Linear systems often involve coefficients that are uncertain or imprecise due to inherent variability and vagueness in the data. In scenarios where only approximate or vague knowledge of the system parameters is available, traditional fuzzy logic is commonly employed. However, conventional fuzzy logic may be inadequate when defining a membership degree with a single, precise value proves difficult. In such cases, Single-Valued Trapezoidal Neutrosophic Numbers (SVTrNNs) offer a more suitable framework, as they account for indeterminacy, alongside truth and falsity. The solution of Single-Valued Trapezoidal Neutrosophic Linear Equations (SVTrNLEs) was explored in this study using an embedding approach. The approach reformulates the SVTrNLEs into an equivalent crisp linear system, enabling the application of conventional solution methods. The solution was then obtained using either the matrix inversion method or the gradient descent optimization algorithm implemented in PyTorch. The robustness and adaptability of gradient-based optimization techniques were thoroughly assessed. The learning process minimizes the residual error iteratively, with convergence behaviour and numerical stability analyzed across various parameter configurations. The results demonstrate rapid convergence, proximity to exact solutions, and significant robustness to parameter variability, highlighting the efficacy of gradient descent for solving uncertain linear systems. These findings provide a foundation for the extension of gradient-based methods to more complex systems and broader applications. Furthermore, the existence and uniqueness of the neutrosophic solution to an $n\times n$ linear system were rigorously analyzed, with numerical examples provided to assess the reliability and efficiency of the proposed methods.
The enhancement of governance and the implementation of effective anti-corruption strategies are critical for fostering public trust, accountability, and transparency in developing countries. In this study, a structured approach was adopted to identify and prioritize key strategies for improving governance and combating corruption in Nigeria. An extensive literature review, supplemented by expert consultation, led to the identification of eight fundamental strategies. To systematically determine their relative significance, the Fermatean Fuzzy Stepwise Weight Assessment Ratio Analysis (FF-SWARA) method was employed. The findings indicate that strengthening the legal and regulatory framework through effective enforcement, judicial reforms, and the establishment of independent oversight bodies with legal protection and operational autonomy are the most impactful measures. These strategies are essential for enhancing public trust, accountability, and transparency in Nigeria. The insights derived from this study provide a robust foundation for policymakers and stakeholders seeking to implement targeted anti-corruption reforms in Nigeria and other developing economies facing similar governance challenges.
Ensuring the integrity of goods during cold chain transportation remains a critical challenge in logistics, as it is essential to preserve product quality, freshness, and compliance with stringent safety standards. Strategic decision-making in this context requires the prioritization of customer requirements and the optimal allocation of limited operational resources. In response to these demands, an integrated Multi-Criteria Decision-Making (MCDM) model was developed by combining the Best-Worst Method (BWM), Quality Function Deployment (QFD), and Measurement of Alternatives and Ranking according to Compromise Solution (MARCOS) approach. Within this framework, BWM was utilized to determine the relative importance of user requirements, which were then mapped onto specific operational resources through QFD to identify critical resource elements and derive their corresponding weights. These weights, subsequently treated as evaluation criteria in the MARCOS method, were applied to assess the performance of Third-Party Logistics (3PL) providers. The proposed methodology was validated through a case study involving eight user requirements and seven key resources. The findings indicated that precise temperature control and delivery speed were the most critical user requirements, whereas advanced temperature sensors and vehicles with cooling systems were identified as the most significant resources. Based on the MARCOS evaluation, Provider 1 emerged as the most optimal 3PL alternative. This integrated decision-making model offers a systematic and data-driven approach for aligning customer priorities with resource capabilities, thereby enabling logistics providers to enhance service quality, operational efficiency, and strategic competitiveness in temperature-sensitive supply chains. The model also demonstrates practical scalability and adaptability across diverse cold chain scenarios.
Supply chain digitalization (SCD) has been recognized as a critical enabler of high-quality development in the manufacturing sector. To explore its influence mechanisms, an SCD indicator was constructed through textual analysis of corporate disclosures by Chinese manufacturing firms listed on the Shanghai and Shenzhen A-share markets from 2008 to 2022. Based on the theoretical lens of supply chain integration, the impact of SCD on high-quality development was empirically examined. The findings indicate that SCD significantly promotes high-quality development across manufacturing firms. Further analysis revealed that this relationship is positively mediated by two core mechanisms: supply chain collaborative innovation and the advancement of supply chain finance (SCF). These mediating effects were found to be strengthened under conditions of heightened environmental dynamism, underscoring the adaptive value of digital supply chain capabilities in volatile contexts. Heterogeneity analysis demonstrated that the positive effects of SCD are more pronounced in non-state-owned enterprises, firms in growth or decline stages, and those characterized by low levels of resource slack. Additionally, the long-term economic consequences of SCD were evaluated, and it was observed that enhanced digitalization contributes to the stable growth of firms’ long-term value by reinforcing their high-quality development trajectories. By clarifying the pathways through which SCD influences development outcomes, this study offers empirical evidence that enriches the existing body of literature on digital transformation within supply chains. Moreover, practical implications are provided for policy formulation and strategic decision-making aimed at fostering digitally integrated, innovation-driven, and financially resilient manufacturing ecosystems.
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