Hyperstructures and their hierarchical extensions, the Superhyperstructures, furnish a flexible framework for modelling multilayered phenomena across a wide range of disciplines. Viewed through the lens of functions, these ideas manifest as HyperFunctions and SuperHyperFunctions, whose values belong to iterated powersets rather than to ordinary codomains. Although the structural and computational aspects of hyperstructures have been explored well beyond mathematics—including notable work in chemistry—the corresponding functional counterparts remain largely unexamined in that context. To address this gap, the present paper introduces several precise definitions of HyperFunctions and SuperHyperFunctions tailored to chemical systems and investigates their fundamental properties. These set-valued constructs capture nested reactivity patterns and multi-step pathways, thereby opening new avenues for describing complex chemical processes.
Takaaki Fujita (Tue,) studied this question.