Restricted dissimilarity functions (RDFs) were introduced to overcome problems resulting from the adoption of the standard difference. Based on those RDFs, Bustince et 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 paper 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 multi-criteria 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.

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 (FRBCS’s) and in multi-criteria 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 FRBCS’s, 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 are the $C_{F}$-integrals, which are pre-aggregation functions that may present interesting non-averaging 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 paper 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 FRBCS’s represents a good alternative towards 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 twenty functions $F$. The analysis of the results are 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.

Suicide is a severe health problem, with high rates in individuals with addiction. Considering the lack of studies exploring suicide predictors in this population, we aimed to investigate factors associated with attempted suicide in inpatients diagnosed with cocaine use disorder using two analytical approaches. This is a cross-sectional study using a secondary database with 247 men and 442 women hospitalized for cocaine use disorder. Clinical assessment included the Addiction Severity Index, the Childhood Trauma Questionnaire, and the Structured Clinical Interview for the Diagnostic and Statistical Manual of Mental Disorders, totalling 58 variables. Descriptive Poisson regression and predictive Random Forest algorithm were used complementarily to estimate prevalence ratios and to build prediction models, respectively. All analyses were stratified by gender. The prevalence of attempted suicide was 34% for men and 50% for women. In both genders, depression (PR_M = 1.56, PR_W = 1.27) and hallucinations (PR_M = 1.80, PR_W = 1.39) were factors associated with attempted suicide. Other specific factors were found for men and women, such as childhood trauma, aggression, and drug use severity. The men's predictive model had prediction statistics of AUC = 0.68, Acc. = 0.66, Sens. = 0.82, Spec. = 0.50, PPV = 0.47 and NPV = 0.84. This model identified several variables as important predictors, mainly related to drug use severity. The women's model had higher predictive power (AUC = 0.73 and all other statistics were equal to 0.71) and was parsimonious. Our findings indicate that attempted suicide is associated with depression, hallucinations and childhood trauma in both genders. Also, it suggests that severity of drug use may be a moderator between predictors and suicide among men, while psychiatric issues shown to be more important for women.

The normality analysis in the distribution of residuals is a determining criterion to verify and validate a model. For example, in modeling financial time series by linear regression, the residuals should be independent of each other, identically distributed, have a normal distribution, and be homoscedastic. Thus, it was aimed to study the performance of some normality tests applied on the residuals obtained from linear regression modeling of time series tendency using polynomials of different degrees. The Jarque-Bera, Anderson-Darling, Kolmogorov-Smirnov-Lilliefors, Doornik-Hansen, and Shapiro-Wilk tests were used, there was agreement in almost all test results, with the exception of the Doornik-Hansen test.