World Journal of Mathematics and Statistics is an international, peer-reviewed open access journal dedicated to advancing research the field of mathematics and statistics. The journal provides a rapid publication process to ensure wide dissemination of high-quality articles to scientists, professionals, and interested individuals worldwide. Our goal is to serve as an efficient, reliable, and trusted platform for scholars and readers, publishing cutting-edge research in the field.
Abstract: In modern manufacturing’s end-to-end production system, it is essential not only to take into account the production status of components and the final completion level of products, but also to incorporate the crucial factor of product qualification rate into the scope of consideration for enterprise production. According to consumer demand, the market requires that both the price and quality of finished goods be tested. This necessitates a comprehensive evaluation of whether to carry out various operations on finished products by analyzing cost factors across multiple dimensions - including inspection costs, disassembly costs, and replacement costs. The present study primarily utilizes well‑designed algorithms and fully applies statistical methods such as hypothesis testing, confidence intervals, and rejection regions to derive optimal solutions. These approaches enable the determination of how to inspect components and how to conduct qualification‑rate testing on finished products, thereby helping firms achieve maximum profit. Furthermore, the research takes specific practical conditions into account and proposes targeted, actionable decision schemes. By following these schemes, enterprises can more effectively plan and execute their production and operational activities, enhancing overall efficiency and competitiveness. In summary, integrating component-level inspection strategies with finished‑product qualification assessments within a cost‑benefit analytical framework provides a systematic pathway for manufacturers to align product quality assurance with economic objectives under real‑world constraints. This methodology supports data‑driven decision making and facilitates sustainable growth in increasingly demanding markets.Abstract: In modern manufacturing’s end-to-end production system, it is essential not only to take into account the production status of components and the final completion level of products, but also to incorporate the crucial factor of product qualification rate into the scope of consideration for enterprise production. According to consumer demand, the ma...Learn More
Abstract: Artificial neural networks (ANNs) are powerful models inspired by the structure and function of the human brain. They are widely used for tasks such as classification, prediction, and model recognition. This study examines the stability of fractional-order neural networks with neuronal conditions, dynamic behavior, synchronization, and delays of time "σ" . Synchronization and stability for delayed neural network models are two important aspects of dynamic behavior. For a calculated fractional-order, the state of the state variable wi(t) are synchronized with each other. Weight synchronization of wi (i=1, 2, 3,..., 6) provides coherent updates during training, helping neural networks to study stable models. The incommensurate fractional-orders are linked to a system where each dynamic component develops with a different value, i.e. qi ≠ qj (i≠j) is inconsistent. These fractional-orders are calculated for the system’s eigenvalues and their singular points within the stability region defined by the Matignon-based stability. As the time delay decreases, more activation functions are induced, and the variable state of w4(t) requires longer relaxation times to be more stable than the variable state of w3(t). The Grunwald-Letnikov method is used to solve a fractional neural network system numerically and effectively handle fractional derivatives. This approach helps to more accurately simulate memory in neural networks.Abstract: Artificial neural networks (ANNs) are powerful models inspired by the structure and function of the human brain. They are widely used for tasks such as classification, prediction, and model recognition. This study examines the stability of fractional-order neural networks with neuronal conditions, dynamic behavior, synchronization, and delays of ti...Learn More
Abstract: This paper discusses the optimality conditions for the strong efficient solutions of set-valued optimization problems. Firstly, by using the second-order weak subdifferential of set-valued mappings and the relationship between the strong efficient solutions of set-valued optimization problems and the optimal solutions of composite optimization problems, one establishes the optimality necessary and sufficient conditions of the strong efficient solutions for unconstrained set-valued optimization problems. Meanwhile, by using the second-order weak subdifferential of set- valued mappings, several optimality necessary and sufficient conditions of unconstrained composite optimization problems are obtained under the assumption of generalized cone sub-convexlikeness. Secondly, one introduces a class of saddle points for constrained set-valued optimization problems. Then, several sufficient optimality conditions for strong efficient solutions of constrained set-valued optimization problems are established under the assumptions of generalized cone sub-convexlikeness and saddle points for constrained set-valued optimization problems. Additionally, by using the second-order weak subdifferential of set-valued mappings, the sufficient optimality conditions for strong efficient solutions of constrained set-valued optimization problems are established under the assumption of generalized cone sub-convexlikeness. Finally, two optimality sufficient conditions for the optimal solutions of the constrained composite optimization problem are obtained under the assumption of generalized cone sub-convexlikeness.Abstract: This paper discusses the optimality conditions for the strong efficient solutions of set-valued optimization problems. Firstly, by using the second-order weak subdifferential of set-valued mappings and the relationship between the strong efficient solutions of set-valued optimization problems and the optimal solutions of composite optimization prob...Learn More
