A Mathematical Model for Continuous Expression of Urban Underground Space Resource Multi-Object Evaluation

Urban underground space resource (UUSR) constitutes a critical natural resource and a vital component of the natural environment, whose rational utilization is essential for the sustainable development of cities. Mathematical models are indispensable for the multi-object evaluation of UUSR. However, in previous research based on traditional mathematical models, neither the continuous expression of evaluation results has been considered, nor has the comparability been addressed. In this paper, the interval continuous mathematical model (ICMM) is presented at the theoretical level for UUSR multi-object evaluation. By achieving the continuous distribution of quantitative values of evaluation indicators, removing the step-like output features of evaluation results, and eliminating predefined grade boundaries, the ICMM achieves continuous expression of the results and improves their comparability across different areas. The correlation analysis conducted on the UUSR evaluation indicators demonstrates a significant monotonic relationship between the indicator value and the evaluation result, regardless of the increasing trend or the decreasing trend. Finally, a numerical experiment clearly demonstrates that the ICMM is valid for evaluating different UUSR objects.