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Article Relation of Complete Correlation and Its Implication on Interval Operations(2026) Števuliáková, Petra; Alijani, ZahraThis paper lays the groundwork for defining division and multiplication on fuzzy intervals under complete correlation. We introduce joint possibility distributions to model dependencies between fuzzy variables with complete correlation expressed via a linear relation. We then examine its impact on interval operations and the inverse property. Our results show that fuzzy arithmetic requires more nuanced approaches than simple point-wise interval analogies.Article Evaluation of Machine-Learning Models in Polymer Chemistry with Prediction of Not Reported Measurements(2026) Singh, Shivani; Mondal, Sourov; Nieves, Juan Carlos; Torra, VicençArticle Fuzzy transform for operational matrices in fractional equations(2026) Pham, Thi Minh Tam; Perfilieva, IrinaArticle Verification of Validity of Logical Syllogisms with New Forms of Intermediate Quantifiers Based on Grades(2026) Pavliska, Viktor; Murinová, PetraIn this contribution, we continue our investigation of fuzzy Peterson syllogisms. Whereas the previous study concentrated on validating these syllogisms through the construction of formal proofs and semantic verification, the present work focuses on assessing their validity using Peterson’s grade-based rules.Article Measuring the Temporal Stability of Fuzzy Linguistic Summaries about Time Series with Drifts(2026) Ostrowski, Marcin; Kaczmarek-Majer, Katarzyna; Hryniewicz, OlgierdArticle Verification of Validity of Syllogisms Related to Graded Peterson Cube of Opposition(2026) Murinová, Petra; Novák, VilémIn this article, we will examine the validity of selected forms of logical syllogisms with intermediate quantifiers. We will focus in particular on forms related to the graded Peterson’s cube of opposition. Our verification will be based on the application of graded Peterson’s rules using the distribution index.Article Linguistic Interpretation of Natural Data using New Forms of Intermediate Quantifiers(2026) Murinová, Petra; Fiala, KarelThis paper examines the application of fuzzy natural logic in the analysis of scientific data and their representation through special linguistic expressions. We use the theory of evaluative linguistic expressions, which make it possible to describe quantitative data using imprecise espressions such as “very small”, “medium”, “large”, and similar. They occur in the definition of the, so called, intermediate quantifiers using which we characterize given data.Article Few-shot learning in industrial applications(2026) Molek, Vojtech; Alijani, ZahraThis paper reports on the empirical performance of few-shot learning (FSL) for visual defect classification using confidential industrial datasets. We evaluate 16 combinations of four backbone models (Perception Encoder, DINOv2, DINOv3, ConvNeXt-v2) and four FSL classifiers (Prototypical Networks, Neighborhood Component Analysis, Relation Networks, Linear Adapter). The evaluation covers three conditions: a baseline comparison, deterministic support set augmentation, and a learnable attention preprocessor. Results demonstrate that support set augmentation is a highly effective strategy, improving performance in nearly all configurations. Furthermore, the DINOv2 and ConvNeXt-V2-T backbones emerged as top performers, achieving the most competitive and highest-accuracy results, respectively. These findings suggest that for industrial FSL applications, combining a strong, pre-trained backbone with a simple augmentation strategy is a practical approach for building data-efficient classification systems.Article Qualitative Criteria for Fuzzy Linguistic Summaries with Absolute Linguistic Expressions(2026) Miś, Katarzyna; Kaczmarek-Majer, Katarzyna; Baczyński, MichałArticle Towards Responsible Time Series Forecasting(2026) Kälin, Remo; Portmann, EdyArticle On the Dissimilarity of Fuzzy Information Granules(2026) Kaczmarek-Majer Katarzyna; Daňková, MartinaArticle Predicting Subgoals in Ricochet Robots with a Graph Neural Network(2026) Hyner, Petr; Mrógala, Jan; Adamczyk, David; Hůla, JanArticle Large Language Models in SAT Reasoning(2026) Hyner, Petr; Dušek, František; Adamczyk, David; Hůla, JanArticle Properties of Graded Peterson's Square of Opposition as Immediate Inferences(2026) Fiala, Karel; Murinová, PetraImmediate inferences are arguments where the conclusion is supported by just one premise. There are several ways to infer a conclusion from a premise. We can use conversion, obversion, contraposition or the properties of some structure of opposition. In this article, we will focus on the study of immediate inference for several forms of intermediate quantifiers that form a graded Peterson’s square of opposition which describes properties of contrary, contradictory, subcontrary, subaltern, and superaltern between these quantifiers.Article A General Framework for Multiplets Selection: Algorithmization and Complexity Analysis(2026) Daňková, Martina; Šustek, JanIn this contribution, we present the multiplets algorithm for constructing and selecting optimal sets of disjoint hyperedges across multiple groups in tabular data. We describe its 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.Article On Inference Mechanisms of Fuzzy-Probabilistic Inference Systems(2026) Cao, Nhung; Holčapek, Michal; Valášek, RadekThis 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 $L_1$-based minimization approaches, remains open. This gap motivates a deeper investigation of the foundations of the inference mechanism for FPIS.Article On Data-Driven Fuzzy Partition in the Fuzzy-Probabilistic Inference System Framework(2026) Cao, Nhung; Holčapek, Michal; Valášek, RadekArticle Fuzzy-Probabilistic Inference Systems Based on Piecewise Linear Weighted Quantiles(2026) Cao, Nhung; Holčapek, Michal; Valášek, RadekArticle Discovering Fuzzy and Statistical Patterns in Data: The Nuggets R Package(2026) Burda, MichalArticle A General Framework for Context-Aware Fuzzification of Four Ordered Categories: A Case Study on BMI Categories(2026) Alijani, Zahra; Daňková, MartinaThis paper presents a general methodological framework for constructing context-aware fuzzy partitions that extend conventional crisp categorizations. The approach is based on Nov´ak’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.