Medical SuperHyperStructure and Healthcare SuperHyperStructure
Takaaki Fujita *
Independent Researcher, Tokyo, Japan.
*Author to whom correspondence should be addressed.
Abstract
We develop a rigorous, set–theoretic framework for modeling clinical and health-system decision making using Hyperstructures and their iterated counterparts, Superhyperstructures. On the clinical side, we formalize a Medical HyperStructure on a space of patient states equipped with (i) a valuation into a partially ordered commutative monoid V capturing risk, cost, workload, and related quantities; (ii) policy/feasibility correspondences that encode guidelines and contraindications; (iii) observation maps for measurable summaries; and (iv) convex-cone bounds on admissible changes in valuations. Lifting these ingredients to iterated powersets yields Medical SuperHyperStructures of order (m,n), which capture cohorts, multi-stage care pathways, and protocol families via set-valued outputs and lifted observations.
On the operational side, we analogously define Healthcare Hyper/SuperHyperStructures on system states (queues, capacities, rosters, inventories) with KPI vectors and policy constraints. The framework unifies many rule-based and protocol-driven processes as special cases—e.g., (m,n) = (0, 1) recovers classical hyperoperations—while supporting uncertainty, aggregation across levels, and resource/safety budgets through convex-cone admissibility. The paper is purely theoretical (no data or simulation). Worked examples—empiric antibiotics, insulin titration, neuroimaging triage, ED admission policy, OR day scheduling, inventory replenishment, and outpatient overbooking—illustrate expressiveness and suggest directions for quantitative validation in future studies.
Keywords: HyperStructure, SuperHyperStructure, Medical SuperHyperStructure, Healthcare SuperHyperStructure