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This paper focuses on fuzzy--probabilistic IF--THEN rule-based systems, where antecedents encode fuzzy information and consequents represent probability distributions of the output variable. By combin…

This paper focuses on fuzzy--probabilistic IF--THEN rule-based systems, where antecedents encode fuzzy information and consequents represent probability distributions of the output variable. By combining both types of uncertainty within a unified framework, this approach is effective for time series analysis and forecasting.Given a fuzzy covering of the input universe and an output random variable defined on a probability space, the rules state that if the input belongs to a given fuzzy set, then the output is described by a corresponding quantile function. In practice, uniform or generalized fuzzy partitions are typically constructed by shifting equidistant fuzzy sets along the domain axis. The consequent quantile functions are estimated from data as weighted quantiles, where the weights are given by the membership degrees of input values. These weighted quantiles are obtained by minimizing an asymmetric absolute loss functional. The inference mechanism then evaluates the output quantile at a given input as a normalized weighted average of the rule-wise quantile functions.Although fuzzy--probabilistic inference systems have demonstrated effectiveness in various applications, the construction of an appropriate fuzzy partition remains challenging. Uniform partitions are simple but fail to capture complex structures hidden in the data. This motivates the question of whether a data-driven fuzzy partition can better reflect local behaviour under a well-defined criterion. In this paper, we introduce three algorithmic methods for designing non-uniform, data-dependent fuzzy partitions, while a detailed theoretical analysis is left for future work. 

Bipolar affective disorder and depression are among the most prevalent mental health conditions, with recent advances highlighting the role of sensors and computational methods in monitoring them. How…

Bipolar affective disorder and depression are among the most prevalent mental health conditions, with recent advances highlighting the role of sensors and computational methods in monitoring them. However, current Artificial Intelligence (AI)-based systems, while accurate, often lack transparency, limiting their trustworthiness and clinical adoption. Further-more, the state-of-the-art is still missing clear guidelines on how to design advanced human-centric validation approaches for interpretations or explanations of intelligent systems with the aim of paving the way towards trustworthy AI systems ready to be adopted by clinicians. This paper presents a novel evaluation approach integrating supervised learning with fuzzy information granules derived from fuzzy association rules and linguistic summaries to enhance interpretability. Itsmain innovation lies in the human-centric evaluation methodology. Our use case study in the mental health monitoring setting demonstrates the framework’s ability to reveal meaningful relationships between sensor data and mental states. Thus, this work contributes to the development of trustworthy AI systems in compliance with emerging regulatory standards. Our findings confirm that fuzzy logic-based interpretations constructed about the patients’ acoustic features would be beneficial for both clinicians and patients. 75% of respondents agreed that interpretations addressed important aspects of the clinical problem, and 91.7% of respondents agreed that additional interpretations would help psychiatrists in daily patient care. However, evaluations were more critical concerning the clarity and evidential support. Further work should focus on improving the conciseness and clarity of the automatically constructed fuzzy information granules.

Generalized anxiety disorder (GAD) is characterized by persistent, excessive, and difficult-to-control worry. The Contrast Avoidance Model (CAM) proposes that individuals with GAD use worry to sustain…

Generalized anxiety disorder (GAD) is characterized by persistent, excessive, and difficult-to-control worry. The Contrast Avoidance Model (CAM) proposes that individuals with GAD use worry to sustain negative emotional arousal, thereby avoiding sharp negative emotional contrasts that would otherwise follow unexpected adverse events. A virtual reality (VR) protocol was developed to simulate such contrasts by alternating guided relaxation with brief anxiety-inducing scenarios (skyline plank, crowded elevator, and loose dog encounter). This study evaluated the usability and feasibility of this protocol in 20 subclinical adults aged 18–45 who met a screening threshold of GAD-7 ≥ 5, using a Meta Quest 3 headset and Polar H10 heart rate sensor. Exposure segments produced a significant decrease in RMSSD (β = −0.185, p < 0.001), consistent with reduced parasympathetic activity during exposure, whereas heart rate did not differ significantly between conditions. Subjectively, exposure increased SUDS (β = 2.23, p < 0.001) and SAM arousal (β = 1.95, p < 0.001), and decreased SAM valence (β = −2.68, p < 0.001) and dominance (β = −1.70, p = 0.005). Presence scores, cybersickness ratings, and qualitative feedback supported the usability of the protocol and identified concrete design refinements. These results support the feasibility of the protocol and provide a foundation for future controlled clinical evaluation.

This paper presents a general methodological framework for constructing contextaware fuzzy partitions that extend conventional crisp categorizations. The approach isbased on Novák’s theor…

This paper presents a general methodological framework for constructing contextaware fuzzy partitions that extend conventional crisp categorizations. The approach isbased on Novák’s theory of fuzzy contexts and is implemented using the R package lfl. It enables smooth and interpretable transitions between adjacent classes while preserving the original categorical structure. To illustrate the procedure, we apply it to derive fitness-specific fuzzy partitions of Body Mass Index, where the conventional four categories (underweight, normal weight, overweight, obese) are adapted according to individual levels of cardiorespiratory fitness.

The nuggets package provides a flexible and extensible frame-work for discovering interpretable data patterns based on frequent logical conditions. Its designunifies classical association-rule mining …

The nuggets package provides a flexible and extensible frame-work for discovering interpretable data patterns based on frequent logical conditions. Its designunifies classical association-rule mining with linguistic and fuzzy representations, while enablingoptional statistical evaluation for selected pattern types such as conditional contrasts and corre-lations. Pattern generation is driven by support, ensuring efficient mining of relevant conditions,whereas additional quantitative analyses or tests can be seamlessly attached when desired.A major strength of nuggets lies in its extensibility. The framework allows users to definecustom fuzzification schemes and to evaluate an arbitrary R function on every frequent con-dition, thereby enabling the creation of new, user-defined pattern types. This design encour-ages experimentation with alternative logical semantics, statistical measures, and application-specific evaluation criteria, making nuggets not only a tool for applied pattern discovery butalso a research platform for developing new methods. 

Although Body Positivity content (BoPo) has been criticized for emphasizing physical appearance and promoting self-objectification, the specific features driving these effects remain unclear. The pres…

Although Body Positivity content (BoPo) has been criticized for emphasizing physical appearance and promoting self-objectification, the specific features driving these effects remain unclear. The present study examined whether depictions of female bodies act as triggers for self-objectification in BoPo on Instagram. In a between-subjects online experiment involving 158 women aged 18-29 (M = 21.6, SD = 2.4), exposure to female bodies in BoPo posts did not heighten state self-objectification. Trait self-objectification and negative mood did not moderate these effects; however, women with negative attitudes toward BoPo reported higher levels of state self-objectification. These findings underscore the potential importance of subjective appraisals in shaping the impacts of BoPo content. Overall, the study contributes to the ongoing debate about the potentially negative effects of BoPo on Instagram, suggesting that body depictions alone may not reinforce self-objectification. Future research should examine the distinct influence of different types of body portrayals to further clarify the impact of BoPo content on body image. From a practical perspective, prevention efforts and social media campaigns should aim to raise awareness of BoPo features that continue to overemphasize appearance, helping women better protect their body image from potential adverse effects.

In this work, we consider a particular construction of IF--THEN rules and the associated inference mechanism, which coincide with the so-called quantile fuzzy transform (or L1-fuzzy transform). Given …

In this work, we consider a particular construction of IF--THEN rules and the associated inference mechanism, which coincide with the so-called quantile fuzzy transform (or L1-fuzzy transform). Given a suitable fuzzy partition of the underlying universe and a random variable defined on a probability space, the system is formulated through rules stating that if the input belongs to the $k$-th fuzzy set, then the output is modeled by a corresponding quantile function.The consequent is represented by weighted quantile functions that provide statistical estimates of the output distribution conditioned on the input's membership in the respective fuzzy set. A crucial step in the inference process is the estimation of these quantile functions from data. Traditionally, weighted quantiles are computed via linear programming. We have recently introduced an alternative and computationally efficient method for evaluating weighted quantiles based on the analysis of the right derivative of the associated convex objective function.Although classical weighted quantiles are computationally efficient, they may be inadequate for accurately capturing the local positions of output quantiles over fuzzy inputs. To overcome this limitation, we have extended the weighted quantile approach into a piecewise linear functional form. In this contribution, we propose a slight modification of this construction to enhance its applicability to forecasting tasks. We describe the modified approach, demonstrate its improved inference performance compared to scalar weighted quantiles, and highlight its relevance for forecasting applications. 

This work studies the inference mechanism of fuzzy-probabilistic inference systems (FPIS), a class of rule-based models where antecedents encode fuzzy information and consequents represent conditional…

This work studies the inference mechanism of fuzzy-probabilistic inference systems (FPIS), a class of rule-based models where antecedents encode fuzzy information and consequents represent conditional probability distributions of the output variable. A system of m rules is considered: if the input belongs to a fuzzy set A_k, then the output follows a probability distribution described by an empirical quantile function. The antecedents form a covering fuzzy partition of the universe, ensuring that every input has positive membership in at least one fuzzy set. In practice, uniform or generalized partitions are typically employed. Local quantile functions are estimated from data as weighted quantiles, with weights given by membership degrees. The inference mechanism produces an empirical quantile function for any input as a linear combination of these local quantile functions, using normalized membership weights. Fuzzy rule-based systems capture input-output relationships in a rough manner, while the inference mechanism refines this into a complete mapping usable in practice. Previous studies compared the standard weighted average of quantile functions with several alternatives on synthetic and real datasets. However, a theoretical analysis of these mechanisms, including the original weighted average and related L1-based minimization approaches, remains open. This gap motivates a deeper investigation of the foundations of the inference mechanism for FPIS. 

In this contribution, we present the multiplets algorithm for constructing and selecting optimal sets of disjoint hyperedges across multiple groups in tabular data. We describes main computational ste…

In this contribution, we present the multiplets algorithm for constructing and selecting optimal sets of disjoint hyperedges across multiple groups in tabular data. We describes main computational steps and provide a complexity analysis covering both the edge construction and optimization phases, based on the Linear Sum Assignment method and the Constraint Programming SAT-based solver.