This work aims to apply the spherical fuzzy set (SFS), a flexible framework for handling ambiguous human opinions, to improve decision-making processes in recycled water. It specifically looks at the application of Sugeno-Weber (SW) triangular norms in the spherical fuzzy (SF) information domain, providing reliable approximations that are necessary for decision-making. A new class of aggregation operators is presented in this paper. These operators are specifically made for spherical fuzzy information systems and include the interval value spherical fuzzy Sugeno–Weber power weighted average (IVSFSWPA), interval value spherical fuzzy Sugeno–Weber power geometric (IVSFSWPWG), and interval value spherical fuzzy Sugeno–Weber power weighted average (IVSFSWPWA). The realistic features and special cases of these operators are demonstrated, highlighting how well they fit into practical scenarios. A new method for multi-attribute decision-making (MADM) is used for a range of real-world applications with different requirements or characteristics. The efficacy of the recommended methodologies is demonstrated with an example of a recycled water selection process. Additionally, a thorough comparison method is provided to show how the suggested aggregation strategies work and are relevant by contrasting their results with those of the current methods. The study's conclusion highlights the potential contribution of the recommended research to the advancement of decision-making techniques in dynamic and complex environments. It also summarizes its findings and discusses its prospects moving forward.
The incorporation of fractional calculus into nanofluid models has proven effective in capturing the complex dynamics of nanofluid flow and heat transfer, thereby enhancing the precision of predictions in this intricate field. In this study, the dynamics of a viscoelastic second-grade nanofluid model are examined through the application of the Laplace transform technique on a vertical plate. Initially, the model is formulated as coupled partial differential equations to describe the second-grade nanofluid system. The governing equations are then rendered dimensionless using appropriate dimensionless parameters. The non-dimensional model is subsequently generalized by introducing a modified Caputo fractional derivative operator. To model a homogenous nanofluid, nanoparticles of $\mathrm{Al}_2 \mathrm{O}_3$ in nanometer-sized form are suspended in mineral transformer oil. The Laplace transform is employed to solve the momentum, energy, and mass diffusion equations, providing analytical solutions. Graphical and tabular analyses are conducted to assess the influence of various physical parameters—including the fractional order, nanoparticle volume fraction, and time parameter—on the velocity, thermal, and concentration profiles. The results indicate that increasing the nanoparticle volume fraction, fractional order, and time parameter significantly enhances the rate of heat transfer. Additionally, it is observed that the velocity, temperature, and concentration profiles are notably affected by increasing the volume fraction of nanoparticles. The accuracy and reliability of the obtained solutions are validated through comparisons with existing literature. This work advances the understanding of nanofluid dynamics and presents valuable insights for industrial applications, particularly in enhancing heat transfer performance.
This study investigates the regional logistics efficiency of Sichuan Province, China, from 2011 to 2019, using a combination of the Data Envelopment Analysis-Banker, Charnes, and Cooper (DEA-BCC) model and the Tobit model. The primary objective is to assess the efficiency of the logistics industry and identify the key determinants influencing this efficiency within the context of high-quality development. A comprehensive input-output index system and a set of influencing factor variables were constructed to evaluate logistics performance across various regions of the province. The findings indicate that factors such as the level of economic development, urbanization, and geographical location significantly enhance regional logistics efficiency. In contrast, the level of informatization and the industrial structure exhibit clear inhibitory effects. Specifically, a higher degree of informatization does not necessarily correspond with improved logistics efficiency, potentially due to inefficiencies in technology adoption or uneven infrastructure development. Furthermore, the current industrial structure, with its reliance on traditional industries, may hinder the optimization of logistics systems. Based on these results, several policy recommendations are put forward, including the optimization of the industrial structure, better integration of information technologies in logistics processes, and the strategic utilization of Sichuan’s geographical advantages. This research provides valuable insights for policymakers aiming to enhance logistics efficiency as part of the region’s broader economic development strategy.
This study proposes an advanced framework for performance evaluation by extending the Malmquist Productivity Index (MPI) to accommodate interval data, addressing the inherent uncertainty and imprecision frequently encountered in institutional assessments. In many contexts, input-output data are often reported as intervals rather than precise values, which poses significant challenges for evaluating productivity changes. The extended MPI model allows for a more comprehensive analysis of performance by incorporating such interval data, thus providing a robust mechanism for assessing both progress and regression in the productivity of Decision-Making Units (DMUs). A case study on university departments is employed to demonstrate the practical application of this interval-based model. The results highlight notable variations in efficiency and technological advancement, offering valuable insights for institutional decision-makers. The proposed methodology enhances the accuracy of performance evaluation in dynamic and uncertain environments, making it a powerful tool for strategic planning and policy formulation. Furthermore, it is suggested that this interval-based approach offers a significant improvement over traditional models by accounting for the uncertainty present in real-world data. The study contributes to the broader field of strategic performance analytics by advancing the methodological understanding of productivity analysis, offering a more nuanced and reliable framework for institutional assessment.
Efficient classification of interval data presents considerable challenges, particularly when group overlaps and data uncertainty are prevalent. This study introduces an innovative two-stage Mixed Integer Programming (MIP) framework for discriminant analysis (DA), which is designed to minimize misclassification of vertices while effectively addressing the problem of overlapping groups. By incorporating interval data structures, the proposed model captures both the shared characteristics within groups and the distinct separations between them. The first stage of the model focuses on the identification of group-specific boundaries, while the second stage refines classification by incorporating probabilistic estimates of group memberships. A Monte Carlo simulation is employed to evaluate the robustness of the model under conditions of imprecision and noise, and the results demonstrate its superior capability in handling overlapping data and classifying uncertain observations. Validation through numerical experiments illustrates the model’s effectiveness in accurately resolving group overlaps, thereby improving classification performance. The approach offers significant advantages over traditional methods by probabilistically estimating group memberships, thus enhancing decision-making processes in uncertain environments. These findings suggest that the proposed MIP framework holds substantial promise for applications across a range of complex decision-making scenarios, such as those encountered in finance, healthcare, and engineering, where data imprecision is a critical concern.
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