Showing papers in "Computers & Mathematics With Applications in 2003"
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TL;DR: The authors define equality of two soft sets, subset and super set of a soft set, complement of asoft set, null soft set and absolute soft set with examples and De Morgan's laws and a number of results are verified in soft set theory.
Abstract: In this paper, the authors study the theory of soft sets initiated by Molodtsov. The authors define equality of two soft sets, subset and super set of a soft set, complement of a soft set, null soft set, and absolute soft set with examples. Soft binary operations like AND, OR and also the operations of union, intersection are defined. De Morgan's laws and a number of results are verified in soft set theory.
2,114 citations
TL;DR: In this article, three main variations have been proposed for solving elliptic PDEs by means of collocation with radial basis functions (RBFs), and then compared them across the full range of values for the shape parameter of the RBFs.
Abstract: During the last decade, three main variations have been proposed for solving elliptic PDEs by means of collocation with radial basis functions (RBFs). In this study, we have implemented them for infinitely smooth RBFs, and then compared them across the full range of values for the shape parameter of the RBFs. This was made possible by a recently discovered numerical procedure that bypasses the ill conditioning, which has previously limited the range that could be used for this parameter. We find that the best values for it often fall outside the range that was previously available. We have also looked at piecewise smooth versus infinitely smooth RBFs, and found that for PDE applications with smooth solutions, the infinitely smooth RBFs are preferable, mainly because they lead to higher accuracy. In a comparison of RBF-based methods against two standard techniques (a second-order finite difference method and a pseudospectral method), the former gave a much superior accuracy.
373 citations
TL;DR: A new arithmetical principle is proposed and a new method is proposed that is easy to interpret the multiplication operation with the membership functions of fuzzy numbers and the canonical representation of multiplication operation on fuzzy numbers is computed.
Abstract: The representation of multiplication operation on fuzzy numbers is very useful and important in the fuzzy system such as the fuzzy decision making. In this paper, we propose a new arithmetical principle and a new arithmetical method for the arithmetical operations on fuzzy numbers. The new arithmetical principle is the L−1-R−1 inverse function arithmetic principle. Based on the L−1-R−1 inverse function arithmetic principle, it is easy to interpret the multiplication operation with the membership functions of fuzzy numbers. The new arithmetical method is the graded multiple integrals representation method. Based on the graded multiple integrals representation method, it is easy to compute the canonical representation of multiplication operation on fuzzy numbers. Finally, the canonical representation is applied to a numerical example of fuzzy decision.
178 citations
TL;DR: The analytic hierarchy process (AHP) provides a decision maker with a way of examining the consistency of entries in a pairwise comparison matrix and the hierarchy as a whole through the consistency ratio measure.
Abstract: The analytic hierarchy process (AHP) provides a decision maker with a way of examining the consistency of entries in a pairwise comparison matrix and the hierarchy as a whole through the consistency ratio measure. It has always seemed to us that this commonly used measure could be improved upon. The purpose of this paper is to present an alternative consistency measure and demonstrate how it might be applied in different types of matrices.
160 citations
TL;DR: In this article, the authors presented a class of quadrature rules on triangles in R 2 which, somewhat similar to Gaussian rules on intervals in R 1, have rapid convergence, positive weights, and symmetry.
Abstract: We present a class of quadrature rules on triangles in R 2 which, somewhat similar to Gaussian rules on intervals in R 1, have rapid convergence, positive weights, and symmetry. By a scheme combining simple group theory and numerical optimization, we obtain quadrature rules of this kind up to the order 30 on triangles. This scheme, essentially a formalization and generalization of the approach used by Lyness and Jespersen over 25 years ago, can be easily extended to other regions in R 2 and surfaces in higher dimensions, such as squares, spheres. We present example formulae and relevant numerical results.
156 citations
TL;DR: Explicit filtering is considered as a means of controlling the numerical errors that result when finite-difference methods are used in large eddy simulation (LES) as discussed by the authors, where the explicit filtering operation allows a separation between the filter size and the mesh spacing and can be used to control the impact of numerical errors.
Abstract: Explicit filtering is considered as a means of controlling the numerical errors that result when finite-difference methods are used in large eddy simulation (LES) The notion that the finite-difference expressions themselves act as an effective filter is shown to be false for three-dimensional simulations performed on nonuniform meshes For consistency, the nonlinear terms in the Navier-Stokes equations should be filtered explicitly at each time step in order to insure that the spectral content of the solution remains fixed at the desired filter level The explicit filtering operation allows a separation between the filter size and the mesh spacing and can be used to control the impact of the numerical errors Numerical tests of the explicit filtering approach in turbulent channel flow are used to investigate the effectiveness of the explicit filtering approach and to assess its associated cost Explicit filtering is shown to improve the computed results, but this improvement comes at a rather high computational cost The explicitly-filtered approach is also compared with straightforward mesh refinement as an alternative means of improving the computed results Mesh refinement is also seen to increase the accuracy of the simulation but some traces of numerical error appear to persist in the solution
140 citations
TL;DR: In this article, the problem of global asymptotic stability of a class of high-order Hopfield type neural networks with time delays was studied and sufficient conditions for the global stability of the equilibrium point of such neural networks in terms of linear matrix inequality were derived.
Abstract: This paper studies the problem of global asymptotic stability of a class of high-order Hopfield type neural networks with time delays. By utilizing Lyapunov functionals, we obtain some sufficient conditions for the global asymptotic stability of the equilibrium point of such neural networks in terms of linear matrix inequality (LMI). Numerical examples are given to illustrate the advantages of our approach.
132 citations
TL;DR: A posteriori error estimates for locally mass conservative methods for subsurface flow based on discontinuous approximation spaces and referred to as discontinued Galerkin methods are presented and h adaptivity is investigated for flow problems in 2D.
Abstract: A posteriori error estimates for locally mass conservative methods for subsurface flow are presented. These methods are based on discontinuous approximation spaces and referred to as discontinuous Galerkin methods. In the case where penalty terms are added to the bilinear form, one obtains the nonsymmetric interior penalty Galerkin methods. In a previous work, we proved optimal rates of convergence of the methods applied to elliptic problems. Here, h adaptivity is investigated for flow problems in 2D. We derive global explicit estimators of the error in the L 2 norm and we numerically investigate an implicit indicator of the error in the energy norm. Model problems with discontinuous coefficients are considered.
101 citations
TL;DR: In this paper, an explicit symmetric multistep method is presented, which is exponentially fitted and trigonometrically-fitted and is of algebraic order 8. The effectiveness of the exponential fitting is proved by the application of the new method and the classical one (with constant coefficients) to well-known periodic problems.
Abstract: An explicit symmetric multistep method is presented in this paper. The new method is exponentially fitted and trigonometrically-fitted and is of algebraic order eight. The effectiveness of the exponential fitting is proved by the application of the new method and the classical one (with constant coefficients) to well-known periodic problems.
95 citations
TL;DR: A modified Elman recurrent neural network in modeling and predicting software failures is investigated and the effects of different feedback weights in the proposed model are studied.
Abstract: When analysing software failure data, many software reliability models are available and in particular, nonhomogeneous Poisson process (NHPP) models are commonly used. However, difficulties posed by the assumptions, their validity, and relevance of these assumptions to the real testing environment have limited their usefulness. The connectionist approach using neural network models are more flexible and with less restrictive assumptions. This model-free technique requires only the failure history as inputs and then develops its own internal model of failure process. Their ability to model nonlinear patterns and learn from the data makes it a valuable alternative methodology for characterising the failure process. In this paper, a modified Elman recurrent neural network in modeling and predicting software failures is investigated. The effects of different feedback weights in the proposed model are also studied. A comparative study between the proposed recurrent architecture, with the more popular feedforward neural network, the Jordan recurrent model, and some traditional parametric software reliability growth models are carried out.
90 citations
TL;DR: This paper presents polynomial time self-stabilizing algorithms for finding a dominating bipartition, a maximal independent set, and a minimal dominating set in any graph.
Abstract: In the self-stabilizing algorithmic paradigm for distributed computation each node has only a local view of the system, yet in a finite amount of time, the system converges to a global state satisfying some desired property. In this paper we present polynomial time self-stabilizing algorithms for finding a dominating bipartition, a maximal independent set, and a minimal dominating set in any graph.
TL;DR: In this paper, the authors presented some Lyapunov type inequalities for discrete linear scalar Hamiltonian systems when the coefficient c(t) is not necessarily nonnegative valued and when the end points are not usual zeros, but rather, generalized zeros.
Abstract: In this paper, we present some Lyapunov type inequalities for discrete linear scalar Hamiltonian systems when the coefficient c(t) is not necessarily nonnegative valued and when the end-points are not necessarily usual zeros, but rather, generalized zeros. Applying these inequalities, we obtain some disconjugacy and stability criteria for discrete Hamiltonian systems
TL;DR: In this article, the complex modified Korteweg-de Vries (CMKdV) equation is solved numerically by three different split-step Fourier schemes, the main difference among the three schemes is in the order of the splitting approximation used to factorize the exponential operator.
Abstract: In this study, the complex modified Korteweg-de Vries (CMKdV) equation is solved numerically by three different split-step Fourier schemes. The main difference among the three schemes is in the order of the splitting approximation used to factorize the exponential operator. The space variable is discretized by means of a Fourier method for both linear and nonlinear subproblems. A fourth-order Runge-Kutta scheme is used for the time integration of the nonlinear subproblem. Classical problems concerning the motion of a single solitary wave with a constant polarization angle are used to compare the schemes in terms of the accuracy and the computational cost. Furthermore, the interaction of two solitary waves with orthogonal polarizations is investigated and particular attention is paid to the conserved quantities as an indicator of the accuracy. Numerical tests show that the split-step Fourier method provides highly accurate solutions for the CMKdV equation.
TL;DR: In this article, the authors considered a two-component system where component 1 failures occur according to a Poisson process and each component 1 failure causes a random amount of damage to component 2 leading to its failure when the total damage exceeds a specified level.
Abstract: In this paper, we consider a two component system where component 1 failures occur according to a Poisson process. Each component 1 failure causes a random amount of damage to component 2 leading to its failure when the total damage exceeds a specified level. We study a two-parameter maintenance policy which minimizes the expected cost per unit of time for infinite time operation.
TL;DR: In this paper, the authors considered a continuous distillation process under stochastic rate of inflows collected in a feed tank, and the aim was to find a robust control of extracting feed from the tank over a certain time horizon such that some level constraints in the feed tank will be met with high probability.
Abstract: The paper deals with a continuous distillation process under stochastic rate of inflows collected in a feed tank. The aim of analysis is to find a robust control of extracting feed from the tank over a certain time horizon such that—without knowledge of future realizations of the inflow rate—some level constraints in the feed tank will be met with high probability. This approach relies on formulating and numerically treating probabilistic constraints. The inflow rate is considered as a stochastic process for which two basically different model assumptions are made: the first model assumes a Gaussian process, and thus reflects the superposition of many independent elementary inflows; the second model treats maybe the simplest case of a single elementary inflow profile, namely rectangular inflows with fixed rate and duration but stochastic starting time. Numerical results illustrating both assumptions are presented, and advantages over the simple anticipation of nominal inflow profiles are highlighted.
TL;DR: Fuzzy theory techniques are applied to susceptible-infectious SI epidemiological models and the transmission coefficient is considered as a fuzzy set and the mean number of infected individuals is compared with the trajectory of the mean virus charge.
Abstract: Fuzzy theory techniques are applied to susceptible-infectious SI epidemiological models. The transmission coefficient is considered as a fuzzy set and the mean number of infected individuals is compared with the trajectory of the mean virus charge I( v , t) . Also, the basic reproduction value Rf0f is discussed for this formulation and, using RF0f, a control policy of the disease is discussed.
TL;DR: The method for obtaining the fuzzy least squares estimators with the help of the extension principle in fuzzy sets theory is proposed and the methodology for evaluating the predicted fuzzy output from the given fuzzy input data is provided.
Abstract: The method for obtaining the fuzzy least squares estimators with the help of the extension principle in fuzzy sets theory is proposed. The membership functions of fuzzy least squares estimators will be constructed according to the usual least squares estimators. In order to obtain the membership value of any given value taken from the fuzzy least squares estimator, optimization problems have to be solved. We also provide the methodology for evaluating the predicted fuzzy output from the given fuzzy input data.
TL;DR: An overview of the state of the research and practice in the architecture-based approach to quantitative assessment of software systems and the key models in each class are described in detail with a focus on their relation and unification.
Abstract: With growing emphasis on reuse, the software development process moves toward component-based software design. As a result, there is a need for modeling approaches that are capable of considering the architecture of the software made out of components. This paper presents an overview of the state of the research and practice in the architecture-based approach to quantitative assessment of software systems. First, the common requirements of the architecture-based models are identified and the classification is proposed. Then, the key models in each class are described in detail with a focus on their relation and unification. Finally, a critical analysis of the underlying assumptions, limitations, and applicability of these models is provided, which should be helpful in determining the directions for future research.
TL;DR: In this article, sufficient conditions are derived for the existence of a globally attracting positive equilibrium of a two species competition system with feedback controls; the indirect controls can act instantaneously or with a fixed discrete delay.
Abstract: Sufficient conditions are derived for the existence of a globally attracting positive equilibrium of a two species competition system with feedback controls; the indirect controls can act instantaneously or with a fixed discrete delay.
TL;DR: In this paper, a comparison theorem for the solutions of a rational matrix difference equation, generalizing the Riccati difference equation and existence and convergence results for the solution of this equation were proved.
Abstract: We prove a comparison theorem for the solutions of a rational matrix difference equation, generalizing the Riccati difference equation, and existence and convergence results for the solutions of this equation. Moreover, we present conditions ensuring that the corresponding algebraic matrix equation has a stabilizing or almost stabilizing solution.
TL;DR: In this paper, the existence and uniqueness results for solutions of second-order nonlinear difference equations on a finite discrete segment with periodic boundary conditions were proved based on the notion of upper and lower solutions.
Abstract: We prove existence and uniqueness results for solutions of second-order nonlinear difference equations on a finite discrete segment with periodic boundary conditions. The results are based on the notion of upper and lower solutions.
TL;DR: Some new bounds for the first inequality of Ostrowski-Gruss type can be much better than some recently obtained bounds and applications in numerical integration are given.
Abstract: Some new bounds for the first inequality of Ostrowski-Gruss type are derived. These new bounds can be much better than some recently obtained bounds. Applications in numerical integration are also given.
TL;DR: The local and global convergence properties of the nonmonotone adaptive trust region method are proved and its efficiency is tested by numerical results.
Abstract: In this paper, we combine the new trust region subproblem proposed in [1] with the nonmonotone technique to propose a new algorithm for unconstrained optimization—the nonmonotone adaptive trust region method. The local and global convergence properties of the nonmonotone adaptive trust region method are proved. Its efficiency is tested by numerical results.
TL;DR: In this paper, a nonstandard finite difference scheme is constructed using methods generated by the previous work of Mickens, and a functional relationship is obtained between the space and time step-sizes.
Abstract: A number of important phenomena in ecology can be modeled by one-dimensional, nonlinear reaction-diffusion PDEs. This paper considers a modified Fisher PDE for which the diffusion term is nonlinear. A nonstandard finite difference scheme is constructed using methods generated by the previous work of Mickens. As a check on the mathematical properties of this scheme, a linear stability analysis is carried out for the two fixed-points appearing in the differential and difference equations. The finite difference scheme is shown to have solutions which satisfy a positivity condition as well as the requirement of boundedness. Further, the scheme is explicit and a functional relationship is obtained between the space and time step-sizes. A numerical test of the scheme is done for a particular initial/boundary value problem. A brief discussion of how the work can be extended and/or generalized is also given.
TL;DR: In this paper, a new approach for the derivation of hybrid explicit Numerov type methods is presented, which does not require the intermediate use of high accuracy inter- polatory nodes, since we only need the Taylor expansion of the internal points.
Abstract: We present in this paper a new approach for the derivation of hybrid explicit Numerov type methods. The new methodology does not require the intermediate use of high accuracy inter- polatory nodes, since we only need the Taylor expansion of the internal points. As a consequence, a sixth-order method is produced at a cost of only four stages per step instead of six stages needed for the methods which have appeared in the literature until now. Numerical results over some well-known problems in physics and mechanics indicate the superiority of the new method. (~) 2003 Elsevier Science Ltd. All rights reserved.
TL;DR: In this article, a class of singularly perturbed two-point boundary value problems (BVP) for second-order ODEs is considered, and the domain is divided into two subdomains.
Abstract: A class of singularly perturbed two-point boundary-value problems (BVP) for second-order ordinary differential equations is considered here. To avoid the numerical difficulties in the solution to these problems, we divide the domain into two subdomains. The first BVP is a layer domain problem and the second BVP is a regular domain problem. Error estimates are derived for the numerical solution. Numerical examples are provided in support of the proposed method.
TL;DR: In this paper, the hp-version of discontinuous Galerkin FEM on geometrically refined meshes in polygons is shown to converge with exponential convergence and several variants of interior penalization are covered.
Abstract: We prove exponential convergence of the hp-version of discontinuous Galerkin FEM on geometrically refined meshes in polygons. Several variants of interior penalization are covered. Numerical experiments indicate the sharpness of the theoretical results as well as the weak dependence of the DGFEM approximation on the particular choice of interior penalization and the penalty parameter.
TL;DR: In this article, three limit cycles are constructed for a three-dimensional Lotka-Volterra competitive system with a heteroclinic cycle, which gives a partial answer to a problem proposed by Hofbauer and So in [1].
Abstract: Three limit cycles are constructed for a three-dimensional Lotka-Volterra competitive system with a heteroclinic cycle. This gives a partial answer to a problem proposed by Hofbauer and So in [1]
TL;DR: In this article, the authors considered replacement and minimal repair policies for an extended cumulative damage model with maintenance at each shock, where shocks occur at a nonhomogeneous Poisson process.
Abstract: This paper considers replacement and minimal repair polices for an extended cumulative damage model with maintenance at each shock: shocks occur at a nonhomogeneous Poisson process. A system undergoes maintenance at each shock when the total damage does not exceed a failure level K, undergoes minimal repair at each shock when the total damage exceeds a failure level K, and is replaced at time T∗ or at failure N∗ whichever occurs first. The expected cost rate is obtained and the optimal T∗ and N∗ minimizing the expected cost are analytically discussed. It is shown that this model would be applied to the backup of secondary storage files in a database system as an example.
TL;DR: In this paper, the fourth-order compact finite difference schemes were employed with multigrid techniques to simulate the two-dimensional square driven cavity flow with small to large Reynolds numbers.
Abstract: Fourth-order compact finite difference schemes are employed with multigrid techniques to simulate the two-dimensional square driven cavity flow with small to large Reynolds numbers. The governing Navier-Stokes equation is linearized in streamfunction and vorticity formulation. The fourth-order compact approximation schemes are coupled with fourth-order approximations for velocities and vorticity boundaries. Numerical solutions are obtained for square driven cavity flow at high Reynolds numbers and are compared with solutions obtained by other researchers using other approximation methods.