Determining the membership degree by fuzzy hypergraphs

Abstract

This study introduces an innovative method using fuzzy hypergraph theory for determining the closest fuzzy membership function to reality, based on expert opinions. The approach, novel in its application of fuzzy hypergraphs, effectively addresses complex and uncertain scenarios typical in disaster management and urban planning. Our methodology is clearly illustrated through detailed tables and figures, such as a diagram comparison chart of community intersection and union operators in Figure 5, demonstrating the efficiency and application of the method. Key findings include enhanced granular structure in granular computing and improved multivariate data clustering results, closely aligned with real-world scenarios, as depicted in these visual aids. A pivotal aspect of our research is its practical application, exemplified through a case study in a highly earthquake-prone region. The method was implemented to assess the seismic vulnerability of an urban district, encompassing over 37000 buildings, based on the opinions of 10 experts. This case study highlights the method's utility in urban seismic vulnerability (USV) assessment, underscoring its practical implications and benefits in natural hazard analysis and urban resilience. Our findings contribute significantly to the field, offering a novel perspective on handling imprecise data in disaster management and urban planning.