This paper presents a new approach using shifted Delannoy polynomials to tackle the nonlinear fourth-order integro-differential equations smoothly. We are using what makes these polynomials special to build our system, which turns the initial problem into a set of nonlinear algebraic equations we can solve with Newton’s method. We have carefully solidified the mathematics to ensure our method works, and it turns out the error gets smaller fast when dealing with smooth functions. Tests show our method is super accurate, reaching errors as small as $$10^{-16}$$ , better than other existing methods. It’s easy to set up, converges quickly, and is numerically stable. Aside from the theory, this method can be used in beam mechanics, viscoelastic systems, and other memory effect models.

To optimize infection control and bolster productivity within the poultry industry, it is imperative to accurately classify Chicken Eimeria species. There are several methods for determining Eimeria disease in chickens. Traditional methods involve watching for clinical symptoms, and macroscopic lesions, and studying the parasite’s biology and oocyst morphology. These methods are frequently time-consuming and labor-intensive, necessitating the manual collection and analysis of samples, which can be especially difficult in large chicken farms. Deep learning algorithms, on the other hand, provide automated, accurate, and non-invasive methods for the detection of Eimeria. This paper proposed a classification model for the automatic classification of chicken Eimeria species. The proposed model is mainly based on integrating neutrosophic set theory and InceptionV3 deep-learning architecture. Three primary phases make up the proposed chicken Eimeria species classification model: the data preprocessing phase, the neutrosophic image conversion phase, and the image classification phase. To address the issue of class imbalance in the adopted dataset and enhance the model’s generalizability, the random oversampling method, and data augmentation techniques are employed during the data preprocessing phase. The preprocessed data is considered to feed the neutrosophic set-based segmentation algorithm, where true, false, and intermediate subsets are extracted. Finally, the true subset is utilized to feed the optimized InceptionV3. To determine the optimal hyperparameter values for InceptionV3, a modified version of the Brown Bear optimization algorithm is proposed in this paper. To evaluate the effectiveness of the proposed model, a real benchmark dataset comprising images of different Eimeria species is adopted. The experimental results revealed that the proposed model offers a more efficient and accurate alternative to traditional methods and state-of-the-art models, enabling faster and more effective diagnosis and treatment of Eimeria infections. It achieved an overall accuracy, specificity, sensitivity, and F1-score of nearly 100%. Additionally, the results showed that the high performance of the proposed model can reduce labor costs and boost throughput, thereby enhancing economic viability even more.

Identity verification using authenticity evaluation of handwritten signatures is an important issue. There have been several approaches for the verification of signatures using dynamics of the signing process. Most of these approaches extract only global characteristics. With the aim of capturing both dynamic global and local features, this paper introduces a novel model for verifying handwritten dynamic signatures using neutrosophic rule-based verification system (NRVS) and Genetic NRVS (GNRVS) models. The neutrosophic Logic is structured to reflect multiple types of knowledge and relations among all features using three values: truth, indeterminacy, and falsity. These three values are determined by neutrosophic membership functions. The proposed model also is able to deal with all features without the need to select from them. In the GNRVS model, the neutrosophic rules are automatically chosen by Genetic Algorithms. The performance of the proposed system is tested on the MCYT-Signature-100 dataset. In terms of the accuracy, average error rate, false acceptance rate, and false rejection rate, the experimental results indicate that the proposed model has a significant advantage compared to different well-known models.