Integrating TreeSoft and HyperSoft Paradigms into Urban Elderly Care Evaluation: A Comprehensive n-SuperHyperGraph Approach

Abstract

The rapid aging of global urban populations has compelled cities to reimagine how elderly care 
services are delivered, structured, and evaluated. Traditional models such as TreeSoft, which rely 
on hierarchical and clearly defined service flows, are well-suited for institutional settings but 
often fail to capture informal or uncertain care dynamics. On the other end of the spectrum, 
HyperSoft frameworks emphasize flexibility and allow for the modeling of indeterminate or 
overlapping relationships common in community-based or volunteer-driven services but they 
often lack operational coherence. 
This research proposes a hybrid evaluation model that integrates TreeSoft and HyperSoft 
paradigms within the powerful mathematical structure of the n-SuperHyperGraph (n-SHG). 
Grounded in ecosystem theory, the n-SHG framework enables the modeling of nested, layered, 
and partially uncertain relationships between service actors such as families, clinics, local 
authorities, and digital providers. 
Using data collected from three urban districts, we evaluate five smart elderly care service modes 
using connectivity, redundancy, and uncertainty indicators derived from the n-SHG structure. 
The results not only differentiate modes by performance but also demonstrate how both 
structured (TreeSoft-like) and fluid (HyperSoft-like) care systems can be understood, compared, 
and optimized under one unified analytical framework. 
This hybrid modeling approach provides a roadmap for policymakers, urban planners, and 
researchers seeking to develop adaptive, inclusive, and resilient elderly care ecosystems. Also, we 
show a case study of TreeSoft set with four criteria and five alternatives. We compute the criteria 
weights in the main criteria and each sub-criteria. We use the MARCOS method to rank the 
alternatives.

DOI: 10.5281/zenodo.15399218