A Bipolar Neutro-Spatial Graph Model for Evaluating Sustainable Regeneration Spatial Design Schemes in Historic Urban Areas

Abstract

Urban areas with historical value often face serious challenges of physical decay, social 
decline, and environmental degradation. Sustainable regeneration of these areas requires 
a careful evaluation of design schemes, balancing multiple and sometimes conflicting 
factors such as heritage conservation, green space inclusion, community acceptance, and 
economic feasibility. Traditional evaluation models cannot fully capture the uncertainty, 
contradictions, and ambiguity present in such contexts. 
This paper introduces a new mathematical model called the Bipolar Neutro-Spatial Graph 
Model (BNSGM), which uses a customized form of neutrosophic bipolar vague 
representation to evaluate spatial regeneration schemes. Each urban element (like a 
building, plaza, or street) is represented as a node with positive, neutral, and negative 
evaluation scores for each sustainability criterion. Relationships between these elements, 
such as spatial influence or policy conflict, are modeled as directed edges with bipolar 
weights. The model provides a complete evaluation score for each regeneration scheme, 
considering both supportive and opposing indicators, as well as uncertain aspects. 
A full case study is presented, using real spatial data and indicators from an old urban 
district. The results show how the model supports better decision-making in complex 
urban regeneration processes, where uncertainty and disagreement are unavoidable. This 
work offers a new way to mathematically structure and evaluate sustainable design 
strategies in old cities with historical, social, and economic challenges.

DOI: 10.5281/zenodo.16496521