The 12th International Conference on Fuzzy Systems and Data Mining (FSDM 2026)

Abstract: An Ω‑algebra is a kind of fuzzy algebra in the lattice-valued framework, with an algebra equipped with a lattice‑valued equality. Algebra identities are satisfied as special lattice-valued formulas, and as a consequence, cuts of the equality correspond to weak congruences of the underlying crisp algebra. In earlier work, we investigated many types of Ω‑algebras. Recently, in an attempt to study consequences of our work in the classical setting with the [0,1] interval, we have studied connections with chains in weak congruence lattices. Building on this foundation, we now turn to the classical setting of Ω‑groups and Ω‑quasigroups, where subgroup lattices and weak congruence lattices interact directly with the solvability of equations.
Classical group theory provides deep results on solvability: equations in groups are closely tied to subgroup chains, normal series, and congruence relations. In particular, solvability of equations often reflects the structure of chains in subgroup lattices, such as composition series or chains of normal subgroups. These chains serve as algebraic witnesses to the existence of solutions, linking lattice‑theoretic properties with equation solvability. Similarly, in quasigroups, congruence chains impose constraints on the solvability of functional equations, revealing structural parallels with group theory.
Our contribution demonstrates that chains of weak congruences in Ω‑groups can be systematically aligned with chains in subgroup lattices, thereby providing a lattice‑valued framework for analyzing solvability of equations. Extending this approach to Ω‑quasigroups, we show how weak congruence chains capture algebraic conditions that govern equation solvability in non‑associative settings. These results enrich the representation theory of Ω‑algebras by connecting chains of weak congruences with classical solvability theory, offering a unified perspective that bridges discrete subgroup lattices, weak congruence structures, and equation systems in both groups and quasigroups. In this way, by dealing with numbers, we are able to approximately solve some types of equations.

Keywords: Ω‑algebra, fuzzy algebra, approximate solving of equations

Abstract: To be updated

Abstract: To be updated

Abstract: To be updated

Abstract: Enhancing the resilience of electricity transmission infrastructure requires timely situational awareness, reliable diagnostics, and actionable early warnings under uncertain and heterogeneous conditions. The presented results are achieved from an integrated research effort focused on digital technologies and analytical models for critical infrastructure monitoring, with emphasis on experimental validation in controlled and pre-operational settings. It covers a modular approach combining remote sensing, field telemetry, operational logs, and physical simulation to support future digital twin and early-warning capabilities.
The presented work is derived from multiple data modalities and demonstrators. Airborne hyperspectral campaigns (VNIR/SWIR) over selected Slovak localities produced a georeferenced and annotated dataset enabling ecological and infrastructure mapping, including a labelled geodatabase of vegetation and non-vegetation structures. Complementary LiDAR point clouds were processed into classified outputs and canopy height models suitable for 3D integration. For condition monitoring, acoustic diagnostics assessed the feasibility of detecting patterns related to high-voltage insulators using large-scale audio recordings and power lines audio embeddings, while telemetric meteorological observations were analysed to identify conditions linked to moisture-driven degradation, and dust contamination. On the operational side, SCADA/RIS logs and PMU phasor measurements were investigated for synchronization, causality inference, and precursor detection using deep learning concepts (e.g., sequence models and graph-based architectures). Finally, fire-risk assessment was explored through Fire Dynamics Simulator scenarios to study vegetation heterogeneity effects and establish methodological foundations for calibration to local conditions.

Abstract: The digital transformation of decentralized healthcare demands integrated multi-omics datasets, population health records and translational evidence to support primary care clinical decisions. However, fragmented biological databases and disconnected analytical pipelines create major barriers to translating aging research into real-world healthcare practice. To tackle this challenge, we built AI-Aging, a unified AI-based digital infrastructure delivering an end-to-end translational pipeline spanning multi-omics profiling to population-wide aging health management. The system consists of four standardized, interoperable sub-platforms: HALDxAI, a large-scale aging knowledge graph containing 2.8 million biological nodes and 180 million relational links to dissect aging mechanisms; ARIES, a literature-derived evidence graph enabling traceable causal connections between geroprotective chemicals, molecular pathways and aging phenotypes; AITED, a translational database curating more than 8,700 aging interventions to measure translational gaps and safety signals for clinical trial design; and Fluxera, an interpretable predictive model trained on a cohort of 178,000 participants to map population aging trajectories and forecast individual health risks. Uniform data schemas, open APIs and traceable evidence chains are implemented across all modules, forming a closed-loop system for omics fusion, mechanistic interpretation, intervention assessment and population health forecasting. This infrastructure connects fundamental multi-omics findings with on-the-ground decentralized primary care, establishing a solid digital framework for precision aging intervention and equalized longevity health management.

Keywords: digital health transformation; multi-omics integration; AI knowledge graph; longitudinal health trajectory; ageing translational database; decentralized primary care; longevity research