Energy of Fuzzy Hypersoft Sets with Application in Machine Learning for Decision Making

This study advances the application of fuzzy hypersoft sets (FHSS) in machine learning (ML) decision-making by introducing a novel energy metric to quantify multi-sub-attribute uncertainty. Building on fuzzy set theory, soft sets, and hypersoft sets, FHSS integrates fuzzy membership with multi-sub-attribute parameterization, addressing limitations of traditional uncertainty models in handling complex, high-dimensional datasets. Inspired by spectral graph theory, the proposed energy metric — the sum of singular values of the FHSS matrix — quantifies systemic significance and enables a robust ranking of alternatives. An algorithm leveraging this metric has been developed and validated through applications in healthcare (heart risk profiling) and energy systems, achieving 90.83% accuracy and an F1-score of 0.8706 in a dataset of 500 participants. A comparative analysis demonstrates the superiority of FHSS energy over fuzzy soft and hypersoft sets, particularly in capturing attribute interdependencies. Despite the computational challenges posed by large matrices, the framework provides interpretable and scalable solutions for ML-driven decision-making under uncertainty. Future work will optimize computational efficiency and extend applications to domains such as financial risk analysis, further reinforcing FHSS energy as a transformative tool for precise, uncertainty-aware decision-making.