A Novel Technique to Solve the Fuzzy System of Equations

The aim of this research is to apply a novel technique based on the embedding method to solve the n×n fuzzy system of linear equations (FSLEs). By using this method, the strong fuzzy number solutions of FSLEs can be obtained in two steps. In the first step, if the created n×n crisp linear system has a non-negative solution, the fuzzy linear system will have a fuzzy number vector solution that will be found in the second step by solving another created n×n crisp linear system. Several theorems have been proved to show that the number of operations by the presented method are less than the number of operations by Friedman and Ezzati’s methods. To show the advantages of this scheme, two applicable algorithms and flowcharts are presented and several numerical examples are solved by applying them. Furthermore, some graphs of the obtained results are demonstrated that show the solutions are fuzzy number vectorsThis research was funded by partially supported by Agencia Estatal de Investigación (AEI) of Spain under grant MTM2016-75140-P, co-financed by the European Community fund FEDER, and XUNTA de Galicia under grants ED431C 2019-02 and R2016-022S

On a regularized solution of the Cauchy problem for matrix factorizations of the Helmholtz equation

In this paper, we consider the problem of recovering solutions for matrix factorizations of the Helmholtz equation in a multidimensional bounded domain from their values on a part of the boundary of this domain, i.e., the Cauchy problem. An approximate solution to this problem is constructed based on the Carleman matrix method.Publisher's Versio

A Novel Technique to Control the Accuracy of a Nonlinear Fractional Order Model of COVID-19: Application of the CESTAC Method and the CADNA Library

In this paper, a nonlinear fractional order model of COVID-19 is approximated. For this aim, at first we apply the Caputo–Fabrizio fractional derivative to model the usual form of the phenomenon. In order to show the existence of a solution, the Banach fixed point theorem and the Picard–Lindelof approach are used. Additionally, the stability analysis is discussed using the fixed point theorem. The model is approximated based on Indian data and using the homotopy analysis transform method (HATM), which is among the most famous, flexible and applicable semi-analytical methods. After that, the CESTAC (Controle et Estimation Stochastique des Arrondis de Calculs) method and the CADNA (Control of Accuracy and Debugging for Numerical Applications) library, which are based on discrete stochastic arithmetic (DSA), are applied to validate the numerical results of the HATM. Additionally, the stopping condition in the numerical algorithm is based on two successive approximations and the main theorem of the CESTAC method can aid us analytically to apply the new terminations criterion instead of the usual absolute error that we use in the floating-point arithmetic (FPA). Finding the optimal approximations and the optimal iteration of the HATM to solve the nonlinear fractional order model of COVID-19 are the main novelties of this studyThe work of J.J.N. has been partially supported by the Xunta de Galicia under grant ED431C 2019/02, as well as by Instituto de Salud Carlos III and the Ministerio de Ciencia e Innovación of Spain, research grant COV20/00617. The work of S. Noeiaghdam has been supported by a grant from the Academic Council in the direction of the scientific school of Irkutsk National Research Technical University No. 14-NSH-RAN-2020S

Comparisons of SVM Kernels for Insurance Data Clustering

This paper will study insurance data clustering using Support Vector Machine (SVM) approaches. It investigates the optimum condition employing the three most popular kernels of SVM, i.e., linear, polynomial, and radial basis kernel. To explore sum insured datasets, kernel comparisons for Root Mean Square Error (RMSE) and density analysis have been provided. It employs these kernels to classify based on sum insured datasets. The objective of this research is to demonstrate to industrial researchers that data grouping may be accomplished in an organized, error-free, and efficient manner utilizing R programming and the SVM approach. In this study, we check the insurance data for the sum insured with statistical methods in the form of Model Performance Evaluation (MPE), Receiver Operating Characteristics (ROC), Area Under Curve (AUC), partial AUC (pAUC), smoothing, confidence intervals, and thresholds. Then, sum insured data are followed up to classify using SVM kernels. This paper finds new ideas for evaluating insurance data using the SVM approach with multiple kernels. This novel research emphasizes the statistical analysis methods for insurance data and uses the SVM method for more accurate data classification. Finally, it informs that this research is a pure finding, and there has never been any research on this subject. This research was conducted using the sum insured data as a sample from the Office of the Insurance Commission (OIC) in Thailand as an independent insurance institution providing actual data. Doi: 10.28991/ESJ-2022-06-04-014 Full Text: PD

Mixed convection of thermomicropolar AgNPs-GrNPs nanofluid: An application of mass-based hybrid nanofluid model

Here, a mass-based hybridity model is applied to inquire about the mixed convection of a thermomicropolar binary nanofluid (TMBNF) upon a shrinking and porous plate. The nanoparticles are the silver (AgNPs) and the graphene (GrNPs), in a spherical shape, suspended in an aqua base fluid. The applied methodology considers the masses of base fluid and nanoparticles as an alternative to the first and second nanoparticles volume fraction, according to the single-phase approach named the Tiwari-Das model. By using the similarity transformation technique, the dominating PDEs are changed to a system of ODEs that can be solved numerically by the bvp4c pattern of Matlab. To validate the numerical method, a comparison is implemented for the heat transfer, the shear stress, and the gradient of microrotation values, with results reported previously that consequently a supreme agreement is observed. The variations of the angular velocity, velocity, temperature distribution, gradient of microrotation, shear stress, and the heat transfer of the TMBNF with the prominent parameters are presented and analyzed by the tabular and graphical results. The originality of this work is related to the use of the mass-based model for TMBNF flow and the derivation of a new configuration of governing equations. It is concluded that the mass-based model with its significant benefits can be utilized successfully with tremendous assurance to abundant theoretical problems of micropolar binary nanofluid flow and heat transfer. New models for the nanofluid hybridity can undoubtedly be quite helpful in the many fields where cooling technologies are essential.The work of U⋅F.-G. was supported by the government of the Basque Country for the ELKARTEK21/10 KK-2021/00014 and ELKARTEK22/85 research programs, respectively

The Best Approximation of Generalized Fuzzy Numbers Based on Scaled Metric

The ongoing study has been vehemently allocated to propound an ameliorated α-weighted generalized approximation of an arbitrary fuzzy number. This method sets out to lessen the distance between the original fuzzy set and its approximation. In an effort to elaborate the study, formulas are designed for computing the ameliorated approximation by using a multitude of examples. The numerical samples will be exemplified to illuminate the improvement of the nearest triangular approximation (Abbasbandy et al., Triangular approximation of fuzzy numbers using α-weighted valuations, Soft Computing, 2019). A variety of features of the ameliorated approximation are then proved. © 2022 Tofigh Allahviranloo et al

Thermosolutal natural convection energy transfer in magnetically influenced casson fluid flow in hexagonal enclosure with fillets

Current disquisition is aimed to adumbrate thermosolutal convective diffusion transport in Casson fluid filled in hexagonal enclosure under effectiveness of inclined magnetic field. Partially iso-concentration and iso-temperature distributions at base wall of enclosure is provided along with incorporation of fillets at corners of flow domain. Governing formulation in 2D are expressed in a velocity-pressure, energy and concentration bal-ance equations. Numerical computations are executed by employing COMSOL Multiphysics software based on finite element scheme. Domain discretization in manifested by performing hybrid meshing in view of 2D ele-ments. Linear and quadric interpolating polynomials for pressure and other associated distributions are capi-talized. Non-linearized discretization system is handled by non-linear solver renowned as PARADISO. Results and code validation is assured by performing comparison and grid convergence test respectively. The impact of flow concerning variables by considering wide ranges like Casson parameter (0.1 <= beta <= 10), Rayleigh number (10(4) <= Ra <= 10(7)), Hartmann number (20 <= Ha <= 80) and Lewis number (0.1 <= Le <= 10) on velocity, isothermal and isoconcentration fields are visualized through graphs and tables. Visualization about kinetic energy along with heat and mass transfer rates are disclosed through graphs and tables.Funding The work of U.F.-G. was supported by the Government of the Basque Country for the ELKARTEK21/10KK-2021/00014 and ELKARTEK22/85 research programs, respectively