ABSTRACT Understanding financial behaviour, particularly in the stock market, has attracted significant interest in recent years due to advancements in artificial intelligence and its impact on the global economy. The field of stock market prediction, which explores the interaction between finance and computer science to create predictive models, aims to forecast the behaviour of various securities in the financial market. One of the most well‐known and widely used techniques is Deep Learning, which employs different deep neural network structures for learning nonlinear models. In this study, we used open data from some of the largest companies in Brazil—Petrobras (PETR4), Itaúsa (ITSA4), and Vale (VALE3)—provided by BovDB, a historical dataset containing the stock prices of all companies listed on the Brazilian stock exchange (B3) from 2000 to 2020. As part of the preprocessing, a price correction factor was applied to neutralise the effects of market events on stock behaviour, enabling the recurrent neural network (RNN) model to process this information better. The results showed that using this correction factor significantly improves predictions, reducing abrupt behaviours in stock prices and decreasing the model's prediction error. For instance, the prediction error in VALE3 stock was reduced by < 10% compared with uncorrected data. These findings highlight the potential of using an event correction factor in stock data processed by an RNN, facilitating its training and providing more reliable forecasts.

Managing big data traffic plays an important role in contemporary communication and is essential for efficiently handling an unprecedented volume of information. In the globalized context of the internet, the ability to measure and predict this traffic is a strategically valuable resource that requires a deep understanding of historical data. This article proposes a predictor based on a generalization of the Choquet integral, which aggregates data, reducing the complexity and dimensionality of traffic predictions. The approach is assessed using real data, demonstrating that the Choquet integral achieves higher accuracy with the appropriate$\alpha$parameter. Considering the worst-case scenario in terms of wasted time, and given that the overall algorithm achieved a satisfactory error rate, we can conclude that the least efficient algorithm was the brute force search. In comparison, binary search and random binary search demonstrated a time efficiency improvement of 56.75 % and 59.49 %, respectively. Among the integrals evaluated, the Choquet (a) integral yielded the smallest errors.

Abstract In this work, we explore the impact of adaptive fuzzy measures on edge detection, aiming to enhance how computers interpret images by identifying edges more accurately. Traditional methods rely on analysing changes in image brightness to locate edges, but they often use fixed rules that do not account for the unique characteristics of each image. Our approach differs by adjusting fuzzy measures based on the information within specific areas of an image under a sliding window approach, utilizing a variety of fusion functions and generalizations of the Choquet integral to analyse and combine pixel data. The proposed method is flexible, allowing for the adaptation of measures in response to the image's local features. We put our method to the test against the well‐established Canny edge detector to evaluate its effectiveness. Our experimental results suggest that by adapting fuzzy measures for each image section, we can improve edge detection results.

In data stream (DS) learning, the system has to extract knowledge from data generated continuously, usually at high speed and in large volumes, making it impossible to store the entire set of data to be processed in batch mode. Hence, machine learning models must be built incrementally by processing the incoming examples, as data arrive, while updating the model to be compatible with the current data. In fuzzy DS clustering, the model can either absorb incoming data into existing clusters or initiate a new cluster. As the volume of data increases, there is a possibility that the clusters will overlap to the point where it is convenient to merge two or more clusters into one. Then, a cluster comparison measure (CM) should be applied, to decide whether such clusters should be combined, also in an incremental manner. This defines an incremental fusion process based on aggregation functions that can aggregate the incoming inputs without storing all the previous inputs. The objective of this article is to solve the fuzzy DS clustering problem of incrementally comparing fuzzy clusters on a formal basis. First, we formalize and operationalize incremental fusion processes of fuzzy clusters by introducing recursively extendable (RE) aggregation functions, studying construction methods and different classes of such functions. Second, we propose two approaches to compare clusters: 1) similarity and 2) overlapping between clusters, based on RE aggregation functions. Finally, we analyze the effect of those incremental CMs on the online and offline phases of the well-known fuzzy clustering algorithm d-FuzzStream, showing that our new approach outperforms the original algorithm and presents better or comparable performance to other state-of-the-art DS clustering algorithms found in the literature.

This work introduces an innovative approach from modeling to simulations, integrating quantum fuzzy interpretations, focusing on the expression of membership degrees in quantum circuits, interpreted as a unitary quantum transformation. Our research contrasts Quantum Fuzzy Computing with Classical Computing, particularly in the context of the prisoner's dilemma and parent-child relationships. Through the Qiskit framework, we conduct simulations, demonstrating the differences in results obtained by both approaches. Well-known fuzzy connectives, such as “exclusive or” and “arithmetic means”, provide an algebraic description for the corresponding composition of quantum operators and circuit representations. Thus, such algorithms can easily extend to model multiple agents' relationships, described by multidimensional quantum registers. The Qiskit simulations provide the structure for the algorithms' computation on the actual quantum platforms, indicating a promising direction for future research in this hybrid research area.

This study introduces an innovative quantum fuzzy approach for modeling and simulating complex decision-making processes, utilizing quantum circuits to express membership degrees as unitary transformations. We contrast Quantum Fuzzy Computing with Classical Computing, highlighting advancements in modeling the prisoner's dilemma. Using the Qiskit framework, we demonstrate how quantum fuzzy algorithms featuring connectives such as ‘exclusive or’ and ‘arithmetic mean’ enable detailed modeling of multi-agent relationships via multidimensional quantum registers, showcasing potential advancements in this hybrid research area.

This study is given at the intersection of three important areas: Modal Logic (ML), Fuzzy Logic (FL), and Quantum Computing (QC), leveraging from their main features. On the one hand, we have the QC ability to handle complex data more efficiently, taking advantage of the quantum mechanics concepts. On the other hand, ML and FL allow us to express uncertainties by mathematically modeling the imprecision of the natural language. Therefore, we first provide an algebraic model to interpret modal operators on fuzzy logic, and then we represent them in a quantum computing environment. Besides, we present some case studies simulating the fuzzy modal connectives in the Qiskit platform, aiming to better understand the evolution of quantum circuits.

The Choquet integral (CI) is an averaging aggregation function that has been used, e.g., in the fuzzy reasoning method (FRM) of fuzzy rule-based classification systems (FRBCSs) and in multicriteria decision making in order to take into account the interactions among data/criteria. Several generalizations of the CI have been proposed in the literature in order to improve the performance of FRBCSs and also to provide more flexibility in the different models by relaxing both the monotonicity requirement and averaging conditions of aggregation functions. An important generalization is the$C_{F}$-integrals, which are preaggregation functions that may present interesting nonaveraging behavior depending on the function$F$adopted in the construction and, in this case, offering competitive results in classification. Recently, the concept of d-Choquet integrals was introduced as a generalization of the CI by restricted dissimilarity functions (RDFs), improving the usability of CIs, as when comparing inputs by the usual difference may not be viable. The objective of this article is to introduce the concept of$dC_{F}$-integrals, which is a generalization of$C_{F}$-integrals by RDFs. The aim is to analyze whether the usage of$dC_{F}$-integrals in the FRM of FRBCSs represents a good alternative toward the standard$C_{F}$-integrals that just consider the difference as a dissimilarity measure. For that, we consider six RDFs combined with five fuzzy measures, applied with more than 20 functions$F$. The analysis of the results is based on statistical tests, demonstrating their efficiency. Additionally, comparing the applicability of$dC_{F}$-integrals versus$C_{F}$-integrals, the range of the good generalizations of the former is much larger than that of the latter.

Several generalizations of the Choquet integral have been applied in the Fuzzy Reasoning Method (FRM) of Fuzzy Rule-Based Classification Systems (FRBCS’s) to improve its performance. Additionally, to achieve that goal, researchers have searched for new ways to provide more flexibility to those generalizations, by restricting the requirements of the functions being used in their constructions and relaxing the monotonicity of the integral. This is the case of CT-integrals, CC-integrals, CF-integrals, CF1F2-integrals and dCF-integrals, which obtained good performance in classification algorithms, more specifically, in the fuzzy association rule-based classification method for high-dimensional problems (FARC-HD). Thereafter, with the introduction of Choquet integrals based on restricted dissimilarity functions (RDFs) in place of the standard difference, a new generalization was made possible: the d-XChoquet (d-XC) integrals, which are ordered directional increasing functions and, depending on the adopted RDF, may also be a pre-aggregation function. Those integrals were applied in multi-criteria decision making problems and also in a motor-imagery brain computer interface framework. In the present paper, we introduce a new FRM based on the d-XC integral family, analyzing its performance by applying it to 33 different datasets from the literature.

Restricted dissimilarity functions (RDFs) were introduced to overcome problems resulting from the adoption of the standard difference. Based on those RDFs, Bustinceet al.introduced a generalization of the Choquet integral (CI), called d-Choquet integral, where the authors replaced standard differences with RDFs, providing interesting theoretical results. Motivated by such worthy properties, joint with the excellent performance in applications of other generalizations of the CI (using its expanded form, mainly), this article introduces a generalization of the expanded form of the standard Choquet integral (X-CI) based on RDFs, which we named d-XC integrals. We present not only relevant theoretical results but also two examples of applications. We apply d-XC integrals in two problems in decision making, namely a supplier selection problem (which is a multicriteria decision-making problem) and a classification problem in signal processing, based on motor-imagery brain-computer interface (MI-BCI). We found that two d-XC integrals provided better results when compared to the original CI in the supplier selection problem. Besides that, one of the d-XC integrals performed better than any previous MI-BCI results obtained with this framework in the considered signal processing problem.

This work aims to evaluate explainable classification methods for the detection of fish species from hydroacoustic data acquired by echo sounders at a region near the coastline of south and southeastern Brazil. Decision trees and fuzzy rule-based methods were adopted. The fitted models were evaluated by quality measures based on the performance of the classifiers and also by an expert which analyzed the usefulness of the rules on describing the schools. The models learned by the algorithms performed well for the available data and were able to represent the documented behavior of the species considered in the studied region, according to the literature.

It 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.

In Multi-Criteria Decision Making, one of the most used algorithm designed to deal with decision making is the Technical Order by Preference to Ideal Solution (TOPSIS), which is based on finding a solution that is close to the best possible solution and distant from the worst possible solution. The Group Modular Choquet Random TOPSIS (GMC-RTOPSIS) is a generalization of the TOPSIS method capable of dealing with multiple and heterogeneous data types and interaction among criteria by means of the discrete Choquet integral. On the other hand, CT-integrals are a generalization of the Choquet integral using t-norms, which are more flexible than the standard Choquet integral. CT-integrals are pre-aggregation functions, which means that we do not require them to be monotonic in the whole domain, just in some specific directions, that is, they are directionally monotonic. Due to the excellent performance of CT-integrals in classification and multimodal fuzzy fusion decision problems, the objective of this paper is to generalize the GMC-RTOPSIS by using CT-integrals and to analyze the results provided by the use of five different t-norms in an example of a decision making problem.

Fuzzy Rule Based Classification Systems are an useful tool to deal with classification problems. In these systems, one fundamental point is the manner of how the available information about the problem is aggregated. The mechanism responsible to perform the aggregation is the Fuzzy Reasoning Method (FRM). Recently, some FRMs using generalizations of the Choquet integral to perform the aggregation were proposed in the literature. Since these generalizations are defined considering a specific fuzzy measure, in this paper we apply different fuzzy measures in the generalizations that presented the best performance in each study in the literature. We analyze how the performance is affected according to each fuzzy measure.

A key component of fuzzy rule-based classification systems (FRBCS) is the fuzzy reasoning method (FRM) since it infers the class predicted for new examples. A crucial stage in any FRM is the way in which the information given by the fired rules during the inference process is aggregated. A widely used FRM is the winning rule, which applies the maximum to accomplish this aggregation. The maximum is an averaging operator, which means that its result is within the range delimited by the minimum and the maximum of the aggregated values. Recently, new averaging operators based on generalizations of the Choquet integral have been proposed to perform this aggregation process. However, the most accurate FRBCSs use the FRM known as additive combination that considers the normalized sum as the aggregation operator, which is nonaveraging. For this reason, this paper is aimed at introducing a new nonaveraging operator named CF1F2-integral, which is a generalization of the Choquet-like Copula-based integral (CC-integral). CF1F2-integrals present the desired properties of an aggregation-like operator since they satisfy appropriate boundary conditions and have some kind of increasingness property. We show that CF1F2-integrals, when used to cope with classification problems, enhance the results of the previous averaging generalizations of the Choquet integral and provide competitive results (even better) when compared with state-of-the-art FRBCSs.

Douro region, in Portugal, is worldwide famous for its Port wine, having a huge economic importance in the region. Among the enological parameters that define the grape maturity, the sugar level is considered one of the most relevant ones. Then, in this study we intend to classify their sugar level based on reflectance measurements obtained by hyperspectral images from grapes collected in this region. Recently, to cope with classification problems, we have applied some generalizations of the Choquet integral in the fuzzy reasoning method of a fuzzy rule-based classification system. These generalizations produced different aggregation and/or pre-aggregation functions, presenting good results. For this reason, in this study, we have compared the performance of different generalizations among themselves and versus classical classifiers found in the specialized literature.

The aim of this paper is to introduce the concept of pre-t-conorms, based on the notion of pre-aggregation function, which was introduced by Lucca et al. as an “aggregation” concept that it is not monotonic in all its domain. We also study the concept of light pre-t-conorms, which are non necessarily associative commutative functions with neutral element e = 0. We present some properties of (light) pre-t-conorms and the classes of (light) pre-t-conorms, showing interesting examples. Finally, we present an application of pre-conorms and pre-negations for defining directional fuzzy implication functions. We notice that the introduction of pre-t-conorms allows applications where the full monotonicity is not required (as in classification problems) and the light pre-t-conorms can be used in applications that do not require the associativity property (as in image processing and decision making).

In a recent paper, it was introduced the concept of Choquet-like Copula-based integral (CC-integral for short). This kind of function extends the standard Choquet integral and generalizes it by copula functions. These functions were applied in the Fuzzy Reasoning Method (FRM) of a Fuzzy Rule-Based Classification System (FRBCS), presenting an example where the CC-integral based on the minimum t-norm had different behaviors according to the values being aggregated. Therefore, the resulting FRM is theoretically more flexible than those associated with classical aggregation functions like the maximum. In this work, we present a methodology to study the flexibility of the aggregation function used in the FRM. Specifically, we conduct an analysis of 3 different methods to aggregate values in the FRM, namely, the CC-integral based on the minimum t-norm, the standard Choquet integral and the maximum (classical FRM of the winning rule - WR). We prove that the CC-integral behaves in different ways according to the values to be aggregated, whereas the Choquet integral offers an averaging behavior and the WR presents an strict behavior, since it considers only the rule having the maximum compatibility with the example.

In this work we introduce the definition of pre-aggregation functions. These functions generalize aggregation functions, in the sense that they fulfill the same boundary conditions as the latter, but only directional monotonicity is demanded to them. We discuss a construction method which is inspired from the way the discrete Choquet integral is built and it replaces the product by other appropriate functions. Finally, we propose to apply them in fuzzy rule-based classification systems.

In this paper, we introduce the notion of preaggregation function. Such a function satisfies the same boundary conditions as an aggregation function, but, instead of requiring monotonicity, only monotonicity along some fixed direction (directional monotonicity) is required. We present some examples of such functions. We propose three different methods to build preaggregation functions. We experimentally show that in fuzzy rule-based classification systems, when we use one of these methods, namely, the one based on the use of the Choquet integral replacing the product by other aggregation functions, if we consider the minimum or the Hamacher product t-norms for such construction, we improve the results obtained when applying the fuzzy reasoning methods obtained using two classical averaging operators such as the maximum and the Choquet integral.

In this paper, we introduce a family of Choquet-based non-associative aggregation functions for application in the fuzzy reasoning method proposed by Barrenechea et al. for fuzzy rule-based classification systems. The family is constructed manipulating the standard definition of Choquet Integral and substituting the product operator by the general definition of the family of overlap functions Cα(x; y) = xy(1 + α(1 - x)(1 - y)), for α ∈ [-1; 0[∪]0; 1], resulting in non-associative aggregation functions. A comparative study considering different values for α and the power measure (whose exponent is learned genetically to adapt it to each class) is presented. The approach is tested in seventeen numerical dataset selected from the KEEL dataset repository. We compare the obtained results with the work presented by Barrenechea et al., showing that the proposed approach can offer also good performance, so providing more flexibility to that proposal, enlarging its scope of applications.