Fatima T. Adilova, Rifqat R. Davronov, Yalkin T. Adilov
Mathematics & AI
· Vol. 1, No. 3
· Sep 2026
The structuring and partitioning of large-scale complex datasets is often limited by the computational complexity of combinatorial optimization, which frequently yields suboptimal, locally extremal solutions. This paper proposes a structured processing methodology based on monotone systems (MS) theory that reformulates structural identification as a globally optimal optimization problem. We analyze the mathematical behavior of element--subset weight functions $\pi(i,H)$ and extend classification through the concept of associative patterns. A functional software architecture for generating monotonic systems is developed and evaluated on two tasks: classification of handwritten digit images from the scikit-learn digits dataset (1797 images, 10 classes) and clinical stratification of patients with ischemic heart disease (IHD). In the image experiment, we compare weight functions of different types: the second-type function~(6) with internal parametrization coefficient $\alpha$ achieves maximum baseline accuracy at $\alpha = 0.6$--$0.9$, while the first-type function~(5) with power parameter $\delta = 2$ combined with an ensemble of random column partitions reaches 97.4\% classification accuracy on the full 10-class problem. In the cardiology case study based on 62 patients with acute myocardial infarction, core extraction with a first-type connection function produces a stability index $g = 0.75$, supporting robust patient grouping. The results demonstrate that MS-based core extraction provides interpretable, globally optimal structure identification for heterogeneous object--feature data.