Neutrosophic Modeling and Redesign Effects Analysis of Abandoned Buildings in the Context of Urban Renewal: A Spatial Probabilistic Framework for Urban Hazard Risk

Urban environments often suffer from the cumulative risks associated with abandoned structures, which can generate hazards such as structural collapses, fires, and socio-economic degradation. Traditional statistical models fail to capture the indeterminacy, vagueness, and incomplete knowledge surrounding such hazards. This paper proposes a fully Neutrosophic probabilistic framework for modeling spatial hazard intensities related to abandoned buildings. We redefine the event intensity function λ as a Neutrosophic-valued quantity λN=(T,I,F) representing degrees of truth, indeterminacy, and falsity regarding the hazard level. A novel Neutrosophic Poisson process is formulated, enabling flexible modeling of uncertainty and ignorance in spatial domains. A numerical case study on a 5×5 urban grid demonstrates the interpretability and robustness of the proposed approach. The results highlight how Neutrosophic logic enhances decision-making in urban renewal planning under real-world uncertainty.