quantitative weights and aggregation based on the strong idempotency of aggregation operators quantitative weights are incorporated into the fusion process our general method is compared with some previous specific cases more details about weighted aggregation based on some penalty function is given further weighted integral based aggregation linked to quantifier based fuzzy measures is investigated especially weighted owa operators several examples are included

on a system of klein gordon type equations with acoustic boundary conditions we prove the existence uniqueness and uniform stabilization of global solutions for a generalized system of klein gordon type equations with acoustic boundary conditions on a portion of the boundary and the dirichlet boundary condition on the rest

uniform stabilization of wave equation with localized damping and acoustic boundary condition abstract in this paper we deal with stability of the nonlinear wave equation with acoustic boundary conditions to non locally reacting boundary

some nonlinear wave equations with acoustic boundary conditions abstract we prove the existence and uniqueness of global solutions to the mixed problem for the carrier equation u tt m u 2 dx u u t u t 0 with acoustic boundary conditions

lipschitz continuity of triangular subnorms this paper deals with the lipschitz property of triangular subnorms unlike the case of triangular norms for these operations the problem is still open and presents an interesting variety of situations we provide some characterization results by weakening the notion of convexity introducing two generalized versions of convexity for real functions called a lower convexity and sub convexity the a lower convex and sub convex real mappings present characteristics quite different from the usual convex real mappings we will discuss the link between such kind of functions and the generators and their pseudo inverse of continuous archimedean triangular subnorms

ablowitz ladik hierarchy of integrable equations on a time space scale we derive the toda s lattice the hirota s network and the nonlinear schrodinger dynamic equations on a time space scale by extension on a time space scale the ablowitz ladik hierarchy of integrable dynamic systems

aggregation functions based on penalties this article studies a large class of averaging aggregation functions based on minimizing a distance from the vector of inputs or equivalently minimizing a penalty imposed for deviations of individual inputs from the aggregated value we provide a systematization of various types of penalty based aggregation functions and show how many special cases arise as the result we show how new aggregation functions can be constructed either analytically or numerically and provide many examples we establish connection with the maximum likelihood principle and present tools for averaging experimental noisy data with distinct noise distributions

decay rate estimates for wave equations of memory type with acoustic boundary conditions abstract a wave equation of memory type u u 0 t g t s u s d s 0 with acoustic boundary conditions is considered this work is devoted to investigating the influence of the kernel function g and proving general rates of decay of solutions when g does not necessarily decay exponentially

uniform stabilization of the wave equation by nonlinear boundary feedback the question of uniformly stabilizing the solution of the wave equation y delta y 0 in omega times 0 infty omega is a bounded domain of bf r n by means of a nonlinear feedback law of the following form is studied partial y partial v k x g y on gamma 0 times 0 infty y 0 on gamma 1 times 0 infty gamma 0 gamma 1 being a suitable partition of the boundary of omega and g a continuous nondecreasing function such that g 0 0 we choose k x in l infty k x geqq 0 such that k x vanishes linearly at the interface points x in bar gamma 0 cap bar gamma 1 then if g s behaves like s p 1 s as s to 0 with p 1 and linearly as s to infty it is proved that the energy of every solution decays like t 2 p 1 as t to infty in the case where p 1 the exponential decay rate is proved

darboux transformations on a space scale abstract using the time space scale calculus introduced by hilger we describe a darboux transformation for partial differential equations on a space scale and extend the classical theorems of darboux and crum to this setting as an application we use the lax equation to deduce a system of korteweg de vries equations on a space scale and obtain a solution to this system by using the darboux transformation

3 soliton solution to sine gordon equation on a space scale hirota s direct method is extended on a variable time space scale using this extension we construct 3 soliton solutions of the sine gordon equation on a variable space scale the determinant form of this solution is given as well hirota s direct method is extended on a variable time space scale using this extension we construct 3 soliton solutions of the sine gordon equation on a variable space scale the determinant form of this solution is given as well

global existence of classical solutions to the damped vlasov klein gordon equations with small data we study the collective dynamics of an ensemble of relativistic charged particles interacting with a self consistent damped klein gordon field in spatial three dimensions for this we derive a priori pointwise decay estimates for a scalar klein gordon field and its derivatives when the initial data are small and compactly supported these pointwise estimates yield the uniform boundedness of the velocity support which establishes the global existence of classical solutions

quasilinear hyperbolic 2 2 systems with a free damping boundary condition we consider a quasilinear system of equations for two functions u x t v x t and a boundary function s t

polynomial stability for wave equations with acoustic boundary conditions and boundary memory damping we study wave equations with acoustic boundary conditions where only one memory damping acts on the acoustic boundary under some conditions on the memory kernel polynomial energy decay rates are established by using higher order energy estimates among some other techniques

mel nikov analysis of numerically induced chaos in the nonlinear schro dinger equation abstract certain hamiltonian discretizations of the periodic focusing nonlinear schrodinger equation nls have been shown to be responsible for the generation of numerical instabilities and chaos in this paper we undertake a dynamical systems type of approach to modeling the observed irregular behavior of a conservative discretization of the nls using heuristic mel nikov methods the existence of a pair of isolated homoclinic orbits is indicated for the perturbed system the structure of the persistent homoclinic orbits that are predicted by the mel nikov theory possesses the same features as the wave form observed numerically in the perturbed system after the onset of chaotic behavior and appears to be the main structurally stable feature of this type of chaos the mel nikov analysis implemented in the pde context appears to provide relevant qualitative information about the behavior of the pde in agreement with the numerical experiments in a neighborhood of the persistent homoclinic orbits the existence of a horseshoe is investigated and related with the onset of chaos in the numerical study

asymptotic stability for a strongly coupled klein gordon system in an inhomogeneous medium with locally distributed damping abstract we consider a strongly coupled klein gordon system posed in an inhomogeneous medium with smooth boundary subject to a local damping distributed around a neighborhood of the boundary according to the geometric control condition we show that the energy of the system goes uniformly and exponentially to zero for all initial data of finite energy taken in bounded sets of finite energy phase space for this purpose refined microlocal analysis arguments are considered by exploiting ideas due to burq and gerard 16 by using sharp l p l q carleman estimates we prove a unique continuation property for coupled systems we also consider a strongly coupled system of wave equations with localized nonlinear damping acting only on one equation considering a compact riemannian manifold we show that the energy of the coupled system goes uniformly to zero

noncommutative self identity aggregation abstract we introduce a number of properties associated with the aggregation of scores notable among these is the property of self identity the property of commutativity is discussed and a number of situations in which this is an inappropriate condition to assume are presented motivated by these examples we consider a linear class of noncommutative aggregation operators we show how the requirement of self identity imposes a useful restriction on the weights associated with this aggregation a number of special families of this class are investigated

strong stability and uniform decay of solutions to a wave equation with semilinear porous acoustic boundary conditions we consider a wave equation with semilinear porous acoustic boundary conditions this is a coupled system of second and first order in time partial differential equations with possibly semilinear boundary conditions on the interface the results obtained are i strong stability for the linear model ii exponential decay rates for the energy of the linear model and iii local exponential decay rates for the energy of the semilinear model this work builds on a previous result showing generation of a well posed dynamical system the main tools used in the proofs are i the stability theorem of arendt batty ii energy methods used in the study of a wave equation with boundary damping and iii an abstract result of i lasiecka applicable to hyperbolic like systems with nonlinearly perturbed boundary conditions

a concise consensus support model for group decision making with reciprocal preference relations based on deviation measures supporting the process of consensus building has become a major research field in group decision making gdm the purpose of this paper is to present a consistency consensus based decision support model for gdm based on reciprocal preference relations inspired by the concept of a deviation measure between two matrices an individual consistency index and a group consensus index are presented in the support model a consistency control process is designed to make an inconsistent reciprocal preference relation one of acceptable consistency to achieve a predefined consensus level an interactive consensus reaching process is provided where the group reciprocal preference relation is seen as a reference when experts change their preferences theoretical foundations are then established for the proposed model the proposed model revises the original information in a simple and straightforward gradual way in the consensus process the individual rationality level in terms of consistency is maintained two examples are examined to demonstrate the model in practical problems

triangular norm based iterative compensatory operators abstract aggregation operators based on a fixed t norm and on suitable transformations of processed data are introduced a special attention is paid to the class of iterative compensatory operators containing also the classical arithmetic geometric and harmonic means several properties of introduced operators are studied e g the symmetry the associativity the idempotency the anihilation etc several examples are given including continuous idempotent bisymmetric iterative compensatory operators with zero anihilator

fuzzy set approach to the utility preference relations and aggregation operators abstract score x x 1 x n describing an alternative is modelled by means of a continuous quasi convex fuzzy quantity x thus allowing to compare alternatives scores by means of fuzzy ordering comparison methods applying some defuzzification method leads to the introduction of operators acting on scores a special stress is put on the mean of maxima defuzzification method allowing to introduce several averaging aggregation operators moreover our approach allows to introduce weights into above mentioned aggregation even in the non anonymous non symmetric case finally ordered weighted aggregation operators owao are introduced generalizing the standard owa operators

multi attribute aggregation operators this paper deals with the idea of aggregation a new enlarged notion of aggregation operator is given along with a classification of classical properties into some main groups the concept of multi attribute aggregation operator which incorporates many classical aggregation methods is provided an extension of different properties to multi attribute aggregation operators is proposed

uninorms in fuzzy systems modeling abstract fuzzy systems modeling provides a framework in which input output relationships can be modeled by partitioning the input into fuzzy regions for which we can describe the output the fuzzy modeling inference process the procedure used to obtain the output of a fuzzy systems model for a given input is shown to involve an aggregation step in which the contributions of the different components of the fuzzy systems model are combined it is shown that the uninorm operator provides a general class of operators to implement this step the uninorm it is recalled is an operator that provides a generalization of the t norm and t conorm by allowing the identity element to be any value in the unit interval another step in the inference process is the determination of the contribution of each component of the model based on its relevancy to the current input the performance of this step requires the use of an operator related to the implication operator which we call a relevancy transformation ret operator it is shown that the form of this ret operator is dependent upon the identity value of the uninorm used in the aggregation step we provide some general formulations for this class of operators we show how the well known forms of fuzzy inference are special cases of our uninorm based approach