An Intelligent MCGDM Model in Green Suppliers Selection Using Interactional Aggregation Operators for Interval-Valued Pythagorean Fuzzy Soft Sets

Green supplier selection is an important debate in green supply chain management(GSCM),attracting global attention from scholars,especially companies and policymakers.Companies frequently search for new ideas and strategies to assist them in realizing sustainable development.Because of the speculative character of human opinions,supplier selection frequently includes unreliable data,and the interval-valued Pythagorean fuzzy soft set(IVPFSS)provides an exceptional capacity to cope with excessive fuzziness,inconsistency,and inexactness through the decision-making procedure.The main goal of this study is to come up with new operational laws for interval-valued Pythagorean fuzzy soft numbers(IVPFSNs)and create two interaction operators-the intervalvalued Pythagorean fuzzy soft interaction weighted average(IVPFSIWA)and the interval-valued Pythagorean fuzzy soft interaction weighted geometric(IVPFSIWG)operators,and analyze their properties.These operators are highly advantageous in addressing uncertain problems by considering membership and non-membership values within intervals,providing a superior solution to other methods.Moreover,specialist judgments were calculated by the MCGDM technique,supporting the use of interaction AOs to regulate the interdependence and fundamental partiality of green supplier assessment aspects.Lastly,a statistical clarification of the planned method for green supplier selection is presented.

Solution approximations for a mathematical model of relativistic electrons with beta derivative

The main aim of this paper is to obtain the exact and semi-analytical solutions of the nonlinear Klein-Fock-Gordon(KFG)equation which is a model of relativistic electrons arising in the laser thermonuclear fusion with beta derivative.For this purpose,both the modified extended tanh-function(mETF)method and the homotopy analysis method(HAM)are used.While applying the mETF the chain rule for beta derivative and complex wave transform are used for obtaining the exact solution.The advantage of this procedure is that discretization or normalization is not required.By applying the mETF,the exact solutions are obtained.Also,by applying the HAM semi-analytical results for the considered equation are acquired.In HAM?curve gives us a chance to find the suitable value of the for the convergence of the solution series.Also,comparative graphical representations are given to show the effectiveness,reliability of the methods.The results show that the m ETF and HAM are reliable and applicable tools for obtaining the solutions of non-linear fractional partial differential equations that involve beta derivative.This study can bring a new perspective for studies on fractional differential equations.On the other hand,it can be said that scientists can apply the considered methods for different mathematical models arising in physics,chemistry,engineering,social sciences and etc.which involves fractional differentiation.Briefly the results may cause a new insight who studies on relativistic electron modelling.

An Innovative Technique for Constructing Highly Non-Linear Components of Block Cipher for Data Security against Cyber Attacks

The rapid advancement of data in web-based communication has created one of the biggest issues concerning the security of data carried over the internet from unauthorized access.To improve data security,modern cryptosystems use substitution-boxes.Nowadays,data privacy has become a key concern for consumers who transfer sensitive data from one place to another.To address these problems,many companies rely on cryptographic techniques to secure data from illegal activities and assaults.Among these cryptographic approaches,AES is a well-known algorithm that transforms plain text into cipher text by employing substitution box(S-box).The S-box disguises the relationship between cipher text and the key to guard against cipher attacks.The security of a cipher using an S-box depends on the cryptographic strength of the respective S-box.Therefore,various researchers have employed different techniques to construct high order non-linear S-box.This paper provides a novel approach for evolving S-boxes using coset graphs for the action of the alternating group A5 over the finite field and the symmetric group S256.The motivation for this work is to study the symmetric group and coset graphs.The authors have performed various analyses against conventional security criteria such as nonlinearity,differential uniformity,linear probability,the bit independence criterion,and the strict avalanche criterion to determine its high cryptographic strength.To evaluate its image application performance,the proposed S-box is also used to encrypt digital images.The performance and comparison analyses show that the suggested S-box can secure data against cyber-attacks.

An Artificial Intelligence Approach for Solving Stochastic Transportation Problems

Recent years witness a great deal of interest in artificial intelligence(AI)tools in the area of optimization.AI has developed a large number of tools to solve themost difficult search-and-optimization problems in computer science and operations research.Indeed,metaheuristic-based algorithms are a sub-field of AI.This study presents the use of themetaheuristic algorithm,that is,water cycle algorithm(WCA),in the transportation problem.A stochastic transportation problem is considered in which the parameters supply and demand are considered as random variables that follow the Weibull distribution.Since the parameters are stochastic,the corresponding constraints are probabilistic.They are converted into deterministic constraints using the stochastic programming approach.In this study,we propose evolutionary algorithms to handle the difficulties of the complex high-dimensional optimization problems.WCA is influenced by the water cycle process of how streams and rivers flow toward the sea(optimal solution).WCA is applied to the stochastic transportation problem,and obtained results are compared with that of the new metaheuristic optimization algorithm,namely the neural network algorithm which is inspired by the biological nervous system.It is concluded that WCA presents better results when compared with the neural network algorithm.

An Efficient Meshless Method for Hyperbolic Telegraph Equations in (1 + 1) Dimensions

Numerical solutions of the second-order one-dimensional hyperbolic telegraph equations are presented using the radial basis functions.The purpose of this paper is to propose a simple novel direct meshless scheme for solving hyperbolic telegraph equations.This is fulfilled by considering time variable as normal space variable.Under this scheme,there is no need to remove time-dependent variable during the whole solution process.Since the numerical solution accuracy depends on the condition of coefficient matrix derived from the radial basis function method.We propose a simple shifted domain method,which can avoid the full-coefficient interpolation matrix easily.Numerical experiments performed with the proposed numerical scheme for several second-order hyperbolic telegraph equations are presented with some discussions.

A Mathematical Approach for Generating a Highly Non-Linear Substitution Box Using Quadratic Fractional Transformation

Nowadays,one of the most important difficulties is the protection and privacy of confidential data.To address these problems,numerous organizations rely on the use of cryptographic techniques to secure data from illegal activities and assaults.Modern cryptographic ciphers use the non-linear component of block cipher to ensure the robust encryption process and lawful decoding of plain data during the decryption phase.For the designing of a secure substitution box(S-box),non-linearity(NL)which is an algebraic property of the S-box has great importance.Consequently,the main focus of cryptographers is to achieve the S-box with a high value of non-linearity.In this suggested study,an algebraic approach for the construction of 16×16 S-boxes is provided which is based on the fractional transformation Q(z)=1/α(z)^(m)+β(mod257)and finite field.This technique is only applicable for the even number exponent in the range(2-254)that are not multiples of 4.Firstly,we choose a quadratic fractional transformation,swap each missing element with repeating elements,and acquire the initial S-box.In the second stage,a special permutation of the symmetric group S256 is utilized to construct the final S-box,which has a higher NL score of 112.75 than the Advanced Encryption Standard(AES)S-box and a lower linear probability score of 0.1328.In addition,a tabular and graphical comparison of various algebraic features of the created S-box with many other S-boxes from the literature is provided which verifies that the created S-box has the ability and is good enough to withstand linear and differential attacks.From different analyses,it is ensured that the proposed S-boxes are better than as compared to the existing S-boxes.Further these S-boxes can be utilized in the security of the image data and the text data.

Modeling of Dark Solitons for Nonlinear Longitudinal Wave Equation in a Magneto-Electro-Elastic Circular Rod

In this paper,sub equation and (1=G’)-expansion methods are proposed to construct exact solutions of a nonlinear longitudinal wave equation(LWE)in a magneto-electro-elastic circular rod.The proposed methods have been used to construct hyperbolic,rational,dark soliton and trigonometric solutions of the LWE in the magnetoelectro-elastic circular rod.Arbitrary values are given to the parameters in the solutions obtained.3D,2D and contour graphs are presented with the help of a computer package program.Solutions attained by symbolic calculations revealed that these methods are effective,reliable and simple mathematical tool for finding solutions of nonlinear evolution equations arising in physics and nonlinear dynamics.

Manakov model of coupled NLS equation and its optical soliton solutions

In the field of maritime transport,motion and energy,the dynamics of deep-sea waves is one of the major problems in ocean science.A mathematical modeling of dynamics of solitary waves in deep sea under the two-layer stratification leads to NLS equation,and consequently,the interaction two of them can be formulated by coupled NLS equation.In this work,extended auxiliary equation and the exp(−ω(χ))-expansion methods are employed to make the optical solutions of the Manakov model of coupled NLS equation.The methods used in this paper,in addition to providing the analysis of individual wave solutions,also provide general optical solutions.Some previously known solutions can be obtained by some special selections of parameters obtained by solving systems of algebraic equations.At this stage,it is more practical and convenient to apply methods with a symbolic calculation system.

Soliton solutions for nonlinear variable-order fractional Korteweg-de Vries(KdV)equation arising in shallow water waves

Nonlinear fractional differential equations provide suitable models to describe real-world phenomena and many fractional derivatives are varying with time and space.The present study considers the advanced and broad spectrum of the nonlinear(NL)variable-order fractional differential equation(VO-FDE)in sense of VO Caputo fractional derivative(CFD)to describe the physical models.The VO-FDE transforms into an ordinary differential equation(ODE)and then solving by the modified(G/G)-expansion method.For ac-curacy,the space-time VO fractional Korteweg-de Vries(KdV)equation is solved by the proposed method and obtained some new types of periodic wave,singular,and Kink exact solutions.The newly obtained solutions confirmed that the proposed method is well-ordered and capable implement to find a class of NL-VO equations.The VO non-integer performance of the solutions is studied broadly by using 2D and 3D graphical representation.The results revealed that the NL VO-FDEs are highly active,functional and convenient in explaining the problems in scientific physics.

Analytic approximate solutions of diffusion equations arising in oil pollution

In this article,modified versions of variational iteration algorithms are presented for the numerical simulation of the diffusion of oil pollutions.Three numerical examples are given to demonstrate the applicability and validity of the proposed algorithms.The obtained results are compared with the existing solutions,which reveal that the proposed methods are very effective and can be used for other nonlinear initial value problems arising in science and engineering.

Impact of Joule heating and multiple slips on a Maxwell nanofluid flow past a slendering surface

This manuscript presents a study of three-dimensional magnetohydrodynamic Maxwell nanofluid flow across a slendering stretched surface with Joule heating.The impact of binary chemical reactions,heat generation,thermal radiation,and thermophoretic effect is also taken into consideration.The multiple slip boundary conditions are utilized at the boundary of the surface.The appropriate similarity variable is used to transfer the flow modeled equations into ODEs,which are numerically solved by the utilization of the MATLAB bvp4c algorithm.The involved parameter's impact on the concentration,velocity,and temperature distribution are scrutinized with graphs.The transport rates(mass,heat)are also investigated using the same variables,with the results reported in tabulated form.It is seen that the fluid relaxation,magnetic,and wall thickness characteristics diminish the velocities of fluid.Further,the velocity,concentration,and temperature slip parameters reduce the velocities of fluid,temperature,and concentration distribution.The results are compared to existing studies and shown to be in dependable agreement.

New mathematical modelings of the human liver and hearing loss systems with fractional derivatives

Fractional derivatives are significant mathematical instruments that have been practiced to model real phenomena in different areas of science.Through the current investigation study,we develop the Human Liver and Hearing Loss models by employing three fractional operators called Atangana-Baleanu-Caputo,Caputo and Caputo-Fabrizio derivatives.The numerical techniques regarding the basic theories of fractional analysis considered to obtain the approximate solutions of the offered systems.Indeed,approximate results are presented for showing the efficacy of the methods during graphs of solutions.To see the performance of the suggested models,different fractional orders are tested.

Dynamics of tuberculosis in HIV-HCV co-infected cases

This work presents a compartmental mathematical model describing transmission and spread of tuberculosis(TB)in HIV-HCV co-infected cases.The novelty of this work comes through mathematical modeling of the dynamics of TB not only in HIV but also in HIV-HCV co-infected cases.We analyze the formulated model by proving the existence of disease-free equilibrium solution.We calculate the basic reproduction number Ro,of the model and construct Lyapunov-Lasalle candidate function to explore the global asymptotic stability of the disease-free equilibrium solution.Result from the mathematical analysis indicates that the disease-free equilibrium solution is globally asymptotically stable if Ro<1.The existence of unique endemic equilibrium solution is established through numerical investigation.Further,the model is reformulated as an optimal control problem,considering time-dependent controls(vaccination and public health education)to minimize the spread of tuberculosis in HIV-HCV co-infected cases,using Pontryagin's maximum principle.Numerical simulations and cost-effectiveness analysis are carried out which reveal that vaccination combined with public health education would reduce the spread of tuberculosis when HIV-HCV co-infected cases have been successfully controlled in the population.

3D numerical study and comparison of thermal-flow performance of various annular finne d-tub e designs

With the increase of heat transfer problems in marine vehicles and submerged power stations in oceans,the search for an efficient finned-tube heat exchanger has become particularly important.The purpose of the present investigation is to analyze and compare the thermal exchange and flow characteristics between five different fin designs,namely:a concentric circular finned-tube(CCFT),an eccentric circular finned-tube(ECFT),a perforated circular finned-tube(PCFT),a serrated circular finned-tube(SCFT),and a star-shaped finned-tube(S-SFT).The fin design and spacing impact on the thermal-flow performance of a heat exchanger was computed at Reynolds numbers varying from 4,300 to 15,000.From the numerical results,and when the fin spacing has been changed from 2 to 7 mm,an enhancement in the Colburn factor and a reduction in the friction factor and fin performances were observed for all cases under study.Three criteria were checked to select the most efficient fin design:the performance evaluation criterion P EC,the global performance criterion G PC,and the mass global performance criterion M G PC.Whatever the value of Reynolds number,the conventional CCFT provided the lowest performance evaluation criterion P EC,while the SCFT gave the highest amount of P EC.The most significant value of G PC was reached with the ECFT;however,G PC remained almost the same for CCFT,PCFT,SCFT,and S-SFT.In terms of the mass global performance criterion,the S-SFT provides the highest M Gpc as compared with the full fins of CCFT(41-73%higher)and ECFT(29-54%higher).Thus,the heat exchanger with S-SFT is recommended to be used in the cooling of offshore energy systems.

Soliton solutions for time fractional ocean engineering models with Beta derivative

In this study,the authors obtained the soliton and periodic wave solutions for time fractional symmetric regularized long wave equation(SRLW)and Ostrovsky equation(OE)both arising as a model in ocean engineering.For this aim modified extended tanh-function(mETF)is used.While using this method,chain rule is employed to turn fractional nonlinear partial differential equation into the nonlinear ordinary differential equation in integer order.Owing to the chain rule,there is no further requirement for any normalization or discretization.Beta derivative which involves fractional term is used in considered mathematical models.Obtaining the exact solutions of these equations is very important for knowing the wave behavior in ocean engineering models.