This research presents a novel approach to supplier selection by integrating economic, environmental, and ethical criteria. The case study of Company 3B, a food production company, illustrates this process. Expert decision-making, using a fuzzy-rough approach, is supported by the fuzzy-rough Logarithm Methodology of Additive Weights (LMAW) and the fuzzy-rough modified Measurement Alternatives and Ranking according to Compromise Solution (MARCOS) methods. The fuzzy-rough LMAW method helps determine the importance of criteria, revealing that experts consider the economic criterion the most significant. The Modified MARCOS (M-MARCOS), a simplified version of the MARCOS method, is used to rank suppliers. Results show that Supplier S3 performs the best. These findings are validated through comparisons with other fuzzy-rough methods and a sensitivity analysis. With the MARCOS method comparisons confirming a consistent ranking order, this paper advances supplier selection methodology by introducing a novel approach and improving the usability of the MARCOS method through modifications.

Diverse fields of modern science, including mathematical modeling and physics, plasma physics, atmospheric sciences, marine sciences, hydrodynamics, nonlinear mechanics, and other complex nonlinear physical phenomena, are expressed through Nonlinear Partial Differential Equations (NLPDEs). Exact solutions play an important role in understanding the behavior of solitary wave solutions and the dynamical properties of significant outcomes for higher-dimensional NLPDEs. As an integrable extension of the nonlinear Schrödinger equation, the nonlocal Kundu-Eckhaus model comprehends higher-order nonlinearities and nonlocal effects. The stability properties of dark, bright, periodic multiple, and singular soliton solutions to the nonlocal Kundu-Eckhaus (KE) equation within the Parity-Time (PT) symmetry model are studied here, whereas past studies have neglected the effects of nonlocal interactions and PT symmetry. is a well-established method, particularly for depicting wave dynamics in nonlinear optical and quantum systems. We attain exact traveling wave solutions evolved in hyperbolic and trigonometric forms, representing several classes of solitons by applying this method. The findings elucidate that the obtained soliton solutions are stable under small perturbations, highlighting their robustness and the persistence of localized waveforms in nonlocal circumstances. We plotted 3D, 2D, and contour graphs for simulating our findings using MATLAB. This research sheds light on the mysterious understanding of nonlocal nonlinear wave behaviors and offers analytical methodologies for future scrutiny in fields such as optical physics and complex nonlinear systems.

This paper investigates the existence, uniqueness, and monotonicity of positive solutions for a new class of hybrid nonlinear fractional integro-differential equations involving the Caputo–Fabrizio derivative. Unlike the classical Caputo operator, the Caputo–Fabrizio derivative is characterized by a non-singular exponential kernel, which leads to improved analytical tractability and better modeling of memory effects. Using Dhage's fixed point theorem, sufficient conditions for the well-posedness of the problem are derived. A concrete example is provided to demonstrate the effectiveness of the theoretical results, showing the relevance of the Caputo–Fabrizio approach in fractional modeling.

Conventional point-based algorithms largely ignore the strict sequential order of rotating multi-beam Light Detection and Ranging (LiDARs). We exploit this intrinsic structure by modeling each scan ring as a discrete curve on a conical manifold, encoded as a one-dimensional complex-valued signal. This representation preserves full 3D information while enabling efficient, principled computation of geodesic curvature via discrete difference calculus. Augmented with local smoothness and range-gradient features, this curvature forms the basis of an unsupervised classification pipeline that uses adaptive ring-wise thresholds to label points as planar, edge, or corner features. A scan-topology graph then aggregates these 1D labels into coherent 3D primitives, all in linear time. Experiments on synthetic and large-scale urban datasets confirm the method's theoretical accuracy and practical utility. Our C++ implementation processes at over 80 Frames Per Second (FPS) on a single Central Processing Unit (CPU) core, significantly outperformings traditional Principal Component Analysis (PCA)-based and clustering methods in geometric accuracy, label purity, and temporal stability. By uniting first-principles differential geometry with real-time performance, our framework provides a transparent, parameter-light alternative to learning-based pipelines, offering robust landmarks for Simultaneous Localization and Mapping (SLAM) and consistent semantics for dynamic scene understanding.

In the present paper, we study the linear stability of perturbations around the Couette flow for a two dimensional compressible non-isentropic Euler-Poisson system in the domain . A Lyapunov type instability result for the density and the temperature is obtained, and in particular, the inviscid damping for the solenoidal component of the velocity field is proved.

The influence of Arrhenius kinetics on magneto-convective flows in regulating temperature variation within the poro-elastic medium in several thermal, industrial, and engineering applications, such as the control of the hot molten, formation of crystals, cooling of nuclear reactors, filtration, and many more, is investigated in the present study. The exothermic nature of the chemical reaction based on Arrhenius, Sensitized, and Bimolecular kinetics suggests nonlinear heat and mass transfer. In this regard, governing equations are formulated for solid displacement in porous materials, fluid flow velocity, energy, and concentration with appropriate boundary conditions. Numerical solutions for nonlinear coupled dimensionless boundary value problems are obtained using the Spectral Chebyshev Collocation Method (SCCM) and Spectral Quasi-Linearization Method (SQLM). The two solutions are shown to be convergent. The results are further validated through the fourth-order Shooting-Runge-Kutta Scheme and presented in graphical and tabular forms. The significant contribution to knowledge in the present study reveals that the reaction parameter is an increasing function of solid displacement, flow velocity, temperature, and concentration. Similarly, increasing fluid activation energy and buoyancy values encourage solid displacement, maximum flow velocity, and temperature distribution within the flow channel while decreasing nanoparticle concentration.

Fractional inequalities and interval analysis are interdependent mathematical fields that have received much interest in recent years. Both concepts have a lot of applications in the field of applied sciences such as physics, signal processing, mathematical modeling, control theory, numerical analysis, uncertainty quantification, engineering and optimization problems. In this article, we present a new concept between two intervals related to center-radius ordered relations. First, we introduce the new definition, namely, interval-valued center-radius order generalized preinvex function. Further, we establish the novel perspective of the Hermite-Hadamard type inequality via a newly investigated concept pertaining to the Riemann-Liouville fractional integral operator in the frame of interval analysis. In addition, fractional Fejér type inequality of the first and second kind is also investigated via a newly introduced concept. Finally, we establish the fractional Pachpatte-type inequality in the frame of interval analysis. The graphical, numerical, and literature validity of the presented inequalities are also estimated. Some special instances of our general results are also stated in the form of corollaries and remarks. The present research provides an improved understanding of integral inequalities with fractional integral operators.

Let us consider the finite commutative ring R, whose unity is 10. The weakly zero-divisor graph, denoted by WΓ(R), is an undirected graph whose distinct vertices c1 and c2 are adjacent if and only if, there exist r ∈ ann(c1) and s ∈ ann(c2) that satisfy the condition rs = 0. This article finds the Seidel Laplacian and Seidel signless Laplacian spectrum for the graph WΓ(Zn) for various values of n.

The present paper aims to explore subclasses of analytic functions that extend the class of Janowski-type functions. We examine specific convolution conditions that ensure functions h fall within the generalized Janowski-type classes of starlike and convex functions. These conditions will serve as foundational results for further analysis in this study. Additionally, we provide sufficient conditions and neighborhood results pertinent to functions within the starlike class. Finally, we investigate the invariance properties of the operator hμ(ϑ) = (1 − μ)ϑ + μh(ϑ), 0 < μ < 1, as it applies to functions in this classification.

Disorders of the skin have been identified as skin diseases. These medical disorders may involve severe skin manifestations, including allergic reactions, frustration, and itching. Numerous skin disorders may be inherited, while other aspects may be caused by lifestyle. To diagnose the various skin disorders based on the symptoms of skin diseases, we introduce the novel idea of Interval-Valued T-Spherical Fuzzy Set (IV-TSFS) that significantly enhances the ability to handle vagueness and unpredictability in the data being gathered. The IV-TSFS takes the concept of T-SFS by incorporating Interval Values (IVs). This innovation greatly improves the capacity to represent and manage uncertainty because they offer a structured and flexible framework that captures real-world ambiguity, vagueness, and unpredictability as compared to other classical fuzzy models. In this article, we construct the extended conventional IV-TSF Evaluation based on Distance from Average Solution (EDAS) approach by using the conventional Evaluation based on Distance from Average Solution (EDAS) method and also identifying a wide range of possibilities and understanding the potential variability in outcomes, which is especially useful in Decision-Making (DM) scenarios. This method provides a balanced view of each alternative's performance, helping decision-makers to rank and select the most suitable option effectively. It is the most powerful way to visualize and compare the performance of various alternatives in a structured and quantitative manner. Firstly, we briefly review the description of T-SFSs and IV-TSFSs and discuss the score function Ṩcr(₮), accuracy function Ἇcr(₮), and the basic Operational Laws (OLs) of IV-TSFVs. Next, we explain the extensive interventions of the extended conventional Interval-Valued T-Spherical Fuzzy (IV-TSF) EDAS method to cope with uncertain and unreliable information, which is especially useful in DM scenarios. Finally, a numerical example is provided to effectively diagnose the favorable skin disease based on the symptoms of skin diseases by using the IV-TSF EDAS approach, and several comparative results of our proposed model with other existing Aggregation Operators (AOs) are carried out to demonstrate the invaluable benefits associated with this strategy.