The main goal of this paper is to propose a novel methodology that combines the spherical fuzzy rough CRITIC (Criteria Importance Through Inter Criteria Correlation) method with the TODIM (an acronym in Portuguese of interactive and multi-criteria decision making) method for supplier selection. Spherical fuzzy rough numbers are used to preserve both the hesitancy of individual experts and the disagreement among them, while TODIM grounds the ranking stage in prospect theory and thus in the bounded rationality of the decision makers. To demonstrate its practical applicability, the proposed framework is applied to a real-world case study in which three experts evaluate five equipment suppliers of a table tennis club against six criteria. Delivery performance and service emerge as the most influential criteria, and A3 is identified as the most suitable supplier. The robustness of the solution is examined by varying the attenuation factor over two orders of magnitude, across which the best alternative remains unchanged, and by comparison with spherical fuzzy rough TOPSIS, WASPAS and MULTIMOORA formulations and with a crisp CRITIC–TODIM baseline. The findings offer valuable insights for managers and policymakers in the sports industry.
Accurate and computationally efficient simulation of nonlinear Klein-Gordon and Sine-Gordon equations is important for analyzing nonlinear wave propagation, oscillatory dynamics and localized structures arising in engineering and physical systems. In this work, two differential quadrature approaches with cubic Uniformly Algebraic Trigonometric (UAT) and Uniformly Algebraic Hyperbolic (UAH) tension B-splines are proposed and compared. The spatial derivatives are discretized by using the corresponding spline-based DQM weighting coefficients. The resulting semi-discrete systems are integrated in time by the Runge-Kutta 4(3) scheme. The methods are tested on the one-dimensional Klein-Gordon and the one- and two-dimensional Sine-Gordon benchmarks. Accuracy is assessed through L ∞ , RMS, and relative errors, exact-numerical solution comparisons, grid- and time-dependent error behavior, and convergence analysis. Matrix/eigenvalue analysis is employed to investigate numerical stability, while computational complexity, CPU time, wall-clock time, and memory requirements are evaluated to assess efficiency. The UAT- and UAH-based formulations produce nearly identical numerical results under matched computational conditions. Representative errors remain bounded, ranging from approximately 10 –9 – 10 –10 for highly accurate Klein–Gordon cases 10 –4 – 10 –5 to for the considered Sine-Gordon benchmarks. The stability and computational analyses further demonstrate reliable performance with modest memory requirements. These results establish both tension B-spline DQM formulations as accurate and computationally viable alternatives for nonlinear wave problems in scientific and engineering applications.
In this paper, we introduced strong neutrosophic metric spaces (SNMS), which satisfied strong triangular inequalities and generalized the strong [Formula: see text]-metric spaces of Kirk and Shahzad [21]. For control functions [Formula: see text] on the membership component [Formula: see text] and [Formula: see text] on the indeterminacy and non-membership components [Formula: see text] and [Formula: see text], the associated pair [Formula: see text] satisfied triangle-type inequalities with respect to the underlying [Formula: see text]-norm and [Formula: see text]-conorm. Using this pair, we defined a Generalized Neutrosophic Reich–Rus–Ćirić Control Contraction (NRRC–CC) via a six-term contractive condition. We proved that a self-map satisfying an NRRC–CC condition on a complete SNMS admitted a unique fixed point, characterized its contraction coefficients, and obtained a Cauchy-completeness criterion. We also gave an example of an exponential SNMS and showed that not every neutrosophic metric space is strong. Finally, we stated and proved the fixed point theorem on SNMS using a single six-term contractive condition.
This paper presents a two-phase Markovian queueing model designed to capture essential operational dynamics of cloud data centers. The model distinguishes between phase 1 with unrestricted capacity and subsequently, phase 2 with limited capacity, reflecting how cloud systems manage flexible workloads before encountering critical bottlenecks. The model further integrates realistic features, including working vacations for energy-efficient service, disaster events with standby server recovery to ensure continuity, and customer balking to represent user behavior under congestion. Steady-state analysis is carried out using the matrix-geometric method, along with performance and cost analyses to evaluate system efficiency and resilience. Numerical results illustrate the impact of various system parameters on service quality and operational effectiveness. The study demonstrates how the proposed model supports the design of cloud infrastructure that remains available, adapts to fluctuating demand, and sustains performance even under disaster scenarios with an emphasis on energy-conscious and user-oriented cloud systems.
This work examines the existence of positive 𝜔-periodic solutions for a class of fourth-order neutral differential equations involving distributed delays. We establish a set of sufficient criteria to ensure that such solutions exist. Our approach relies on the application of the Krasnoselskii fixed point theorem, which plays a central role in the analysis. To further demonstrate the practicality and relevance of our theoretical results, we also include illustrative examples that support and clarify the main findings.
