a fusion approach for managing multi granularity linguistic term sets in decision making the aim of this paper is to present a fusion approach of multi granularity linguistic information for managing information assessed in different linguistic term sets multi granularity linguistic term sets together with its application in a decision making problem with multiple information sources assuming that the linguistic performance values given to the alternatives by the different sources are represented in linguistic term sets with different granularity and or semantic in this context a decision process based on two steps is proposed with a view to obtaining the solution set of alternatives first the fusion of the multi granularity linguistic performance values is carried out in order to obtain collective performance evaluations in this step on the one hand the multi granularity linguistic information is made uniform using a linguistic term set as the uniform representation base the basic linguistic term set on the other hand the collective performance evaluations of the alternatives are obtained by means of an aggregation operator being fuzzy sets on the basic linguistic term set second the choice of the best alternative s from the collective performance evaluations is performed to do that a fuzzy preference relation is computed from the collective performance evaluations using a ranking method of pairs of fuzzy sets in the setting of possibility theory applied to fuzzy sets on the basic linguistic term set then a choice degree may be applied on the preference relation in order to rank the alternatives

operators and comparisons of hesitant fuzzy linguistic term sets the theory of hesitant fuzzy linguistic term sets hfltss is very useful in objectively dealing with situations in which people are hesitant in providing linguistic assessments the purpose of this paper is to develop comparison methods and study the aggregation theory for hfltss we first define operations on hfltss and give possibility degree formulas for comparing hfltss we then define two aggregation operators for hfltss a hesitant fuzzy lwa operator and a hesitant fuzzy lowa operator in actual application we use these operators and the comparison methods to deal with multicriteria decision making problems with different situations in which importance weights of criteria or experts are known or unknown

statistically grounded logic operators in fuzzy sets abstract in this study we are concerned with a category of logic operators for fuzzy sets that is inherently associated with underlying statistical properties of membership grades they operate on these constructs are referred to as statistically grounded logic operators namely statistically grounded ors sors for short and statistically grounded ands sands for short operators in essence they arise as a solution to the optimization problem of the following form arg min m 0 1 k 1 n w x k x k m where xk k 1 2 n are the corresponding membership grades to be combined the weight function w 0 1 0 1 captures the nature of the logic and and or aggregation respectively we show that the weight function could be induced by t norms and t conorms the weight functions could be also implied by some statistical characteristics of data membership grades the choice of the t norm t conorm depends upon the predefined form of the logic operators to be developed we demonstrate that sands and sors offer an efficient operational framework for constructing fuzzy rough sets lead to the increased sensitivity of computing possibility and necessity measures bring a new insight into fuzzy relational equations and deliver an interpretation vehicle for fuzzy clustering that is provided in the form of dependency analysis

design spaces measures and metrics for evaluating quality of time operators and consequences leading to improved algorithms by design illustration to structural dynamics for the first time for time discretized operators we describe and articulate the importance and notion of design spaces and algorithmic measures that not only can provide new avenues for improved algorithms by design but also can distinguish in general the quality of computational algorithms for time dependent problems the particular emphasis is on structural dynamics applications for the purpose of illustration and demonstration of the basic concepts the underlying concepts can be extended to other disciplines as well for further developments in time discretized operators and or for evaluating existing methods from the established measures for computational algorithms the conclusion that the most effective in the sense of convergence namely the stability and accuracy and complexity namely the algorithmic formulation and algorithmic structure computational algorithm should appear in a certain algorithmic structure of the design space amongst comparable algorithms is drawn with this conclusion and also with the notion of providing new avenues leading to improved algorithms by design as an illustration a novel computational algorithm which departs from the traditional paradigm in the sense of lms methods with which we are mostly familiar with and widely used in commercial software is particularly designed into the perspective design space representation of comparable algorithms and is termed here as the forward displacement non linearly explicit l stable fdel algorithm which is unconditionally consistent and does not require non linear iterations within each time step from the established measures for comparable algorithms simply for illustration purposes the resulting design of the fdel formulation is then compared with the commonly advocated explicit central difference method and the implicit newmark average acceleration method alternately the same conclusion holds true against controllable numerically dissipative algorithms which pertain to the class of linear multi step lms methods for assessing both linear and non linear dynamic cases the conclusions that the proposed new design of the fdel algorithm which is a direct consequence of the present notion of design spaces and measures is the most effective algorithm to date to our knowledge in comparison to the class of second order accurate algorithms pertaining to lms methods for routine and general non linear dynamic situations is finally drawn through rigorous numerical experiments

a series of score functions for hesitant fuzzy sets abstract this paper presents a series of score functions for hesitant fuzzy sets hfss which provides us with a variety of new methods for ranking hfss the idea behind the methods is based on the score function for hesitant fuzzy elements hfes that appears to be a subject worthy of further investigations in depth the prominent characteristic of the hfs score based method is that it can determine the priorities of the alternatives directly from the hfs score values in a broad discussion we describe a scheme for choosing an appropriate option from a set of hfs score based methods according to what is expected from the score function and what is the nature of the values to be scored finally the application of hfs ranking methods to multi attribute decision making problems with hesitant fuzzy information is explained

analysis and implementation of a new constant acceleration subcycling algorithm an algorithm for explicit integration of structural dynamics problems with multiple time steps is proposed that averages accelerations to obtain subcycle states at a nodal interface between regions integrated with different time steps with integer time step ratios the resulting subcycle updates at the interface sum to give the same effect as a central difference update over a major cycle the algorithm is shown to have good accuracy and stability properties in linear elastic analysis similar to those of constant velocity subcycling algorithms the implementation of a generalised form of the algorithm with non integer time step ratios is presented c 1997 by john wiley sons ltd

unconditionally stable higher order newmark methods by sub stepping procedure abstract in this paper a procedure to construct unconditionally stable higher order step by step time integration algorithms based on the newmark method is presented the second order accurate newmark method is extended to third fourth and even higher order by linearly combining the numerical results evaluated at some specific sub step locations the weighting factors and the sub step locations are algorithmic parameters they are chosen to eliminate the leading truncation error terms and to control the stability characteristics the ranges of parameters for unconditionally stable third and fourth order algorithms are given besides by using complex time steps a third order l stable and a fourth order a stable non dissipative algorithms are derived furthermore the accuracy of the excitation responses is shown to be improved by the present procedure as well to maintain high order accuracy the excitation may need to be modified the computational procedure is discussed it is found that there are no changes in the implementation of the underlying newmark method and no extra computations of high order gradients as the numerical results at the sub step locations are obtained independent of one another the evaluations can be computed in parallel comparisons with other higher order algorithms are presented

computational algorithms for transient analysis the burden of weight and consequences towards formalizing discrete numerically assigned dna algorithmic markers wp family abstract different from the way we have been looking in the past at developments encompassing modal type and a wide class of step by step time stepping approaches for transient and dynamic field problems and significantly different from the way these have been developed and described in standard text books over the years this paper outlines the theoretical ideas and basis towards providing a generalized methodology and formulations leading to integral and a wide class of integration operators for the resulting solution of these transient equation systems it is herein postulated that integral operators and a wide class of integration operators pertain to and emanate from the same family with the burden which is being carried by a virtual field or weighted function field specifically introduced for the time discretization is strictly enacted in a mathematically consistent manner so as to first permit obtaining the adjoint operator of the original semi discretized equation system subsequently the selection or burden carried by the virtual or weighted function fields originally introduced to facilitate the time discretization process determines the formal development and outcome of exact integral operators approximate integral operators and a wide class of integration operators thus the present developments not only serve as a prelude towards the formal developments for exact integral operators but also demonstrate that the resulting approximate integral operators and a wide class of integration operators and known methods are simply subsets of the generalizations of a standardized w p family and emanate from the principles presented herein the burden of weight and the resulting consequences towards subsequently enabling a formal basis for the selection of discrete numerically assigned dna algorimmic markers to particularly identitfy a wide class of algorithms is described for transient field problems and dynamic field problems respectively

analysis of discrete ill posed problems by means of the l curve when discrete ill posed problems are analyzed and solved by various numerical regularization techniques a very convenient way to display information about the regularized solution is to plot the norm or seminorm of the solution versus the norm of the residual vector in particular the graph associated with tikhonov regularization plays a central role the main purpose of this paper is to advocate the use of this graph in the numerical treatment of discrete ill posed problems the graph is characterized quantitatively and several important relations between regularized solutions and the graph are derived it is also demonstrated that several methods for choosing the regularization parameter are related to locating a characteristic l shaped corner of the graph

a weighted residual development of a time stepping algorithm for structural dynamics using two general weight functions an unconditionally stable single step implicit algorithm for the integration of the equations of motion arising in structural dynamics is presented within a time step the displacement for a single degree of freedom system is approximated by a function which is cubic in time the four coefficients of the cubic are chosen to satisfy the two initial conditions and two weighted integral equations by considering general weight functions six additional coefficients arise in a series of steps these coefficients are selected to i maximize algebraic accuracy by matching terms of taylor s expansions of exact and approximate solutions ii ensure unconditional stability and iii optimize numerical conditioning of the equations in a limiting case equations required to implement the procedure are presented the method as presented has no algorithmic damping of higher modes although it is indicated how this may be achieved the error in period elongation obtained using the proposed method is shown to be far less than using alternative procedures 1998 john wiley sons ltd

a time stepping procedure for structural dynamics using gauss point collocation when a cubic function is interpolated between the prescribed initial displacement and velocity and the exact displacement and velocity at the end of a time step for a single degree of freedom system the error or residual in the governing equation is zero at a number of times it is shown that for a general undamped system in the limit as the time step approaches zero these times correspond to gauss points this observation is verified by considering a general collocation procedure in which the displacement in any time step is approximated as a cubic function of time with two coefficients chosen to satisfy the displacement and velocity at the beginning of the time step with the other two coefficients being chosen to satisfy the governing differential equation at any two times it is shown that optimum accuracy is obtained if these points are the gauss points detailed expressions are then presented for this particular case and stability of the algorithm is investigated showing that the procedure is conditionally stable for time steps which are a small proportion of the least period of vibration of the structure the algorithm is considered to be the most accurate possible procedure based on cubic approximation of the displacement

a new family of explicit time integration methods for linear and non linear structural dynamics a new family of explicit single step time integration methods with controllable high frequency dissipation is presented for linear and non linear structural dynamic analyses the proposed methods are second order accurate and completely explicit with a diagonal mass matrix even when the damping matrix is not diagonal in the linear structural dynamics or the internal force vector is a function of velocities in the non linear structural dynamics stability and accuracy of the new explicit methods are analysed for the linear undamped damped cases furthermore the new methods are compared with other explicit methods

critical assessment of different mass lumping schemes for higher order serendipity finite elements abstract an efficient and robust finite element based transient analysis of structures is important in many engineering applications in this context a diagonal or lumped mass matrix is an essential prerequisite in the last decades several methods to construct such a mass matrix have been proposed and therefore a comprehensive and unbiased evaluation of these approaches is needed in the present article we consequently investigate established mass lumping schemes such as the row sum method and the diagonal scaling method as well as the recently proposed manifold based method furthermore the latter approach is rigorously extended to higher order serendipity finite elements in two and three dimensions note that the manifold based method and the diagonal scaling method are very general approaches in the sense that they are applicable to arbitrary nodal based shape functions with arbitrary polynomial orders while guaranteeing the positive definiteness of the lumped mass matrix with respect to the row sum method the positivity is not ensured and negative or zero diagonal components might be computed consequently a detailed analysis of the influence and performance of these mass lumping schemes on the numerical results is conducted to this end several dynamic benchmark models including modal harmonic and transient analyses are selected showing that only suboptimal rates of convergence are attained if serendipity finite elements based on a diagonal mass matrix are employed

method of multi criteria group decision making based on cloud aggregation operators with linguistic information abstract the cloud model which can synthetically describe the randomness and fuzziness of qualitative concepts and implement uncertain transformations between a qualitative concept and its quantitative instantiations has attracted considerable attention from researchers studying multi criteria group decision making problems involving linguistic information in this paper some operations of clouds and several new aggregation operators are proposed these include the cloud weighted arithmetic averaging cwaa operator cloud ordered weighted arithmetic averaging cowa operator and cloud hybrid arithmetic cha operator the conversion between linguistic variables and clouds is introduced based on this conversion a linguistic multi criteria group decision making method is developed in this method linguistic variables are first converted into clouds and then aggregated using cloud aggregation operators the proposed method is then compared to the existing methods to confirm its feasibility and rationality

extensions of the topsis for group decision making under fuzzy environment the aim of this paper is to extend the topsis to the fuzzy environment owing to vague concepts frequently represented in decision data the crisp value are inadequate to model real life situations in this paper the rating of each alternative and the weight of each criterion are described by linguistic terms which can be expressed in triangular fuzzy numbers then a vertex method is proposed to calculate the distance between two triangular fuzzy numbers according to the concept of the topsis a closeness coefficient is defined to determine the ranking order of all alternatives by calculating the distances to both the fuzzy positive ideal solution fpis and fuzzy negative ideal solution fnis simultaneously finally an example is shown to highlight the procedure of the proposed method at the end of this paper

a novel family of explicit time marching techniques for structural dynamics and wave propagation models abstract in this work a novel family of explicit time marching techniques is presented for hyperbolic models the main features of the proposed procedure are i the family is based only on single step displacement velocity relations being very simple to implement ii as usual in explicit analyses it requires no system of equations to be dealt with being very efficient iii it is truly self starting iv it is second order accurate v it enables controllable algorithmic dissipation in the higher modes vi it provides reduced period elongation errors in the lower modes vii it is conditionally stable and exhibits high stability limits with its critical sampling frequency varying between 3 571 and 4 i e its upper limit is twice that of the central difference method the proposed technique is very effective providing the main positive attributes that are requested from an efficacious explicit time marching procedure numerical results are presented along the paper illustrating the excellent performance of the novel method

a modified euler method for dynamic analyses a modified version of the well known euler method for numerical integration is presented and its application in analyses of the dynamic response of structures is discussed this modified method was first introduced in 1981 and it has been reported that it was discovered by accident when first introduced however valuable information related to the accuracy stability and merits of the method were not provided it is shown that the modified euler method has features that make it an attractive approach for applications in dynamic analyses of structures accuracy and stability analyses are made for the method by considering free vibrational responses of linear undamped single degree of freedom systems the method is explicit and extremely easy to use however it is conditionally stable applications of the method are also made which illustrate its usefulness and inherent simplicity furthermore comparisons of the modified euler method and the newmark beta method are reported which elucidate the relative merits of these methods

convergence analysis of tikhonov type regularization algorithms for multiobjective optimization problems in this paper we introduce a vector valued tikhonov type regularization algorithm for an extended valued multiobjective optimization problem under some mild conditions we prove that any sequence generated by this algorithm converges to a weak pareto optimal solution of the multiobjective optimization problem our results improve and generalize some known results

approximate fundamental solutions and wave fronts for general anisotropic materials abstract the time dependent differential equations of elastodynamics for homogeneous solids with a general structure of anisotropy are considered in the paper a new method of computation of the fundamental solution for these equations is proposed this method consists of the following applying the fourier transformation with respect to space variables to these equations we obtain a system of second order ordinary differential equations whose coefficients depend on fourier parameters using the matrix transformations and properties of the coefficients the fourier image of the fundamental solution is computed finally the fundamental solution is calculated by the inverse fourier transformation to the obtained fourier transform the implementation and justification of the suggested method have been made by computational experiments in matlab these experiments confirm the robustness of the suggested method the visualization of the displacement components in general homogeneous anisotropic solids by modern computer tools allows us to see and evaluate the dependence between the structure of solids and the behavior of the displacement field our method allows users to observe the elastic wave propagation arising from pulse point forces of the form em x t in monoclinic triclinic and other anisotropic solids the visualization of displacement components gives knowledge about the form of fronts of elastic wave propagation in sodium thiosulfate with monoclinic and copper sulphate pentahydrate with triclinic structures of anisotropy

an iterative method for linear discrete ill posed problems with box constraints many questions in science and engineering give rise to linear discrete ill posed problems often it is desirable that the computed approximate solution satisfies certain constraints e g that some or all elements of the computed solution be nonnegative this paper describes an iterative method of active set type for the solution of large scale problems of this kind the method employs conjugate gradient iteration with a stopping criterion based on the discrepancy principle and allows updates of the active set by more than one index at a time

a posteriori parameter choice with an efficient discretization scheme for solving ill posed problems abstract recently rajan m p rajan an efficient discretization scheme for solving the ill posed problems journal of mathematical analysis and applications 313 2 2006 654 677 considered a discretization scheme for solving ill posed problems and obtained optimal error estimates under an a priori parameter choice strategy with a particular smoothness assumption on the solution it is shown that the computational information for solving the system is far less than the traditional projection schemes neubauer a neubauer an a posteriori parameter choice for tikhonov regularization in the presence of modeling error applied numerical mathematics 4 1988 507 519 and engl and gfrerer h w engl h gfrerer a posteriori parameter choice for general regularization methods for solving ill posed problems applied numerical mathematics 4 1988 395 417 suggested an a posteriori method for choosing the regularization parameter which does not require any knowledge about the exact solution respectively under finite dimensional as well as general setting in this paper we consider an a posteriori parameter choice for finite dimensional approximation which does not require any information about the smoothness of the exact solution and apply to the discretization scheme considered by rajan the computational efficiency of the scheme is illustrated through numerical examples

higher order accurate time step integration algorithms by post integration techniques in this paper a framework to construct higher order accurate time step integration algorithms based on the post integration techniques is presented the prescribed initial conditions are naturally incorporated in the formulations and can be strongly or weakly enforced the algorithmic parameters are chosen such that unconditionally a stable higher order accurate time step integration algorithms with controllable numerical dissipation can be constructed for linear problems besides it is shown that the order of accuracy for non linear problems is maintained through the relationship between the present formulation and the runge kutta method the second order differential equations are also considered numerical examples are given to illustrate the validity of the present formulation copyright 2001 john wiley sons ltd

a unified set of single step algorithms part 2 theory part 1 of this paper1 presents a very general single step algorithm sspj for the numerical integration of first and second order time dependent differential equations in part 2 we present and discuss results of the accuracy and stability analysis for ss11 ss21 ss31 ss22 and ss32 there is also a detailed comparison of ss22 and the newmark algorithm

hesitant fuzzy set lexicographical ordering and its application to multi attribute decision making there exist several types of hesitant fuzzy set hfs ranking techniques that have been widely used for handling multi attribute decision making problems with hfs information the main goal of this paper is to present firstly a brief study of some existing hfs ranking techniques by emphasizing their counterintuitive examples and then a novel hfs ranking technique is introduced based on the idea of lexicographical ordering

higher derivative explicit one step methods for non linear dynamic problems part i design and theory a new higher order explicit one step scheme is presented for use in the solution of a certain class of non linear problems in structural dynamics the generalized scheme covers some recently developed multistep algorithms as well as some new one step methods with improved numerical properties a weighted residual approach is used which contains new aspects for design of single step algorithms accuracy and stability are investigated for linear and non linear systems algorithms with higher accurary than the central difference method are developed and optimized to minimize the reduction in the stability limit

time discretized operators part 1 towards the theoretical design of a new generation of a generalized family of unconditionally stable implicit and explicit representations of arbitrary order for computational dynamics the new generation of a generalized family of time discretized operators encompassing implicit and explicit representations that are unconditionally stable and which theoretically inherit nth order time accurate features developed in part 1 are restricted here in part 2 of the exposition to second order time accurate operators as such unconditionally stable implicit representations are first described followed by unconditionally stable explicit representations the theoretical design leading to computational algorithms with excellent algorithmic attributes for applicability to practical situations are also addressed for both the implicit and explicit unconditionally stable representations of time discretized operators attention is first focused on linear problems and extensions to nonlinear situations are subsequently briefly addressed

a time domain fem approach based on implicit green s functions for non linear dynamic analysis the present paper describes an unconditionally stable algorithm to integrate the equations of motion in time the standard fem displacement model is employed to perform space discretization and the time marching process is carried out through an algorithm based on the green s function of the mechanical system in nodal co ordinates in the present implicit green s function approach imga mechanical system green s functions are not explicitly computed rather they are implicitly considered through an iterative pseudo forces process under certain simplifying hypothesis iterations are not necessary and the imga becomes cheaper than standard newmark newton raphson algorithm at the end of the paper numerical examples are presented in order to illustrate the accuracy of the present approach

comparison of some single step methods for the numerical solution of the structural dynamic equation this paper compares the performance of the ss22 and ss23 references 1 and 2 single step algorithms for the numerical solution of the second order structural dynamic equation and a related new algorithm ss32b applied to the equivalent first order system with sine and step forcing functions various aspects of stability relevant to these equations are discussed

a robust self starting explicit computational methodology for structural dynamic applications architecture and representations conventional approaches for computational structural dynamics relevant to time integration methods involve first employing the classical galerkin formulations for the spatial discretization to yield a set of ordinary differential equations in time and then employing finite difference approximations for deriving the appropriate step by step algorithms we introduce new representations and architecture towards providing not only direct self starting features with the elimination of acceleration computations but also for enhancing the computational architecture itself via several other inherent distinguishing characteristics

generalized asymmetric linguistic term set and its application to qualitative decision making involving risk appetites abstract the linguistic term set is an applicable and flexible technique in qualitative decision making qdm to further develop the linguistic term set this paper proposes a generalized asymmetric linguistic term set galts based on the asymmetric sigmoid semantics which belongs to an asymmetric and non uniform linguistic term set and can be used to address the qdm problems involving risk appetites of the decision maker dm then a value at risk fitting varf approach is designed for obtaining the risk appetite parameters of the galts and six desirable properties of the galts are analyzed i e asymmetry non uniformity generality variability range consistency and diminishing utility based on the above approaches and the generalized asymmetric linguistic preference relations galprs a qdm process involving risk appetites of the dm is designed because the galprs consist of subjective information provided by the dm the process is not perfectly consistent and is usually difficult to change or repeat thus a transitivity improvement approach is investigated and the corresponding calculation steps are provided finally an example dealing with the problem of investment decision making is provided and the results fully demonstrate the validity of the proposed methods for qdm involving risk appetites

an unusual amplitude growth property and its remedy for structure dependent integration methods abstract an unusual amplitude growth in the steady state response of a high frequency mode for a structure dependent integration method is numerically and analytically identified this is a brand new type of amplitude growth and it has never been found in the conventional integration methods the root cause of this unusual amplitude growth can be revealed by examining the local truncation error constructed from a forced vibration error where the dominant error term for high frequency modes plays the key role for this unusual amplitude growth an effective remedy is proposed by introducing a load dependent term into the difference equation for displacement and or velocity increment to remove the dominant error term as a result this adverse amplitude growth can be automatically removed consequently the inclusion of the load dependent term in the formulation of the difference equation for displacement increment and or velocity increment is inevitable for a general structure dependent integration method

high order taylor galerkin and adaptive h p methods for second order hyperbolic systems application to elastodynamics a new family of high order taylor galerkin schemes is presented for the analysis of second order hyperbolic systems the use of such schemes within an adaptive h p finite element strategy for spatial approximation in two dimensional problems is described numerical results are presented to demonstrate performance of these methods

linguistic hesitant fuzzy power aggregation operators and their applications in multiple attribute decision making as a generalization of hesitant fuzzy sets hfss and hesitant fuzzy linguistic term sets hfltss linguistic hesitant fuzzy sets lhfss establish a proper interpretation of the hesitancy inconsistency and uncertainty of experts in evaluating decision alternatives in this paper based on the cloud model we discuss multiple attribute decision making problems with linguistic hesitant fuzzy information to extend the applicability of lhfss we introduce the concept of a comprehensive cloud of lhfss that is based on which form of lhfss with different length can be unified utilizing the comprehensive cloud we define the distance measure between two lhfss which makes the support measure of two lhfss possible by extending the power operators to the linguistic hesitant fuzzy environment a series of linguistic hesitant fuzzy power aggregation operators are established we also study the properties and applications of these aggregation operators and develop two approaches for linguistic hesitant fuzzy multiple attribute decision making finally two practical examples are given to demonstrate the applicability and effectiveness of the proposed approach

a hybrid time laplace integration method based on numerical green s functions in conduction heat transfer abstract the present paper describes an efficient time laplace domain approach to analyze numerically heat conduction problems an efficient recurrence relationship for the temperature in the time domain based on the green s functions of the model is presented primarily green s functions in nodal coordinates are explicitly calculated by the finite element method in the laplace domain and subsequently the stehfest and the zakian laplace inversion schemes are employed to compute numerically green s functions that transfer solution at time 0 to time t as a result a new family of highly accurate time integration methods called exga stehfest and exga zakian is obtained finally numerical examples are presented in order to illustrate the high accuracy and potentialities of these novel approaches

transfinite element methodology for non liner linear transient thermal modelling analysis progress and recent advances recent progress and advances in the development and applicability of a novel transfinite element computational methodology is presented for general non linear linear transient thermal problems the proposed methodology and concepts are new and unique and demonstrate the applicability to general transient non linear linear thermal analysis situations by combining classical galerkin schemes and transform approaches with contemporary finite element methods to preserve the modelling versatility and numerical features thereby a hybrid computational methodology is proposed characteristic features and pertinent details of the approach are described for non linear linear transient thermal problems wherein non linearities due temperature dependence of thermophysical properties and or general non linear bound ary conditions to include radiation effects due to phase change etc are considered in addition the use of high continuity formulations in conjuction with the proposed methodology to furnish accurate temperature distributions and temperature gradients making use of a relatively smaller number of degrees of freedom is also demonstrated numerical test cases are presented for a variety of problems to demonstrate the fundamental features and applicability of the proposed formulations the proposed hybrid transfinite element methodology and concepts offer significant potential for extension to several areas of mathematical physics and engineering and to interdisciplinary research areas

a method for group decision making with multi granularity linguistic assessment information this paper proposes a method to solve the group decision making gdm problems with multi granularity linguistic assessment information in the method the multi granularity linguistic information provided by experts is firstly expressed in the form of fuzzy numbers in order to make the collective opinion close to each expert s opinion a linear goal programming model is constructed to integrate the fuzzy assessment information and to directly compute the collective ranking values of alternatives without the need of information transformation then a fuzzy preference relation on the pairwise comparisons of the collective ranking values of alternatives is constructed using the dominance possibility degree of the comparison between the fuzzy numbers by applying a non dominance choice degree to this fuzzy preference relation the ranking of alternatives is determined and the most desirable alternative s is selected an example is used to illustrate the applicability of the proposed method and its advantages

multi criteria semantic dominance a linguistic decision aiding technique based on incomplete preference information a linguistic decision aiding technique for multi criteria decision is presented we define a relation between alternatives as multi criteria semantic dominance mcsd it adopts the similar ideal of the stochastic dominance by utilizing the partial information of the decision maker s preference which is only ordinal or partially cardinal the mcsd rules based on three typical types of semanteme functions are introduced and proven by using these rules all the alternatives under consideration are divided into two mutually exclusive sets called efficient set and inefficient set the decision maker who has such a semanteme function will never choose the alternative from the corresponding inefficient set as the optimal one in such a way when we analyze the linguistic decision information the inherent fuzziness of preference can be handled and several controversial operations of the linguistic terms can be avoided an example is also provided to illustrate the procedure of the proposed method

a new variant of l curve for tikhonov regularization in this paper we introduce a new variant of l curve to estimate the tikhonov regularization parameter for the regularization of discrete ill posed problems this method uses the solution norm versus the regularization parameter the numerical efficiency of this new method is also discussed by considering some test problems

time accurate solution of advection diffusion problems by finite elements abstract the taylor galerkin method recently proposed for the spatial and temporal discretization of hyperbolic equations is employed to derive accurate and efficient numerical schemes for the solution of time dependent advection diffusion problems two distinct numerical strategies are discussed the first is suitable for evolutionary problems while the second is appropriate for situations in which a steady state is eventually reached for purely evolutionary problems the taylor galerkin method is applied to the complete advection diffusion equation and through modifications of the standard mass matrix is shown to generate an incremental form of the crank nicolson time stepping method such an incremental form also lends itself to the derivation of computationally simple but accurate explicit algorithms to deal with transient situations which evolve towards a highly convective steady state the global taylor galerkin method is found to be ineffective since it reduces to the standard galerkin formulation as the temporal term vanishes for such cases we suggest the use of a splitting up method in which advection and diffusion are treated separately by appropriate taylor galerkin methods the proposed methods are illustrated first for linear constant coefficient equations they are successively extended to deal with nonlinear and multi dimensional problems numerical applications indicate their effectiveness

collocation methods with controllable dissipation for linear dynamics abstract this paper introduces a unified set of collocation methods for linear dynamics in which a parameter is used to control the position of the collocation points in this manner both a stable algorithms of order 2 p and l stable algorithms of order 2 p 1 are derived from collocation polynomials of degree p in addition algorithms with intermediate accuracy and stability properties are made available the effects of varying the algorithmic parameter are investigated with particular reference to the numerical dissipation of spurious high frequency modes numerical tests are reported which support the theoretical analysis and demonstrate the performance of the proposed algorithms

high order taylor galerkin methods for linear hyperbolic systems a new family of high order taylor galerkin schemes is presented for the analysis of first order linear hyperbolic systems the schemes are unconditionally stable which makes them very attractive to use in conjunction with adaptive hp finite element methods for spatial approximation

consistency measures for hesitant fuzzy linguistic preference relations hesitant fuzzy linguistic term sets hfltss are used to deal with situations in which the decision makers dms think of several possible linguistic values or richer expressions than a single term for an indicator alternative variable etc compared with fuzzy linguistic approaches they are more convenient and flexible to reflect the dms preferences in decision making for further applications of hfltss to decision making we develop a concept of hesitant fuzzy linguistic preference relations hflprs as a tool to collect and present the dms preferences due to the importance of the consistency measures using preference relations in decision making we develop some consistency measures for hflprs to ensure that the dms are being neither random nor illogical a consistency index is defined to establish the consistency thresholds of hflprs to measure whether an hflpr is of acceptable consistency for hflprs with unacceptable consistency we develop two optimization methods to improve the consistency until they are acceptable several illustrative examples are given to validate the consistency measures and the optimization methods

the design of granular classifiers a study in the synergy of interval calculus and fuzzy sets in pattern recognition in this study we are concerned with a development of a certain category of granular classifiers referred here to as hyperbox driven classifiers hdc the approach fully capitalizes on the two key technologies of granular computing namely set interval calculus and fuzzy sets in dealing with a description of geometry of patterns data belonging to a certain category we take advantage of the capabilities of sets intervals and their cartesian products when describing a core structure of classes of patterns in the form of some hyperboxes their combinations are referred to as a core structure of the feature space next we refine the geometry of the classifier by bringing forward the concepts of regions of the feature space characterized by fuzzy sets they are sought as a secondary structure the construction of the core structure is realized by means of the supervised version of dbscan one of the popular clustering algorithms of data mining the secondary structure is described by fuzzy sets whose membership functions are a solution to some optimization problem of allocation of degrees of belongingness in the formation of the secondary structure we exploit a concept of the hausdorff distance that determines a distance between some information granule of a well defined geometry and a numeric pattern a point in the highly dimensional feature space the two stage description of the granular classifier is also beneficial in the characterization of the classification error by virtue of the design of the core structure the classification error occurring there assumes very small almost zero values on the other hand the secondary structure coming with a substantial level of overlap between classes is characterized by relatively higher values of the classification error being cognizant of that we suggest a way of forming a synthetic measure built on the membership values and named a separability index that helps quantify the classification error in this setting a series of numeric examples are used to demonstrate the effectiveness of the proposed granular classifiers

study of non fickian diffusion problems with the potential field in the cylindrical co ordinate system the present study applies a hybrid numerical scheme of the laplace transform technique and the control volume method in conjunction with the hyperbolic shape functions to investigate the effect of a potential field on the one dimensional non fickian diffusion problems in the cylindrical co ordinate system the laplace transform method is used to remove the time dependent terms in the governing differential equation and the boundary conditions and then the resulting equations are discretized by the control volume scheme the primary difficulty in dealing with the present problem is the suppression of numerical oscillations in the vicinity of sharp discontinuities results show that the present numerical results do not exhibit numerical oscillations and the potential field plays an important role in the present problem the strength of the jump discontinuity can be reduced by increasing the value of the potential gradient the propagation speed of mass wave is independent of the potential gradient and the boundary condition copyright 2003 john wiley sons ltd

feature analysis through information granulation and fuzzy sets feature analysis and feature selection are fundamental pursuits in pattern recognition we revisit and generalize an issue of feature selection by introducing a mechanism of soft fuzzy feature selection the underlying idea is to consider features to be granular rather than numeric by varying the level of granularity we modify the level of contribution of the specific feature to the overall feature space we admit an interval model of the features meaning that their values assume a form of numeric intervals the intervalization of the features exhibits a clear cut interpretation moreover a contribution of the features to the formation of the feature space can be easily controlled the broader the interval the less essential contribution of the feature to the entire feature space in limit when the intervals get broad enough one may view the feature to be completely eliminated dropped from the feature space the quantification of the features in terms of their importance is realized in the setting of the clustering fcm model namely a process of the binary or fuzzy feature selection is carried out and numerically quantified in the space of membership values generated by fuzzy clusters as the focal point of this study concerns an interval like form of information granules we reveal how such feature intervalization helps approximate fuzzy sets described by any type of membership function detailed computations give rise to a detailed quantification of such granular features numerical experiments provide a comprehensive numerical illustration of the problem

combined continuum damage embedded discontinuity model for explicit dynamic fracture analyses of quasi brittle materials summary in this paper a novel constitutive model combining continuum damage with embedded discontinuity is developed for explicit dynamic analyses of quasi brittle failure phenomena the model is capable of describing the rate dependent behavior in dynamics and the three phases in failure of quasi brittle materials the first phase is always linear elastic followed by the second phase corresponding to fracture process zone creation represented with rate dependent continuum damage with isotropic hardening formulated by utilizing consistency approach the third and final phase involving nonlinear softening is formulated by using an embedded displacement discontinuity model with constant displacement jumps both in normal and tangential directions the proposed model is capable of describing the rate dependent ductile to brittle transition typical of cohesive materials e g rocks and ice the model is implemented in the finite element setting by using the cst elements the displacement jump vector is solved for implicitly at the local finite element level along with a viscoplastic return mapping algorithm whereas the global equations of motion are solved with explicit time stepping scheme the model performance is illustrated by several numerical simulations including both material point and structural tests the final validation example concerns the dynamic brazilian disc test on rock material under plane stress assumption copyright 2014 john wiley sons ltd

multi parameter tikhonov regularization and model function approach to the damped morozov principle for choosing regularization parameters in this paper we study the multi parameter tikhonov regularization method which adds multiple different penalties to exhibit multi scale features of the solution an optimal error bound of the regularization solution is obtained by a priori choice of multiple regularization parameters some theoretical results of the regularization solution about the dependence on regularization parameters are presented then an a posteriori parameter choice i e the damped morozov discrepancy principle is introduced to determine multiple regularization parameters five model functions i e two hyperbolic model functions a linear model function an exponential model function and a logarithmic model function are proposed to solve the damped morozov discrepancy principle furthermore four efficient model function algorithms are developed for finding reasonable multiple regularization parameters and their convergence properties are also studied numerical results of several examples show that the damped discrepancy principle is competitive with the standard one and the model function algorithms are efficient for choosing regularization parameters

saddle point principles and numerical integration methods for second order hyperbolic equations abstract this work describes a family of functionals whose stationarity often saddle point condition leads to well known so called variational formulations for structural dynamics such as the weak hamilton ritz formulation and the continuous discontinuous galerkin formulation and in turn to methods for the numerical integration of the equations of motion it is shown that all the time integration methods based on variational formulations do descend from such functionals moreover starting from the described family of functionals it is possible to construct new families of time integration methods which might exhibit computational advantages over the corresponding ones derived from variational formulations only

use of post processing to increase the order of accuracy of the trapezoidal rule at time integration of linear elastodynamics problems in this paper we suggest a very simple and effective post processing procedure to increase the order of accuracy in time for numerical results obtained by the trapezoidal rule we first derive a new exact closed form a priori error estimator for time integration of linear elastodynamics equations by the trapezoidal rule with non uniform time increments based on this error estimator we suggest a new post processing procedure containing additional time integration of elastodynamics equations by the trapezoidal rule with few time increments that systematically improves the order of accuracy of numerical results with the increase in the number of additional time increments used for post processing for example the use of just one additional time increment for post processing after time integration with any number of uniform time increments renders the order of accuracy of numerical results equal to 10 3 numerical examples of the application of the new techniques to a system with a single degree of freedom and to a multi degree system confirm the corresponding increase in the order of convergence of numerical results after post processing because the same trapezoidal rule is used for basic computations and post processing the new technique retains all of the properties of the trapezoidal rule requires no writing of a new computer program for its implementation and can be easily used with any existing commercial and research codes for elastodynamics

an efficient time frequency domain algorithm for modal analysis of non linear models discretized by the fem abstract the present paper describes an efficient time frequency domain approach for modal analysis of non linear models discretized by the fem an efficient recurrence relationship for displacement and velocity based on the green s function of the model and its time derivative is presented in both a time and a frequency domain context in the time domain procedure the green s function related terms are analytical in the frequency domain procedure the fundamental terms are indirectly evaluated taking into account steady state responses of the system the pseudo force method is adopted in order to deal with the model non linearity results for the time frequency domain approaches discussed here showed the same level of accuracy as those obtained by the newmark modified newton algorithm at a lower computational cost

fuzzy sets in pattern recognition methodology and methods abstract an objective of the paper is to discuss a state of the art of methodology and algorithms of fuzzy sets in the field of pattern recognition in real world recognition and classification problems we are faced with fuzziness that is connected with diverse facets of cognitive activity of the human being an origin of sources of fuzziness is related to labels expressed in feature space as well as to labels of classes taken into account in classification procedures an evident difference between a way of information processing by means of probability and fuzzy set theory and a way of interpretation of results is explained in detail in sequel methods of pattern recognition are studied in two main streams namely supervised and unsupervised learning different approaches to designing of classification schemes as e g relation calculus decision making approach etc are put into account a method of feature selection with the aid of fuzzy measure and fuzzy integral is introduced in clustering techniques methods relying on minimization of objective function are analyzed in detail also a problem of cluster validity expressed in terms of clustering indices is addressed numerical examples are also provided

extended framework of hamiltons principle for thermoelastic continua based upon the extended framework of hamiltons principle a variational formulation for fully coupled thermoelasticity is presented the resulting formulation can properly account for all the governing differential equations as well as initial boundary conditions thus it provides the basis for a class of unified spacetime finite element methods by employing bar elements in one dimensional space along with linear shape functions temporally the simplest spacetime finite element method is presented herein with representative examples for its validity

a methodology for the generation of low cost higher order methods for linear dynamics this work presents a methodology which generates efficient higher order methods for linear dynamics by improving the accuracy properties of norsett methods towards those of pade methods the methodology is based on a simple and low cost iterative procedure which is used to implement a set of higher order methods with controllable dissipation a sequence of improved solutions is obtained which correspond to algorithms offering an effective compromise between the efficiency of norsett methods and the accuracy of pade methods moreover a direct control over high frequency dissipation is possible by means of an algorithmic parameter numerical tests are reported which confirm that this set of algorithms is really attractive for linear dynamic analysis copyright 2003 john wiley sons ltd

a taylor galerkin method for convective transport problems a method is described to derive finite element schemes for the scalar convection equation in one or more space dimensions to produce accurate temporal differencing the method employs forward time taylor series expansions including time derivatives of second and third order which are evaluated from the governing partial differential equation this yields a generalized time discretized equation which is successively discretized in space by means of the standard bubnov galerkin finite element method the technique is illustrated first in one space dimension with linear elements and euler leap frog and crank nicolson time stepping several interesting relations with standard galerkin and recently developed petrov galerkin methods emerge and the new taylor galerkin schemes are found to exhibit particularly high phase accuracy with minimal numerical damping the method is successively extended to deal with variable coefficient problems and multi dimensional situations

a unified set of single step algorithms part 1 general formulation and applications a general algorithm for a single step time marching scheme for use in dynamic or diffusion equations is presented this algorithm is easily programmed in its universal form for all orders of approximation and covers most of the currently used schemes as well as presenting many new possibilities in many cases it presents a computationally advantageous form over conventional procedures this is particularly so when compared with the newmark algorighm and its variants

weighting parameters for time step integration algorithms with predetermined coefficients in this paper the effect of using the predetermined coefficients in constructing time step integration algorithms is investigated both first and second order equations are considered the approximate solution is assumed to be in a form of polynomial in the time domain it can be related to the truncated taylor s series expansion of the exact solution therefore some of the coefficients can be predetermined from the known initial conditions if there are m predetermined coefficients and r unknown coefficients in the approximate solution the unknowns can be solved by the weighted residual method the weighting parameter method is used to investigate the resultant algorithm characteristics it is shown that the formulation is consistent with a minimum order of accuracy m r the maximum order of accuracy achievable is m 2r unconditionally stable algorithms exist if m r for first order equations and m 1 r for second order equations hence the dahlquist s theorem is generalized algorithms equivalent to the pade approximations and unconditionally stable algorithms equivalent to the generalized pade approximations are constructed the corresponding weighting parameters and weighting functions for the pade and generalized pade approximations are given explicitly copyright 2000 john wiley sons ltd

a novel time marching scheme using numerical green s functions a comparative study for the scalar wave equation abstract the present paper presents the formulation of a novel time marching method based on the explicit green s approach exga to solve scalar wave propagation problems by means of the weighted residual method in both time and space the time integral expression concerning the exga is readily established the arising exga time integral expression is spatially discretized in a finite element sense and a recursive scheme that employs time domain numerical green s function matrices is adopted to evaluate the displacement and the velocity vectors these green s matrices are computed by the time discontinuous galerkin finite element method only at the first time step the system of coupled equations originated from the time discontinuous galerkin method is then solved by an iterative predictor multicorrector algorithm once the green s matrices are computed no iterative process is required to obtain the displacement and the velocity vectors at any time level at the end of the paper numerical examples are presented in order to compare the proposed approach with other approaches

completeness of zero curve tracing for analytic functions abstract empirical data for the polynomial confirm the efficiency of exploring function structure as a means of isolating the zeros of a scalar analytic function defined on a disk klip 1985 in exceptional cases the tracing is not complete which means that certain arcs may not have been traced a mathematical basis for the algorithm which investigates and restores completeness the so called completeness algorithm is presented the main theorem is that completeness of the tracing as verified at the isolated zeros is sufficient for completeness of the tracing its proof evolves along various lemmas one of which provides a new condition for the location of the critical points the paper concludes with a brief description of the completeness algorithm

an explicit time integration technique for dynamic analyses a simple explicit solution technique for problems in structural dynamics based on a modified trapezoidal rule method mtm approximation of the governing ordinary differential equations is developed the resulting conditionally stable explicit method mtm can be easily implemented and is extremely simple to use particular attention is focused herein on the concept of numerical stability of the proposed method for a free vibrational response of a linear undamped single degree of freedom system sdof to examine the effectiveness strengths and limitations of mtm error analyses for the natural period the displacement the velocity and the associated phase angle for a free undamped simple mass spring system are derived and compared with modified euler method mem and the well known newmark beta method nbm numerical examples for a sdof system and a multi degree of freedom mdof system are presented to illustrate the strengths and the limitations of the proposed method

an analytic approach to the solution of non linear equations abstract isolating the zeros of a scalar function analytic on a disk by means of exploring function structure was shown to be very efficient klip 1985 this will be exemplified in this paper on the hand of data obtained with certain test polynomials it was shown by klip 1987 that the structure of the zero curves for the polynomial leads to a new formulation of the location of the critical points it will be proven that the number of critical points in a branch region of order m equals m 1 completeness of the tracing is an important issue we give an account of the design of the completeness algorithm and discuss the role of a small listprocessing system in registering temporarily stored data as well as modifications of the pathways

on a new time integration method for solving time dependent partial differential equations abstract a numerical time integration algorithm that combines the high accuracy of the precise time integration method and the computational efficiency of the finite difference schemes in this paper the algorithm is explicit and unconditionally stable it can also be modified easily to achieve different levels of accuracy by using more integration points numerical examples of both linear and non linear pde problems are discussed in the paper

mass lumping techniques in the spectral element method on the equivalence of the row sum nodal quadrature and diagonal scaling methods abstract in the context of wave propagation analysis the spectral element method sem in conjunction with a diagonal mass matrix is often the method of choice therefore it is of high importance to investigate the influence of different mass lumping schemes on the accuracy of the numerical results to this end we compare the performance of three established methods including the row sum method the nodal quadrature method and the diagonal scaling method the theoretical analysis of these methods reveals a close connection between them under certain conditions that are discussed in detail in this article we are able to show a direct equivalence between these three approaches in this regard the attainable accuracy of the numerical integration of the mass matrix plays an important role by means of several dynamic benchmark problems we verify the theoretical results and illustrate the convergence properties of the lumped mass matrix sem in comparison to a formulation based on the consistent mass matrix

a fuzzy envelope for hesitant fuzzy linguistic term set and its application to multicriteria decision making decision making is a process common to human beings the uncertainty and fuzziness of problems demand the use of the fuzzy linguistic approach to model qualitative aspects of problems related to decision the recent proposal of hesitant fuzzy linguistic term sets supports the elicitation of comparative linguistic expressions in hesitant situations when experts hesitate among different linguistic terms to provide their assessments the use of linguistic intervals whose results lose their initial fuzzy representation was introduced to facilitate the computing processes in which such expressions are used the aim of this paper is to present a new representation of the hesitant fuzzy linguistic term sets by means of a fuzzy envelope to carry out the computing with words processes this new fuzzy envelope can be directly applied to fuzzy multicriteria decision making models an illustrative example of its application to a supplier selection problem through the use of fuzzy topsis is presented

rudiments of an average case complexity theory for piecewise linear path following algorithms we examine the efficiency of pl path following algorithms in followingft 1 0 whereft is the pl approximation induced by the simplicial triangulationt to a mapf n n 1 in particular we consider the problem of determining an upper bound on the expected number of pivots made per unit length off 1 0 that is approximated we show that if the sizes of the simplices oft are sufficiently small where sufficiently small is an explicitly given quantity dependent on measurements of how nice f is then the average directional density oft as introduced by todd really does give a good approximation to the expected number of pivots made confirming what researchers have believed on intuitive grounds for a decade because what constitutes sufficiently small is a precisely given quantity i e non asymptotic we are able to provide some rigorous justification for the claim that the expected number of pivots grows only polynomially inn the number of variables several other issues are also examined

notes on aggregation functions for typical hesitant fuzzy elements and the action of automorphisms inform sci 255 2014 82 99 the purpose of this note is first to point out several assertions proposition 1 example 4 in bedregal et al 1 are incorrect by counterexamples and second to give some partial orders on h

time finite element discretization of hamilton s law of varying action hamilton s law of varying action is used as a variational source for the derivation of finite element discretization procedure in the time domain three different versions of the proposed algorithms are presented and verified for accuracy and stability the first one is the high precision finite time element analogous to the standard finite elements with cutoff frequency the second version is the step by step one time element from which the unconditionally stable with slightly altered accuracy third algorithm is derived the new operator connected with the proposed algorithms bears attractive properties of much greater accuracy than other existing stable methods and easy computer implementation thus the work herein shows that the reservations expressed against the use of finite elements in time domain seem unjustified

a precise time step integration method by step response and impulsive response matrices for dynamic problems in this paper a precise time step integration method for dynamic problems is presented the second order differential equations for dynamic problems are manipulated directly a general damping matrix is considered the transient responses are expressed in terms of the steady state responses the given initial conditions and the step response and impulsive response matrices the steady state responses for various types of excitations are readily obtainable the computation of the step response and impulsive response matrices and their time derivatives are studied in this paper a direct computation of these matrices using the taylor series solutions is not efficient when the time step size t is not small in this paper the recurrence formulae relating the response matrices at t t to those at t t 2 are constructed a recursive procedure is proposed to evaluate these matrices at t t from the matrices at t t 2m the matrices at t t 2m are obtained from the taylor series solutions to improve the computational efficiency the relations between the response matrices and their time derivatives are investigated in addition these matrices are expressed in terms of two symmetric matrices that can also be evaluated recursively besides from the physical point of view these matrices should be banded for small t both the stability and accuracy characteristics of the present algorithm are studied three numerical examples are used to illustrate the highly precise and stable algorithm 1997 john wiley sons ltd

conjugate gradient method for the robin inverse problem associated with the laplace equation this paper studies a non linear inverse problem associated with the laplace equation of identifying the robin coefficient from boundary measurements a variational formulation of the problem is suggested thereby transforming it into an optimization problem mathematical properties relevant to its numerical computation are established the optimization problem is solved using the conjugate gradient method in conjunction with the discrepancy principle and the algorithm is implemented using the boundary element method numerical results are presented for several benchmark problems with both exact and noisy data and the convergence of the algorithm with respect to mesh refinement and decreasing the amount of noise in the data is investigated copyright 2006 john wiley sons ltd

on the complexity of a piecewise linear algorithm for approximating roots of complex polynomials lets be a triangulation of andf z zd ad 1zd 1 a0 a complex polynomial letf be the piecewise linear approximation off determined bys for certains we establish an upper bound on the complexity of an algorithm which finds zeros off this bound is a polynomial in terms ofn max ai i and measures of the sizes of simplices ins

accelerated landweber iterations for the solution of ill posed equations in this paper the potentials of so calledlinear semiiterative methods are considered for the approximate solution of linear ill posed problems and ill conditioned matrix equations several efficient two step methods are presented most of which have been introduced earlier in the literature stipulating certain conditions concerning the smoothness of the solution a notion of optimal speed of convergence may be formulated various direct and converse results are derived to illustrate the properties of this concept if the problem s right hand side data are contaminated by noise semiiterative methods may be used asregularization methods assuming optimal rate of convergence of the iteration for the unperturbed problem the regularized approximations will be of order optimal accuracy to derive these results specific properties of polynomials are used in connection with the basic theory of solving ill posed problems rather recent results onfast decreasing polynomials are applied to answer an open question of brakhage numerical examples are given including a comparison to the method of conjugate gradients

explicit time integration algorithms for structural dynamics with optimal numerical dissipation abstract a new predictor corrector explicit time integration algorithm is presented for solving structural dynamics problems the basis of the algorithm is the implicit generalized method developed by the authors like its implicit parent the explicit generalized method is a one parameter family of algorithms in which the parameter defines the high frequency numerical dissipation for a given value of high frequency dissipation the explicit generalized method minimizes low frequency dissipation the algorithm can be utilized effectively for structural dynamics calculations in which numerical dissipation is needed to reduce spurious oscillations parameter values are given that enable physical damping to be treated explicitly while maintaining second order accuracy without the need for an expensive second corrector pass

time domain bem analysis for the 2d scalar wave equation initial conditions contributions to space and time derivatives the complete expressions corresponding to space and time derivatives of volterra s integral representation of the time dependent scalar wave equation are presented in this paper the concept of finite part of an integral is used in order to compute boundary kernels contributions time integration of boundary kernels is performed analytically for linear and constant time approximations for the potential and its normal derivative respectively the new integral representations presented in this text are quite general as contributions due to the initial conditions have also been included two examples are presented in order to assess the accuracy of the formulation

interval valued hesitant fuzzy linguistic sets and their applications in multi criteria decision making problems an interval valued hesitant fuzzy linguistic set ivhfls can serve as an extension of both a linguistic term set and an interval valued hesitant fuzzy set this new set combines quantitative evaluation with qualitative evaluation these can describe the real preferences of decision makers and reflect their uncertainty hesitancy and inconsistency this work focuses on multi criteria decision making mcdm problems in which the criteria are in different priority levels and the criteria values take the form of interval valued hesitant fuzzy linguistic numbers ivhflns the new approach to solving these problems is based on the prioritized aggregation operators of ivhflns having reviewed the relevant literature we provide interval valued hesitant fuzzy linguistic operations and apply some linguistic scale functions which have been improved on the basis of psychological theory and prospect theory ultimately two kinds of prioritized aggregation operators of ivhflns are developed which extend to a grouping prioritized situation and are applied to mcdm problems finally an example is provided to illustrate and verify the proposed approach in two separate situations which are then compared to other representative methods

a statistical comparative study of different similarity measures of consensus in group decision making an essential aim in group decision making gdm problems is to achieve a high level of consensus among experts consensus is defined as general or widespread agreement and it is usually modelled mathematically via a similarity function measuring how close experts opinions or preferences are similarity functions are defined based on the use of a metric describing the distance between experts opinions or preferences in the literature different metrics or distance functions have been proposed to implement in consensus models but no study has been carried out to analyse the influence the use of different distance functions can have in the gdm process this paper presents a comparative study of the effect of the application of some different distance functions for measuring consensus in gdm by using the nonparametric wilcoxon matched pairs signed ranks test it is concluded that different distance functions can produce significantly different results moreover it is also shown that their application also has a significant effect on the speed of achieving consensus finally these results are analysed and used to derive decision support rules based on a convergent criterion that can be used to control the convergence speed of the consensus process using the compared distance functions

an efficient hybrid time laplace domain method for elastodynamic analysis based on the explicit green s approach abstract this work aims at presenting a novel hybrid method applied to the numerical solution of elastodynamic problems the formulation is based on the so called explicit green s approach exga recently developed by mansur et al mansur w j loureiro f s soares jr d dors c 2007 explicit time domain approaches based on numerical green s functions computed by finite differences the exga family journal of computational physics 227 851 870 in which a recursive time integration procedure based on green s function is adopted here the finite element method is employed to calculate the green s function in the laplace domain afterwards the zakian s laplace inversion algorithm is employed to compute numerically the green s function in the time domain only at time t t time integration is then carried out by employing the standard exga procedure and another where the convolution integral is replaced by a particular solution that is directly related to the applied load finally some numerical problems are solved to demonstrate the computational efficiency and reliability of the proposed hybrid method

explicit time domain approaches based on numerical green s functions computed by finite differences the exga family the present paper describes a new family of time stepping methods to integrate dynamic equations of motion the scalar wave equation is considered here however the method can be applied to time domain analyses of other hyperbolic e g elastodynamics or parabolic e g transient diffusion problems the algorithms presented require the knowledge of the green s function of mechanical systems in nodal coordinates the finite difference method is used here to compute numerically the problem green s function however any other numerical method can be employed e g finite elements finite volumes etc the green s matrix and its time derivative are computed explicitly through the range 0 dt with either the fourth order runge kutta algorithm or the central difference scheme in order to improve the stability of the algorithm based on central differences an additional matrix called step response is also calculated the new methods become more stable and accurate when a sub stepping procedure is adopted to obtain the green s and step response matrices and their time derivatives at the end of the time step three numerical examples are presented to illustrate the high precision of the present approach

a predictor corrector iterated tikhonov regularization for linear ill posed inverse problems many questions in science and engineering often give rise to linear ill posed inverse problems to enable meaningful approximate solutions of the inverse problems various regularization methods have subsequently been proposed to make these problems less sensitive to perturbations one of the most popular regularization techniques is iterated tikhonov regularization which has attracted considerable attention due to its interesting applications in practical however this regularization often suffers from inaccurate results and low computational efficiency in some situations in this paper we proposed an accelerated predictor corrector iterated tikhonov regularization this method combined the classical iterated tikhonov regularization with modified euler method which could improve computational efficiency without sacrificing numerical accuracy the convergence rate of the accelerated regularization was investigated theoretically when the right hand side was corrupted by noise in particular we derived an error estimate of optimal order for the convergence of the accelerated regularization both one and two dimensional numerical experiments were implemented to illustrate the accuracy and efficiency of the accelerated version of iterated tikhonov regularization