Enhanced Cross-Entropy Technique for Triangular Fuzzy Neutrosophic Multiple-Attribute Decision-Making and Applications to Quality Evaluation of Urban-Park Environmental Design

The evaluation of urban park environmental design quality is essential for ensuring that parks meet community needs and environmental sustainability. By comprehensively considering indicators such as functionality, aesthetics, sustainability, and user experience, this evaluation helps designers optimize spatial layouts and enhance the efficiency and aesthetic value of parks. Additionally, good environmental design promotes ecological protection, improves the quality of life for residents, and adds more green spaces to the city, making parks an integral part of daily urban life. The evaluation of urban park environmental design quality is framed as a multiple-attribute decision-making (MADM) problem. This study introduces the triangular fuzzy neutrosophic number cross-entropy (TFNN-CE) method, which integrates traditional cross-entropy with triangular fuzzy neutrosophic sets (TFNSs). Subsequently, the TFNN-CE technique for MADM is established. A numerical example illustrating the evaluation of urban park environmental design quality is provided, alongside several comparative analyses to highlight the advantages of the proposed approach. The key contributions of this research are as follows: (1) the TFNN-CE technique is introduced through the integration of cross-entropy and TFNSs; (2) the TFNN-CE technique is formulated to address MADM problems using TFNSs; (3) an empirical application for assessing urban park environmental design quality is presented to validate the proposed methodology; (4) comparative studies are conducted to substantiate the rationality of the TFNN-CE technique.