A novel approach for road crack detection and segmentation was proposed, incorporating Einstein operators within an Adaptive Neuro-Fuzzy Inference System (ANFIS). This methodology leverages advanced fuzzy aggregation techniques and adaptive mechanisms, combined with dynamic Einstein sum and product operators, to enhance the identification of cracks. The model was designed to effectively manage varying crack intensities, geometries, and noise levels, thereby ensuring high sensitivity and accuracy in real-world road conditions. In the preprocessing stage, robust fuzzification was applied using Gaussian membership functions alongside Einstein operators, which significantly improved feature extraction. The segmentation framework based on ANFIS ensured precise detection and delineation of cracks. The performance of the proposed model was demonstrated through a comparative analysis, showing superior accuracy (95.2%), precision (94.1%), recall (96.4%), and F1-score (95.2%) when compared to state-of-the-art models. Statistical validation was conducted, with p-values < 0.01 for all performance metrics, confirming the reliability and statistical significance of the results. Advanced post-processing techniques, including fuzzy morphological refinement and adjacency matrix-based connectivity analysis, were employed to accurately identify even faint or disconnected cracks. The proposed method exhibits exceptional resilience to environmental variations, offering a reliable and adaptive solution for road maintenance and monitoring. This work highlights the potential of fuzzy logic, statistical validation, and adaptive mechanisms in addressing realworld challenges in road crack detection.

Graph labeling is the process of assigning labels to vertices and edges under certain conditions. This paper investigates the graceful local antimagic labeling of various graph families, excluding symmetric labelings, using computational experiments and Python-based algorithms. Through these experiments, we identify new results and patterns within specific graph classes. The study expands on the existing literature by offering computational evidence, proposing algorithms for the verification of labelings, and exploring the relationship between the local antimagic labeling and the chromatic number. Our results increase the understanding of graph labeling and offer insights into its computational aspects.

Foggy road conditions present substantial challenges to road monitoring and autonomous driving systems, as existing defogging techniques often fail to accurately recover structural details, manage dense fog, and mitigate artifacts. In response, a novel defogging model is proposed, incorporating Pythagorean fuzzy aggregation, Gaussian Mixture Models (GMM), and the level-set method, aimed at overcoming these limitations. Unlike conventional methods that depend on fixed priors or oversimplified haze models, the proposed framework leverages the advantages of Pythagorean fuzzy aggregation to enhance contrast and detail restoration, GMM to estimate fog density robustly, and the level-set method for precise edge preservation. The performance of the model is quantitatively assessed, revealing a Peak Signal-to-Noise Ratio (PSNR) of up to 37.1 dB and a Structural Similarity Index (SSIM) of 0.96, which significantly outperforms existing defogging techniques. Statistical analyses further confirm the robustness of the approach, with a p-value of less than 0.001 for key performance metrics. Additionally, the model demonstrates an execution time of 0.07 seconds, indicating its suitability for real-time road monitoring applications. Qualitative assessments highlight the model's ability to restore natural road colours and maintain high structural fidelity, even under conditions of dense fog. This work provides a promising advancement over current methods, with potential applications in autonomous driving, traffic surveillance, and smart transportation systems.