The main goal of this article is to reveal a new generalized version of the q-linear Diophantine fuzzy set (q-LDFS) named spherical q-linear Diophantine fuzzy set (Sq-LDFS). The existing concepts of intuitionistic fuzzy set (IFS), q-rung orthopair fuzzy set (q-OFS), linear Diophantine fuzzy set (LDFS), and spherical fuzzy set have a wide range of applications in decision-making problems, but they all have strict limitations in terms of membership degree, non-membership degree, and uncertainty degree. We moot the article of the spherical q-linear Diophantine fuzzy set (Sq-LDFS) with control factors to alleviate these limitations. A Spherical q-linear Diophantine fuzzy number structure is independent of the selection of the membership grades because of its control parameters in three membership grades. An Sq-LDFS with a parameter estimation process can be extremely useful for modeling uncertainty in decision-making (DM). By using control factors, Sq-LDFS may classify a physical system. We highlight some of the downsides of q-LDFSs. By using algebraic norms, we offer some novel operational laws for Sq-LDFSs. We also introduced the weighted average and weighted geometric aggregation operators and their fundamental laws and properties. Furthermore, we proposed the algorithms for a multicriteria decision-making approach with graphical representation. Moreover, a numerical illustration of using the proposed methodology for Sq-LDF data for emergency decision-making is presented. Finally, a comparative analysis is presented to examine the efficacy of our proposed approach.

It is undeniable that convex and non-convex functions play an important role in optimization. As a result of its behavior, convexity also plays a significant role in discussing inequalities. It is clear that convexity and stochastic processes are intertwined. The stochastic process is a mathematical model that describes how systems or phenomena fluctuate randomly. Probability theory generally says that the convex function applied to the expected value of a random variable is bounded above by the expected value of the random variable's convex function. Furthermore, the deep connection between convex inequalities and stochastic processes offers a whole new perspective on the study of inequality. Although Godunova-Levin functions are well known in convex theory, their properties enable us to determine inequality terms with greater accuracy than those obtained from convex functions. In this paper, we established a more refined form of Hermite-Hadamard and Jensen type inequalities for generalized interval-valued h-Godunova-Levin stochastic processes. In addition, we provide some examples to demonstrate the validity of our main findings.

The single-valued neutrosophic hesitant fuzzy set (SV-NHFS) is a hybrid structure of the single-valued neutrosophic set and the hesitant fuzzy set that is designed for some incomplete, uncertain, and inconsistent situations in which each element has a few different values designed by the truth membership hesitant function, indeterminacy membership hesitant function, and falsity membership hesitant function. A strategic decision-making technique can help the decision-maker accomplish and analyze the information in an efficient manner. However, in our real lives, uncertainty will play a dominant role during the information collection phase. To handle such uncertainties in the data, we present a decision-making algorithm in the SV-NHFS environment. In this paper, we first presented the basic operational laws for SV-NHF information under Einstein's t-norm and t-conorm. Furthermore, important properties of Einstein operators, including the Einstein sum, product, and scalar multiplication, are done under SV-NHFSs. Then, we proposed a list of novel aggregation operators' names: Single-valued neutrosophic hesitant fuzzy Einstein weighted averaging, weighted geometric, order weighted averaging, and order weighted geometric aggregation operators. Finally, we discuss a multi-attribute decision-making (MADM) algorithm based on the proposed operators to address the problems in the SV-NHF environment. A numerical example is given to illustrate the work and compare the results with the results of the existing studies. Also, the sensitivity analysis and advantages of the stated algorithm are given in the work to verify and strengthen the study.

In this paper, we investigate the qualitative behavior of the fuzzy difference equation

$$z_{n+1}=\frac{A{z}_{n-s}}{B+C\prod _{i=0}^s{z}_{n-i}}$$

where $n\in {\mathbb{N}}_0=\mathbb{N}\cup \left\{0\right\},(z_n)$ is a sequence of positive fuzzy numbers, $A,B,C$ and the initial conditions $z_{-j},j=0,1,...,s$ are positive fuzzy numbers and $s$ is a positive integer. Moreover, two examples are given to verify the effectiveness of the results obtained.

Taking into account the significance of spherical hesitant fuzzy sets, this research concentrates on an innovative multi-criteria group decision-making technique for dealing with spherical hesitant fuzzy (SHF) situations. To serve this purpose, we explore SHF Aczel Alsina operational laws such as the Aczel-Alsina sum, Aczel-Alsina product and Aczel-Alsina scalar multiplication as well as their desirable characteristics. This work is based on the fact that aggregation operators have significant operative adaptability to aggregate the uncertain information under the SHF context. With the aid of Aczel-Alsina operators, we develop SHF Aczel-Alsina geometric aggregation operators to address the complex hesitant uncertain information. In addition, we describe and verify several essential results of the newly invented aggregation operators. Furthermore, a decision aid methodology based on the proposed operators is developed using SHF information. The applicability and viability of the proposed methodology is demonstrated by using a case study related to breast cancer treatment. Comprehensive parameter analysis and a systematic comparative study are also carried out to ensure the dependability and validity of the works under consideration.

For entire heat transfer practitioners from the last ten years, heat transmission performance in cooling and heating applications has become foremost concern. Hence, research towards innovative heat transference fluids is enormously powerful and stimulating. This study examines flow and thermal management in axisymmetric magneto hydrodynamic Polyethylene glycol (PEG) based hybrid nanofluid flow induced by a swirling cylinder. Flow and heat transfer is analyzed and compared for PEG+ Cu₂O + MgO and PEG+Graphene+ Cu + Ag hybrid nanofluid flow. Shooting technique (R-K 4^th order) is applied to work out the flow equations numerically. Simulated results are demonstrated via graphs. The computational results are validated with the published research work and found a modest concurrence. The foremost outcome of this investigation is found to be the axial, swirl and radial velocities in hybrid nanofluid are observed to decay with improvement in Reynolds number, nanofluid volume fraction and magnetic parameter. Platelet shaped nanoparticle colloidal suspension exhibit more decaying axial, swirl and radial velocity compared to spherical shaped nanoparticle colloidal suspension. It is detected that heat transmission rate is higher in PEG + Cu₂O + MgO Hybrid nanofluid compared with PEG + Graphene + Cu + Ag Hybrid nanofluid. For cooling purpose one can adopt PEG+Cu₂O + MgO hybrid nanofluid.

This paper is concerned with the study of nonlocal fractional differential equation of sobolev type with impulsive conditions. An associated integral equation is obtained and then considered a sequence of approximate integral equations. By utilizing the techniques of Banach fixed point approach and analytic semigroup, we obtain the existence and uniqueness of mild solutions to every approximate solution. Then, Faedo-Galerkin approximation is used to establish certain convergence outcome for approximate solutions. In order to illustrate the abstract results, we present an application as a conclusion.

The dynamical behaviour and thermal transportation feature of mixed convective Casson bi-phasic flows of water-based ternary Hybrid nanofluids with different shapes are examined numerically in a Darcy- Brinkman medium bounded by a vertical elongating slender concave-shaped surface. The mathematical framework of the present flow model is developed properly by adopting the single-phase approach, whose solid phase is selected to be metallic or metallic oxide nanoparticles. Besides, the influence of thermal radiation is taken into consideration in the presence of an internal variable heat generation. A set of feasible similarity transformations are applied for the conversion of the governing PDEs into a nonlinear differential structure of coupled ODEs. An advanced differential quadrature algorithm is employed herein to acquire accurate numerical solutions for momentum and energy equations. Results of the conducted parametric study are explained and revealed in graphs using bvp5c in MATLAB to solve the governing system. The solution with three mixture compositions is provided (Type-I and Type-II). Al₂O₃ (Platelet), GNT (Cylindrical), and CNTs (Spherical), Type-II mixture of copper (Cylindrical), silver (Platelet), and copper oxide (Spherical). In comparison to Type-I ternary combination Type-II ternary mixtures is lesser in terms of the temperature distribution. The skin friction coefficient is more in Type-1 compared to Type-2.

In this manuscript, we aim to establish a connection between the concept of inequalities and the novel Center-Radius order relation. The idea of a Center-Radius (CR)-order interval-valued Godunova-Levin (GL) function is introduced by referring to a total order relation between two intervals. Consequently, convexity and nonconvexity contribute to different kinds of inequalities. In spite of this, convex theory turns to Godunova-Levin functions because they are more efficient at determining inequality terms than other convexity classes. Our application of these new definitions has led to many classical and novel special cases that illustrate the key findings of the paper. Using total order relations between two intervals, this study introduces CR- $(h_1,h_2)$-Goduova-Levin functions. It is clear from their properties and widespread usage that the Center-Radius order relation is an ideal tool for studying inequalities. This paper discusses various inequalities based on the Center-Radius order relation. With the CR-order relation, we can first derive Hermite-Hadamard ( $\mathcal{H}\mathcal{.}\mathcal{H}$) inequalities and then develop Jensen-type inequality for interval-valued functions ( $\mathcal{I}\mathcal{V}\mathcal{F}\mathcal{S}$) of type $(h_1,h_2)$-Godunova-Levin function. Furthermore, the study includes examples to support its conclusions.

This paper proposes Polak-Ribi $\stackrel{`}{e}$re-Polyak (PRP) conjugate gradient (CG) directions based on two efficient scaling strategies. The first scaling parameter is determined by approaching the quasi-Newton direction, and the second by utilizing the well-known Barzilai-Borwein approach. In addition, we proposed two directions that satisfy the sufficient descent criterion regardless of the line search strategy. The proposed directions lead to a matrix-free algorithm for solving monotone-constrained nonlinear systems. The proposed algorithm's global convergence analysis is presented using some underlying assumptions. Furthermore, a detailed numerical comparison with other existing algorithms revealed that the proposed algorithm is both efficient and effective. Finally, the proposed technique is applied to the motion control problem of a two-joint planar robotic manipulator.