Abstracts Track 2026

Nr: 171
Title:

Towards an Axiomatization of Similarity-Based Reasoning
Authors:

Antonin Dvorak, Balasubramaniam Jayaram and Martin Štepnicka
Abstract: The preservation of fuzzy interpolation has long been regarded as one of the fundamental requirements imposed on fuzzy inference systems. More generally, Moser and Navara introduced three natural axioms describing desirable properties of fuzzy inference, namely fuzzy interpolation, non-triviality of inferred outputs, and locality of inference. While these axioms were originally fitting well the Mamdani-Assilian type of fuzzy rules, later studies showed that they have to be reformulated for implicative rules in order to preserve their intended meaning. Recent research on similarity-based reasoning (SBR) has addressed fuzzy interpolation together with the robustness of SBR inference developed through the concept of extensionality. In particular, fuzzy interpolation can be preserved not only for inputs identical to rule antecedents, but also for broader classes of inputs related to them through extensional hulls or extensional bases. This naturally raises the question of whether the remaining Moser–Navara axioms can also be meaningfully formulated and studied within the SBR framework. This contribution focuses on the non-triviality of inferred outputs and on locality, understood as the requirement that rules which are not activated should not influence the final conclusion. Particular attention is paid to the role of extensionality and G-negligibility, which played a crucial role in the investigation of the fuzzy interpolation of SBR systems. It appears to be important also in the treatment of these two axiomatic properties. A major advantage of the SBR framework is that the axiomatization can be developed in a general setting without distinguishing whether the underlying rule-based inference is built on conjunctions, as in Mamdani systems, or on implications, as in implicative systems.
Nr: 172
Title:

A Fuzzy Approach to Text Credibility Assessment via Semantic Attributes
Authors:

Petra Stevuliakova, Jiri Janecek, Petr Sosik and Michal Mistecky
Abstract: We focus on the problem of language trustworthiness and credibility classification to understand the properties of credible, misleading and manipulative texts. The prediction is based solely on the language used in the text itself, instead of checking the factual truthfulness. We developed a fuzzy framework centred at text classification models based on semantic attributes. The set of semantic attributes contains well-interpretable qualities of the text content that are independent of the particular language. The attributes are evaluated by Large Language Models utilising their capability to understand the text context, such that the evaluation within [0, 1] describes the degree of their presence in the text. Our preliminary investigations show that these semantic features yield strong discriminative power for the text credibility assessment. It turns out that specific semantic qualities play a crucial role in capturing manipulative discourse. The current, extended study concentrates on the specific dataset of news articles (Verifee). We propose a fuzzy tree-like classifier and employ other fuzzy classification techniques (fuzzy decision trees, random forests) for comparison. It turns out that fuzzy classification approaches based on semantic attributes provide an effective balance between prediction confidence and transparent decision logic. This approach demonstrates that the interpretable fuzzy system works effectively with semantic attributes that carry the inherent vagueness of natural language. Moreover, the proposed framework for automated credibility analysis contributes to transparent fake-news detection which is exceptionally relevant in the era of AI-generated content.
Nr: 173
Title:

An Optimal Transport Framework for Comparing Fuzzy Association Rule Collections
Authors:

Martina Dankova and David Adamczyk
Abstract: This contribution revisits the optimal-transport-based dissimilarity measure for comparing collections of fuzzy association rules originally introduced in [1] and extends the previous study with additional theoretical properties and experimental results. The approach interprets each rule collection as a discrete probability measure over information granules. The probability mass assigned to an individual rule is obtained by normalizing a non-negative measure of its relevance, such as a combination of its confidence and support. The comparison is based on a ground-cost function that evaluates the dissimilarity between pairs of fuzzy association rules along three complementary dimensions: the structural component captures differences in the variables, linguistic literals, and logical arrangement of the antecedents and consequents. The complete ground cost is defined as a combination of these structural, semantic, and quality components. The dissimilarity between the rule collections is subsequently obtained by minimizing the total transportation cost over all admissible transport plans having the prescribed rule weights as their marginals. The resulting value represents the minimum effort required to transform the weighted distribution corresponding to one rule collection into the distribution corresponding to the other collection. Consequently, a rule may be matched partially with several rules in the second collection, providing a flexible “soft alignment” of information granules. Reference: [1] Daňková, M. (2026). Optimal Transport based Dissimilarity of Fuzzy Association Rules. In B. Vantaggi et al. (Eds.), Proceedings of the IPMU 2026 Short Papers, Rome, Italy, 2026, pp. 65–70. Acknowledgement: This contribution has been produced with the financial support of the European Union under the REFRESH – Research Excellence For REgion Sustainability and High-tech Industries project number CZ.10.03.01/00/22_003/0000048 via the Operational Programme Just Transition
Nr: 175
Title:

On Extending a Product Fuzzy SAT Solver with Support for Intermediate Constants and Model Finding
Authors:

Ivor Uhliarik
Abstract: The field of satisfiability solving in propositional fuzzy logics offers few solutions that address the product case. Most are based on reductions to other problems, such as satisfiability modulo theories or mixed-integer programming. To the best of our knowledge, there is only one solver that is largely self-contained, follows a transparent algorithm, and defers to reductions only as a last resort. However, until recently, this solver lacked support for intermediate constants (values between 0 and 1) in the input and a proper technique for finding models for satisfiable theories. We have added support for both capabilities. The solver prodfsat implements the product fuzzy extension of the DPLL procedure. It traverses the order clausal form of the input theory and applies branching and reducing rules. The solver is transparent because rule selection can be investigated, and it is extensible with additional rules that reduce the solution space. Intermediate constants are handled by injecting clauses informing the procedure about the linear order of the domain. Model finding is designed as an iterative process that assigns value bounds to atoms, eventually determining their exact values. Since the logic includes powers, equality (=), and strict order (<) connectives, circular dependencies between atoms may occur in formulae. Their valuation is performed using an approach that utilizes linear programming in the space of exponents, only for clauses where this is required. Experimental evaluation shows that adding intermediate constants and model finding has no significant impact on previous performance. Introducing constants does not change the solver's core procedure, and model finding is only performed as the last step when necessary. The performance of prodfsat remains state of the art in some experiments. We consider the additions to be the final pieces of a fully functioning and practically usable solver. The project is released as free and open-source software.
Nr: 152
Title:

Incommensurate Fractional Recurrent Neural Networks
Authors:

Zahra Alijani and Babak Shiri
Abstract: Standard recurrent networks treat memory uniformly, with every state component forgetting the past at the same rate, yet real sequential data such as energy consumption, weather, and financial series rarely behave this way. The purpose of this work is to test whether giving each output channel its own trainable memory depth, grounded in the theory of incommensurate fractional difference systems, yields measurably better forecasting. To this end, we build a recurrent architecture whose state evolution is governed by component-wise nabla fractional difference operators, with the vector of fractional orders trained alongside weights and biases. Because the resulting cross-time and cross-layer parameter coupling makes back-propagation structurally impossible, gradients are instead derived recursively during the forward pass through a forward-forward scheme, combined with mini-batch stochastic ADAM optimization, and boundedness of the gradient variance is proven to support training stability. Across synthetic sinusoidal benchmarks and three real-world tasks — transformer oil temperature, daily weather, and household expenses — the proposed network outperforms structurally identical RNNs trained under the same hyperparameters; accuracy improves with the terminal time step up to an optimum, the learned fractional orders preserve their relative ordering, and computational cost grows only linearly with recursion depth. Current experiments are limited to single-layer networks, with multi-layer extensions and convergence analysis ongoing. By enabling more accurate forecasts of energy and weather variables, the approach supports grid management, infrastructure monitoring, and planning, while offering an original framework that unifies fractional calculus with recurrent learning and contains the classical RNN as a limiting case.