a new primal dual weak galerkin finite element method for ill posed elliptic cauchy problems abstract a new numerical method is devised and analyzed for a type of ill posed elliptic cauchy problems by using the primal dual weak galerkin finite element method this new primal dual weak galerkin algorithm is robust and efficient in the sense that the system arising from the scheme is symmetric well posed and is satisfied by the exact solution if it exists an error estimate of optimal order is established for the corresponding numerical solutions in a scaled residual norm in addition a mathematical convergence is established in a weak l 2 topology for the new numerical method numerical results are reported to demonstrate the efficiency of the primal dual weak galerkin method as well as the accuracy of the numerical approximations

the construction of preconditioners for elliptic problems by substructuring i in earlier parts of this series of papers we constructed preconditioners for the discrete systems of equations arising from the numerical approximation of elliptic boundary value problems the resulting algorithms are well suited for implementation on computers with parallel architecture in this paper we will develop a technique which utilizes these earlier methods to derive even more efficient preconditioners the iterative algorithms using these new preconditioners converge to the solution of the discrete equations with a rate that is independent of the number of unknowns these preconditioners involve an incomplete chebyshev iteration for boundary interface conditions which results in a negligible increase in the amount of computational work theoretical estimates and the results of numerical experiments are given which demonstrate the effectiveness of the methods

on the modelling of incompressibility in linear and non linear elasticity with the master slave approach this is the pre peer reviewed version of the following article munoz jose j on the modelling of incompressibility in linear and non linear elasticity with the master slave approach international journal for numerical methods in engineering abril 2008 vol 74 num 2 p 269 293 which has been published in final form at http www3 interscience wiley com journal 116323442 abstract

reciprocal transitive matrices over abelian linearly ordered groups we consider reciprocal matrices over an abelian linearly ordered group in this way we provide a general framework including multiplicative additive and fuzzy matrices in a multi criteria decision making context a pairwise comparison matrix a a i j is a reciprocal matrix that represents a useful tool for determining a weighting vector w for a set x of decision elements but when a is inconsistent the weighting vector usually proposed in literature may provide a ranking on x that does not agree with the expressed preference intensities a i j thus it is unreliable we analyze a condition of transitivity for a reciprocal matrix a a i j over an abelian linearly ordered group that whenever a is a pairwise comparison matrix allows us to state a qualitative dominance ranking on x and obtain ordinal evaluation vectors in this way we get a first tool for checking the reliability of a weighting vector we also provide tools to check the transitivity

a new paradigm for parallel adaptive meshing algorithms we present a new approach to the use of parallel computers with adaptive finite element methods this approach addresses the load balancing problem in a new way requiring far less communication than current approaches it also allows existing sequential adaptive pde codes such as pltmg and mc to run in a parallel environment without a large investment in recoding in this new approach the load balancing problem is reduced to the numerical solution of a small elliptic problem on a single processor using a sequential adaptive solver without requiring any modifications to the sequential solver the small elliptic problem is used to produce a posteriori error estimates to predict future element densities in the mesh which are then used in a weighted recursive spectral bisection of the initial mesh the bulk of the calculation then takes place independently on each processor with no communication using possibly the same sequential adaptive solver each processor adapts its region of the mesh independently and a nearly load balanced mesh distribution is usually obtained as a result of the initial weighted spectral bisection only the initial fan out of the mesh decomposition to the processors requires communication two additional steps requiring boundary exchange communication may be employed after the individual processors reach an adapted solution namely the construction of a global conforming mesh from the independent subproblems followed by a final smoothing phase using the subdomain solutions as an initial guess we present a series of convincing numerical experiments which illustrate the effectiveness of this approach the justification of the initial refinement prediction step as well as the justification of skipping the two communication intensive steps is supported by some recent j xu and a zhou math comp to appear and not so recent j a nitsche and a h schatz math comp 28 1974 pp 937 958 a h schatz and l b wahlbin math comp 31 1977 pp 414 442 a h schatz and l b wahlbin math comp 64 1995 pp 907 928 results on local a priori and a posteriori error estimation

parallel spectral element solution of the stokes problem abstract in this paper we present a high efficiency medium grained parallel spectral element method for numerical solution of the stokes problem in general domains the method is based upon naturally concurrent uzawa and jacobi preconditioned conjugate gradient iterative methods geometry based data parallel distribution of work amongst processors nearest neighbor sparsity and high order substructuring for minimum communication general locally structured globally unstructured parallel constructs and efficient embedding of vector reduction operations for inner product and norm calculation an analysis is given for the computational complexity of the algorithm on a native medium grained parallel processor and the potential communication superiority of high order discretizations is described lastly the method is implemented on the fast intel vector hypercube and the performance of this algorithm architecture coupling is evaluated in a technical and economic framework that reflects the true advantages of parallel solution of partial differential equations

primal dual weak galerkin finite element methods for elliptic cauchy problems abstract the authors propose and analyze a well posed numerical scheme for a type of ill posed elliptic cauchy problem by using a constrained minimization approach combined with the weak galerkin finite element method the resulting euler lagrange formulation yields a system of equations involving the original equation for the primal variable and its adjoint for the dual variable and is thus an example of the primal dual weak galerkin finite element method this new primal dual weak galerkin algorithm is consistent in the sense that the system is symmetric well posed and is satisfied by the exact solution a certain stability and error estimates were derived in discrete sobolev norms including one in a weak l 2 topology some numerical results are reported to illustrate and validate the theory developed in the paper

coupled fe be method for eigenvalue analysis of elastic structures submerged in an infinite fluid domain summary for thin elastic structures submerged in heavy fluid e g water a strong interaction between the structural domain and the fluid domain occurs and significantly alters the eigenfrequencies therefore the eigenanalysis of the fluid structure interaction system is necessary in this paper a coupled finite element and boundary element fe be method is developed for the numerical eigenanalysis of the fluid structure interaction problems the structure is modeled by the finite element method the compressibility of the fluid is taken into consideration and hence the helmholtz equation is employed as the governing equation and solved by the boundary element method bem the resulting nonlinear eigenvalue problem is converted into a small linear one by applying a contour integral method adequate modifications are suggested to improve the efficiency of the contour integral method and avoid missing the eigenvalues of interest the burton miller formulation is applied to tackle the fictitious eigenfrequency problem of the bem and the optimal choice of its coupling parameter is investigated for the coupled fe be method numerical examples are given and discussed to demonstrate the effectiveness and accuracy of the developed fe be method copyright 2016 john wiley sons ltd

substructuring preconditioners for the q_1 mortar element method the q 1 mortar element method is a non conforming finite element method with q 1 elements based on domain decomposition for the laplace equation it yields an ill conditioned linear system for solving the linear system the so called preconditioned conjugate gradient method in a subspace is used preconditioners are proposed and estimates on condition numbers and arithmetical complexity are given finally numerical experiments are presented

bv estimates for mortar methods in linear elasticity this paper is concerned with the convergence of mortar methods applied to linear elasticity we prove that the conventional mesh dependent norms used in the analysis of mortar methods are bounded below by the bv norm when combined with standard results this bound establishes a decomposition independent and mesh independent proof of the convergence of mortar methods in linear elasticity

stability of compacton solutions of fifth order nonlinear dispersive equations we consider fifth order nonlinear dispersive k m n p type equations to study the effect of nonlinear dispersion using simple scaling arguments we show how instead of the conventional solitary waves such as solitons the interaction of the nonlinear dispersion with nonlinear convection generates compactons the compact solitary waves free of exponential tails this interaction also generates many other solitary wave structures such as cuspons peakons tipons etc which are otherwise unattainable with linear dispersion various self similar solutions of these higher order nonlinear dispersive equations are also obtained using similarity transformations further it is shown that like the third order nonlinear k m n equations the fifth order nonlinear dispersive equations also have the same four conserved quantities and furthermore even any arbitrary odd order nonlinear dispersive k m n p type equations also have the same three and most likely the four conserved quantities finally the stability of the compacton solutions for the fifth order nonlinear dispersive equations are studied using linear stability analysis from the results of the linear stability analysis it follows that unlike solitons all the allowed compacton solutions are stable since the stability conditions are satisfied for arbitrary values of the nonlinear parameters

compacton solutions in a class of generalized fifth order korteweg de vries equations solitons play a fundamental role in the evolution of general initial data for quasilinear dispersive partial differential equations such as the korteweg de vries kdv nonlinear schrodinger and the kadomtsev petviashvili equations these integrable equations have linear dispersion and the solitons have infinite support we have derived and investigate a new kdv like hamiltonian partial differential equation from a four parameter lagrangian where the nonlinear dispersion gives rise to solitons with compact support compactons the new equation does not seem to be integrable and only mass momentum and energy seem to be conserved yet the solitons display almost the same modal decompositions and structural stability observed in integrable partial differential equations the compactons formed from arbitrary initial data are nonlinearly self stabilizing and maintain their coherence after multiple collisions the robustness of these compactons and the inapplicability of the inverse scattering tools that worked so well for the kdv equation make it clear that there is a fundamental mechanism underlying the processes beyond integrability we have found explicit formulas for multiple classes of compact traveling wave solutions when there are more than one compacton solution for a particular set of parameters the wider compacton is the minimum of a reduced hamiltonian and is the only one that is stable

the reflection of narrow slow quantum packets from mirrors we study the reflection of narrow in space quantum wavepackets from nonabsorptive mirrors totally or partially reflecting if the initial mean value of the momentum component perpendicular to the mirror surface is less than the momentum uncertainty then the mean value of this component gradually increases with time at the expense of shrinking the packet in the momentum space as a consequence very slow particles moving initially in the direction parallel to the mirror surface will be deflected to appreciable angles even when they pass at macroscopical distances from the mirror we give analytical expressions describing the asymptotical behaviour of wavefunctions and density matrices in the coordinate and momentum representations for arbitrary narrow initial packets we show that the asymptotical mean values and variances do not depend on the phases of the complex reflection and transmission coefficients moreover they are insensitive to the concrete form of the reflective potential in the case of totally reflecting mirrors for partially reflecting mirrors we introduce the concept of conditional wavefunctions and mean values the dependences of the asymptotical values of different quantities characterizing the packet e g the momentum transformation coefficient and the invariant uncertainty product on the parameters of the reflecting potential the height and width or characteristic length of the transition region are analysed in the examples of the potentials of epstein s type and their limit cases the ideal reflecting wall and the delta potential a possibility for the verification of the effect of quantum deflection in experiments with ultracold atoms is briefly discussed

stability of compacton solutions the stability of the recently discovered compacton solutions is studied by means of both linear stability analysis as well as lyapunov stability criteria from the results obtained it follows that unlike solitons all the allowed compacton solutions are stable as the stability condition is satisfied for arbitrary values of the nonlinearity parameter the results are shown to be true even for the higher order nonlinear dispersion equations for compactons some new conservation laws for the higher order nonlinear dispersion equations are also presented

wavelet stabilization of the lagrange multiplier method we propose here a stabilization strategy for the lagrange multiplier formulation of dirichlet problems the stabilization is based on the use of equivalent scalar products for the spaces h 1 2 partial omega and h 1 2 partial omega which are realized by means of wavelet functions the resulting stabilized bilinear form is coercive with respect to the natural norm associated to the problem a uniformly coercive approximation of the stabilized bilinear form is constructed for a wide class of approximation spaces for which an optimal error estimate is provided finally a formulation is presented which is obtained by eliminating the multiplier by static condensation this formulation is closely related to the nitsche s method for solving dirichlet boundary value problems

flow rate boundary problems for an incompressible fluid in deformable domains formulations and solution methods in this paper we consider the numerical solution of the interaction of an incompressible fluid and an elastic structure in a truncated computational domain as well known in this case there is the problem of prescribing realistic boundary data on the artificial sections when only partial data are available this problem has been investigated extensively for the rigid case in this work we start considering the compliant case by focusing on the flow rate conditions for the fluid we propose three formulations of this problem different algorithms for its numerical solution and carry out several 2d numerical simulations with the aim of comparing the performances of the different algorithms

algebraic representations of the weighted mean abstract we introduce a general framework for the algebraic representation of the weighted mean in the case in which priorities and values refer to a common aggregation domain for instance in hierarchical multicriteria decision models of the ahp type the general framework proposed is based on the semifield structure of open interval domains and provides a natural algebraic description of weighted mean aggregation including the essential mechanism of normalization which transforms priorities into weights such description necessarily involves two operations addition abelian semigroup and multiplication abelian group which generalize the role of addition and multiplication in p 0 in this sense the semifield framework extends recent work by cavallo d apuzzo and squillante on the multiplicative group structure on the basis of the representation of pairwise comparison matrices and their associated priority vectors we consider open interval domains s r whose semifield structures are generated by bijections s r p continuous thus strictly monotonic bijections play a central role in such case continuous strict triangular conorms norms and uninorms emerge naturally in the representation of the semifield structure and in their weighted version they also provide the representation of the weighted mean in both the arithmetic and geometric forms

analysis and classification of nonlinear dispersive evolution equations in the potential representation a potential representation for the subset of travelling solutions of nonlinear dispersive evolution equations is introduced the procedure involves reduction of a third order partial differential equation to a first order ordinary differential equation the potential representation allows us to deduce certain properties of the solutions without the actual need to solve the underlying evolution equation in particular the paper deals with the so called k n m equations starting from their respective potential representations it is shown that these equations can be classified according to a simple point transformation as a result e g all equations with linear dispersion join the same equivalence class with the korteweg devries equation being its representative and all soliton solutions of higher order nonlinear equations are thus equivalent to the kdv soliton certain equations with both linear and quadratic dispersions can also be treated within this equivalence class

exact compact breather like solutions of two dimensional fermi pasta ulam lattice we demonstrate that two dimensional fermi pasta ulam lattice support exact discrete compact breather like solutions we also find exact compact breather solutions of the same lattice in presence of long range interaction with r s dependence on the distance in the continuum limit the usefulness of these solutions for energy localization and transport in various physical systems are discussed

prolongation structures and exact solutions of k m n equations in this paper rosenau and hyman s phys rev lett 70 564 1993 k m n equations are studied by prolongation technique it is proved that k m n equations are lax integrable only for certain special parameters m n the nontrivial prolongation structures and lax pairs for the integrable cases are given finally as an example the one and two soliton solutions for the k 12 12 equation are derived by means of inverse scattering method

a repository of equations with cosine sine compactons nonlinear evolution equations with cosine sine compacton solutions are reviewed including the rosenau hyman equation and generalizations of korteweg de vries camassa holm boussinesq benjamin bona mahony klein gordon and other equations each equation is generalized to three dimensions and the conditions for its cosine solitary waves to be either a compacton or a soliton are determined several equations claimed in the literature to be different among them are found to be equivalent

incomplete pairwise comparison and consistency optimization this paper proposes a new method for calculating the missing elements of an incomplete matrix of pairwise comparison values for a decision problem the matrix is completed by minimizing a measure of global inconsistency thus obtaining a matrix which is optimal from the point of view of consistency with respect to the available judgements the optimal values are obtained by solving a linear system and unicity of the solution is proved under general assumptions some other methods proposed in the literature are discussed and a numerical example is presented

ensuring reliability of the weighting vector in the context of pairwise comparison matrices pcms defined over abelian linearly ordered group consistency and transitivity represent a full coherence of the decision maker dm and the minimal logical requirement that dm s preferences should satisfy respectively moreover the mean vector wm is proposed as weighting vector for the decision elements related to the pcm in this paper we investigate the effects of inconsistency of a transitive pcm on wm and in order to ensure its reliability as weighting vector we provide the notion of weak consistency it is weaker than consistency and stronger than transitivity and ensures that vectors associated with a pcm by means of a strictly increasing synthesis functional are reliable for assigning a preference order on the set of related decision elements the mean vector wm is associated with a pcm by means of one of these functionals finally we introduce an order relation on the rows of the pcm that is a simple order if and only if the condition of weak consistency is satisfied the simple order allows us to easily determine the actual ranking on the set of related decision elements

the application of fuzzy integrals in multicriteria decision making abstract this paper presents a synthesis on the application of fuzzy integrals as an innovative tool for criteria aggregation in decision problems the main point is that fuzzy integrals are able to model interaction between criteria in a flexible way the methodology has been elaborated mainly in japan and has been applied there successfully in various fields such as design reliability evaluation of goods etc it seems however that this technique is still very little known in europe it is one of the aims of this review to disseminate this emerging technology in many industrial fields

discrete compactons some exact results in this letter we use the method of constructing exact solutions on lattices proposed by kinnersley and described in schmidt 1979 phys rev b 20 4397 to obtain exact compacton solutions in discrete models we examine the linear stability of such solutions both for the bright compacton and for the dark compacton cases we focus on a quantization condition that the width of the profile should satisfy we also use this quantization condition to examine the possibility of compact coherent structures travelling in discrete settings our results are obtained for sinusoidal profiles and then generalized to elliptic functions of arbitrary modulus the possibility of multi compacton solutions is considered

the mortar finite element method with lagrange multipliers the present paper deals with a variant of a non conforming domain decomposition technique the mortar finite element method in the opposition to the original method this variant is never conforming because of the relaxation of the matching constraints at the vertices and the edges in 3d of subdomains it is shown that written under primal hybrid formulation the approximation problem issued from a discretization of a second order elliptic equation in 2d is nonetheless well posed and provides a discrete solution that satisfies optimal error estimates with respect to natural norms finally the parallelization advantages consequence of this variant are also addressed

coupling finite element and spectral methods first results a poisson equation on a rectangular domain is solved by coupling two methods the domain is divided in two squares a finite element approximation is used on the first square and a spectral discretization is used on the second one two kinds of matching conditions on the interface are presented and compared in both cases error estimates are proved

fuzzy integral in multicriteria decision making abstract this paper presents a synthesis on the use of fuzzy integral as an aggregation operator in multicriteria decision making definitions essential properties are given and compared to those of usual aggregation operators a quick survey on applications is given

an iterative stabilized fractional step algorithm for finite element analysis in saturated soil dynamics abstract the discretization of the u p model for saturated porous media results in the semi discrete system of mixed type in displacements and pressures the babuska brezzi condition or the simpler patch test proposed by zienkiewicz and taylor precludes the use of elements with the equal low order of interpolation for u and p unless special stabilization techniques such as the fractional step algorithms are used the purpose of this paper is to present a modified version of the fractional step algorithm which allows much larger time step sizes than those for the existing ones the method is based on introducing an iteration algorithm the numerical experiments demonstrate the effectiveness and improved performance of the proposed modified version of the fractional step algorithm

a weak galerkin mixed finite element method for second order elliptic problems abstract a new weak galerkin wg method is introduced and analyzed for the second order elliptic equation formulated as a system of two first order linear equations this method called wg mfem is designed by using discontinuous piecewise polynomials on finite element partitions with arbitrary shape of polygons polyhedra the wg mfem is capable of providing very accurate numerical approximations for both the primary and flux variables allowing the use of discontinuous approximating functions on arbitrary shape of polygons polyhedra makes the method highly flexible in practical computation optimal order error estimates in both discrete h and l norms are established for the corresponding weak galerkin mixed finite element solutions

the harmonic consistency index for the analytic hierarchy process a new consistency measure the harmonic consistency index is obtained for any positive reciprocal matrix in the analytic hierarchy process we show how this index varies with changes in any matrix element a tight upper bound is provided for this new consistency measure when the entries of matrix are at most 9 as is often recommended using simulation the harmonic consistency index is shown to give numerical values similar to the standard consistency index but it is easier to compute and interpret in addition new properties of the column sums of reciprocal matrices are obtained

two level finite element discretization of viscoelastic fluid flow abstract we propose and analyze a two level method of discretizing the equations of steady state flow of a viscoelastic fluid obeying an oldroyd type constitutive equation with no slip boundary condition the two level algorithm consists of solving a small non linear system of equations on the coarse mesh and then using that solution to solve a larger linear system on the fine mesh specifically following najib and sandri numer math 72 1995 223 we linearize the oldroyd type constitutive equation about the coarse mesh solution thus nullifying the difficulties brought by the advection term our theoretical error estimates show that it has optimal order accuracy provided the true solution is smooth and its norm is sufficiently small in addition our computational error estimates exhibit the validity of our analysis

a review of methods for capacity identification in choquet integral based multi attribute utility theory applications of the kappalab r package the application of multi attribute utility theory whose aggregation process is based on the choquet integral requires the prior identification of a capacity the main approaches to capacity identification proposed in the literature are reviewed and their advantages and inconveniences are discussed all the reviewed methods have been implemented within the kappalab r package their application is illustrated on a detailed example

axiomatic foundation of the analytic hierarchy process this paper contains an axiomatic treatment of the analytic hierarchy process ahp the set of axioms corresponding to hierarchic structures are a special case of axioms for priority setting in systems with feedback which allow for a wide class of dependencies the axioms highlight 1 the reciprocal property that is basic in making paired comparisons 2 homogeneity that is characteristic of people s ability for making comparisons among things that are not too dissimilar with respect to a common property and hence the need for arranging them within an order preserving hierarchy 3 dependence of a lower level on the adjacent higher level 4 the idea that an outcome can only reflect expectations when the latter are well represented in the hierarchy the ahp neither assumes transitivity or the stronger condition of consistency nor does it include strong assumptions of the usual notions of rationality a number of facts are derived from these axioms providing an operational basis for the ahp

k order additive discrete fuzzy measures and their representation abstract in order to face with the complexity of discrete fuzzy measures we propose the concept of k orderadditive fuzzy measure including usual additive measures and fuzzy measures every discrete fuzzy measure is a k order additive fuzzy measure for a unique k a related topic of the paper is to introduce an alternative representation of fuzzy measures called the interaction representation which sets and extends in a common framework the shapley value and the interaction index proposed by murofushi and soneda

vendor selection by integrated fuzzy mcdm techniques with independent and interdependent relationships vendor selection is an evaluation process that is based on many criteria that uses inaccurate or uncertain data but while the criteria are often numerous and the relationships between higher level criteria and lower level sub criteria are complex most conventional decision models cannot help us clarify the interrelationships among the sub criteria our proposed integrated fuzzy multiple criteria decision making mcdm method addresses this issue within the context of the vendor selection problem first we use triangular fuzzy numbers to express the subjective preferences of evaluators second we use interpretive structural modeling ism to map out the relationships among the sub criteria third we use the fuzzy analytical hierarchy process ahp method to compute the relative weights for each criterion and we use non additive fuzzy integral to obtain the fuzzy synthetic performance of each common criterion fourth the best vendor is determined according to the overall aggregating score of each vendor using the fuzzy weights with fuzzy synthetic utilities fifth we use an empirical example to show that our proposed method is preferred to the traditional method especially when the sub criteria are interdependent finally our results provide valuable suggestions to vendors on how to improve each sub criterion so that they can bridge the gap between actual and aspired performance values in the future

stabilized finite element methods for nonsymmetric noncoercive and ill posed problems part ii hyperbolic equations in this paper we consider stabilized finite element methods for hyperbolic transport equations without coercivity abstract conditions for the convergence of the methods are introduced and these conditions are shown to hold for three different stabilized methods the galerkin least squares method the continuous interior penalty method and the discontinuous galerkin method we consider both the standard stabilization methods and the optimization based method introduced in e burman siam j sci comput 35 2013 pp a2752 a2780 the main idea of the latter is to write the stabilized method in an optimization framework and select the discrete function for which a certain cost functional in our case the stabilization term is minimized some numerical examples illustrate the theoretical investigations

multigrid methods for saddle point problems optimality systems abstract we develop multigrid methods for an elliptic distributed optimal control problem on convex domains that are robust with respect to a regularization parameter we prove the uniform convergence of the w cycle algorithm and demonstrate the performance of v cycle and w cycle algorithms through numerical experiments

stability and dynamical properties of rosenau hyman compactons using pade approximants we present a systematic approach for calculating higher order derivatives of smooth functions on a uniform grid using pade approximants we illustrate our findings by deriving higher order approximations using traditional second order finite difference formulas as our starting point we employ these schemes to study the stability and dynamical properties of k 2 2 rosenau hyman compactons including the collision of two compactons and resultant shock formation our approach uses a differencing scheme involving only nearest and next to nearest neighbors on a uniform spatial grid the partial differential equation for the compactons involves first second and third partial derivatives in the spatial coordinate and we concentrate on four different fourth order methods which differ in the possibility of increasing the degree of accuracy or not of one of the spatial derivatives to sixth order a method designed to reduce round off errors was found to be the most accurate approximation in stability studies of single solitary waves even though all derivates are accurate only to fourth order simulating compacton scattering requires the addition of fourth derivatives related to artificial viscosity for those problems the different choices lead to different amounts of spurious radiation and we compare the virtues of the different choices

inconsistency and non additive capacities the analytic hierarchy process in the framework of choquet integration we examine the ahp in the framework of choquet integration and we propose an extension of the standard ahp aggregation scheme on the basis of the shapley values associated with the criteria in our model a measure of dominance inconsistency between criteria is defined in terms of the totally inconsistent matrix associated with the main pairwise comparison matrix of the ahp the measure of dominance inconsistency is then used to construct a non additive capacity whose associated shapley values reduce to the standard ahp priority weights in the consistency case in the general inconsistency case however the extended aggregation scheme based on the shapley weighted mean tends to attenuate resp emphasize the priority weights of the criteria with higher resp lower average dominance inconsistency with respect to the other criteria

an interpretation of fuzzy measures and the choquet integral as an integral with respect to a fuzzy measure abstract in this paper the non additivity of sugeno s fuzzy measures is interpreted in terms of addition and the rationality of the choquet integral is discussed it is pointed out that a fuzzy measure on a set x expresses the interaction between the subsets of x and can be represented by an additive measure it is shown through concrete examples that the choquet integral is reasonable as an integral with respect to a fuzzy measure it is also found that the choquet integral is closely related with the representation of a fuzzy measure

a characterization of the 2 additive choquet integral through cardinal information in the context of multiple criteria decision analysis we present the necessary and sufficient conditions to represent a cardinal preferential information by the choquet integral w r t a 2 additive capacity these conditions are based on some complex cycles called cyclones

on micro to macro connections in domain decomposition multiscale methods abstract micro to macro connection techniques constitute a key ingredient in the formulation of multiscale strategies in this contribution several connection methods are explored for the concurrent multiscale analysis of brittle heterogeneous materials particularly these techniques are investigated in a domain decomposition strong coupling multiscale framework the structural component under analysis is partitioned into a number of non overlapping domains and a fine scale resolution is assigned therein in an adaptive manner exploiting a zoom in technique mesh refinement is employed in the domains where crack coalescence and growth take place the original contribution presented in this manuscript consists in the study of different strong and weak locality constraints that connect coarse and fine resolution domains standard collocation and average compatibility are considered and serve as a basis for the development of two new interscale links the influence of different locality constraints is studied in terms of the mechanical response and the error distribution is compared to a full fine scale analysis