity to the interval-valued setting and we propose the concepts of ordered and strengthened ordered directional monotonicity for this general setting. Moreover, we study the main properties of the functions that satisfy the introduced properties and present some construction methods.

Pre-aggregation functions have extended the framework of valid functions to fuse data with respect to aggregation functions, in the sense that the monotonicity requirements are relaxed. Moreover, this class of functions has proven to be useful in classification problems. In this work we present the concept of directional monotonicity for interval-valued functions and use it to define the concept of interval-valued pre-aggregation functions. Additionally, we present some relevant properties of directionally monotone interval-valued functions and a method to construct interval-valued pre-aggregation functions from standard pre-aggregation functions.

In this work we present a neighbourhood-based image comparison algorithm that makes use of the class of matrix resemblance functions. Based on the concepts of restricted equivalence functions and inclusion grade in the terms of Sinha and Dougherty, we discuss two construction methods for matrix equivalence functions. Moreover, we study the conditions under which this class of functions satisfy a set of properties that are favourable for image comparison operators. We conclude this work with an instance of a potential application for this proposal in video motion detection.

In this paper, we introduce the notion of ordered directionally monotone function as a type of function which allows monotonicity along different directions in different points. In particular, these functions take into account the ordinal size of the coordinates of the inputs in order to fuse them. We show several examples of these functions and we study their properties. Finally, we present an illustrative example of an application which justifies the introduction and the study of the concept of ordered directional monotonicity.

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.

In this paper we study the relation between L-fuzzy morphology and L-fuzzy concepts over complete lattices. In particular, we show how the erosion and dilation operators of the former can be understood in terms of the derivation operators of the latter, even when the set of objects is different from the set of attributes.

The final goal of this study is to adapt the concept of fuzzy entropy of De Luca and Termini to deal with type-2 fuzzy sets. We denote this concept type-2 fuzzy entropy set. However, the construction of the notion of entropy measure on an infinite set, such us [0,1], is not effortless. For this reason, we first introduce the concept of quasi-entropy of a fuzzy set on the universe [0,1]. Furthermore, whenever the membership function of the considered fuzzy set in the universe [0,1] is continuous, we prove that the quasi-entropy of that set is a fuzzy entropy in the sense of De Luca and Termini. Finally, we present an illustrative example, where we use type-2 fuzzy entropy sets instead of fuzzy entropies in a classical fuzzy algorithm.