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

finite difference lattice boltzmann method for compressible thermal fluids a splitting method to solve the modeled lattice boltzmann equation the splitting technique permits the boundary conditions for the lattice boltzmann equation to be set as conveniently as those required for the finite difference solution of the navier stokes equations it is shown that the compressible navier stokes equation can be recovered fully from this approach however the formulation requires the solution of a poisson equation governing a secondorder tensor thus constructed the method has no arbitrary constants the proposed method is used to simulate thermalcouette flow aeroacoustics andshockstructureswithanextendedthermodynamicsmodel thesimulations are carried out using a high order finite difference scheme with a two dimensional nine velocity lattice all simulations are performed using a single relaxation time and a set of constants deduced from the derivation it is found that the finite difference lattice boltzmann method is able to correctly replicate viscous effects in thermal couette flows aeroacoustics andshockstructures thesolutionsobtainedareidenticaleithertoanalyticalresults or obtained by solving the compressible navier stokes equations using a direct numerical simulation technique

study on gas kinetic unified algorithm for flows from rarefied transition to continuum the modified bgk equation adapted to various flow regimes can be presented by the aid of the basic characteristics on molecular movement and collision approaching to equilibrium the discrete velocity ordinate method is developed and applied to the velocity distribution function to remove its continuous dependency on the velocity space and then the velocity distribution function equation is cast into hyperbolic conservation law form with nonlinear source terms based on the unsteady time splitting method and the non oscillatory containing no free parameters and dissipative nnd scheme the gas kinetic finite difference second order scheme is constructed for the computation of the discrete velocity distribution functions the mathematical model on the interaction of molecules with solid surface is studied and used in the numerical method four types of numerical quadrature rules such as the modified gauss hermite formula the composite newton cotes integration method the gauss legendre numerical quadrature rule and the golden section number theoretic integral method are developed and applied to the discretized velocity space to evaluate the macroscopic flow parameters at each point in the physical space as a result a unified simplified gas kinetic algorithm is established for the flows from rarefied transition to continuum regime based on analyzing the inner parallel degree of the unified algorithm the parallel strategy adapted to the gas kinetic numerical algorithm is studied and then the hpf parallel processing software for the unified algorithm is developed to test the present method the one dimensional shock tube problems the flows past two dimensional circular cylinder and the flows around three dimensional sphere and spacecraft shape with various knudsen numbers are simulated the computational results are found in high resolution of the flow fields and good agreement with the theoretical dsmc n s and experimental results

selecting the individual numerical scale and prioritization method in the analytic hierarchy process a 2 tuple fuzzy linguistic approach the validity of the priority vector used in the analytic hierarchy process ahp relies on two factors the selection of a numerical scale and the selection of a prioritization method the traditional ahp selects only one numerical scale e g the saaty scale and one prioritization method e g the eigenvector method for each particular problem for this traditional selection approach there is disagreement on which numerical scale and prioritization method is better in deriving a priority vector in fact the best numerical scale and the best prioritization method both rely on the content of the pairwise comparison data provided by the ahp decision makers by defining a set of concepts regarding the scale function and the linguistic pairwise comparison matrices lpcms of the priority vector and by using lpcms to unify the format of the input and output of ahp this paper extends the ahp prioritization process under the 2 tuple fuzzy linguistic model based on the extended ahp prioritization process we present two performance measure criteria to evaluate the effect of the numerical scales and prioritization methods we also use the performance measure criteria to develop a 2 tuple fuzzy linguistic multicriteria approach to select the best numerical scales and the best prioritization methods for different lpcms in this paper we call this type of selection the individual selection of the numerical scale and prioritization method we also compare this individual selection with traditional selection by using both random and real data and show better results with individual selection

state estimation for delayed neural networks in this letter the state estimation problem is studied for neural networks with time varying delays the interconnection matrix and the activation functions are assumed to be norm bounded the problem addressed is to estimate the neuron states through available output measurements such that for all admissible time delays the dynamics of the estimation error is globally exponentially stable an effective linear matrix inequality approach is developed to solve the neuron state estimation problem in particular we derive the conditions for the existence of the desired estimators for the delayed neural networks we also parameterize the explicit expression of the set of desired estimators in terms of linear matrix inequalities lmis finally it is shown that the main results can be easily extended to cope with the traditional stability analysis problem for delayed neural networks numerical examples are included to illustrate the applicability of the proposed design method

group decision making with a fuzzy linguistic majority abstract the determination of solutions in group decision making is considered the point of departure is a collection of individual fuzzy preference relations a solution is derived either directly from the individual fuzzy preference relations or by constructing first a social fuzzy preference relation as opposed to conventional approaches in which a crisp threshold type majority rule is used we employ a fuzzy majority rule specified by a fuzzy linguistic quantifier e g most much more than 50 etc a calculus of linguistically quantified propositions is applied using the fuzzy majority various solution concepts are derived mainly of the type of core minimax opposition set and consensus winner

a note on fung fu s theorem abstract the axiomatic approach to rational decision malting in a fuzzy environment proposed by fung and fu 1975 lays down a too restrictive family of aggregation rules because of such axioms the independence of the size of the groups under aggregation is assumed moveover in a general problem these groups are fuzzy sets

a soft measure of consensus in the setting of partial fuzzy preferences abstract consensus as traditionally meant to be a full and unanimous agreement is often not reachable in practice a degree of consensus for indicating how far a particular group of individuals is from consensus may be therefore very useful we propose a new measure degree of consensus which is more human consistent in the sense that it better reflects a real human perception of the essence of consensus in practice basically our consensus measure expresses the degree to which say most of the important individuals agree as to their testimonies concerning almost all of the relevant options the point of departure is the set of individual testimonies which are here the individual fuzzy preference relations as a formal tool we use a fuzzy logic based calculus of linguistically quantified propositions

lattice boltzmann model for the compressible navier stokes equations with flexible specific heat ratio we have developed a lattice boltzmann model for the compressible navier stokes equations with a flexible specific heat ratio several numerical results are presented and they agree well with the corresponding solutions of the navier stokes equations in addition an explicit finite difference scheme is proposed for the numerical calculation that can make a stable calculation with a large courant number

global exponential synchronization of multiple memristive neural networks with time delay via nonlinear coupling this paper presents theoretical results on the global exponential synchronization of multiple memristive neural networks with time delays a novel coupling scheme is introduced in a general topological structure described by a directed or undirected graph with a linear diffusive term and discontinuous sign term several criteria are derived based on the lyapunov stability theory to ascertain the global exponential stability of synchronization manifold in the coupling scheme simulation results for several examples are given to substantiate the effectiveness of the theoretical results

weighted aggregation operators based on minimization minimization based aggregation operators a g d are discussed special attention is paid to weighting function g based cases related to some fixed dissimilarity function d when d 2 x y x y 2 we recognize mixture operators and we recall some sufficient conditions for g ensuring the monotonicity of a g d for d 1 x y x y and non decreasing non increasing g a g d is shown to be the upper lower median whenever a g d is an aggregation operator

on the relation between compromise programming and ordered weighted averaging operator this paper will demonstrate a strong relationship between the compromise programming cp method and the ordered weighted averaging owa operator we will mathematically prove that the application of the cp method reflects the pessimistic view of the decision maker dm if the distance from the ideal point is minimized it will however present an optimistic dm if the distance from the nadir is maximized the owa operator may cover all of the optimistic neutral and pessimistic views a practical relationship will be developed between the power value of the cp method and the optimism degree of the dm based on fuzzy quantifiers the theoretical results will be illustrated by a real case study of a water resources management problem

short communication an impossibility theorem for indicators aggregation using the fuzzy set theory we prove that there is no indicator at the same time aggregated and sensitive anticatastrophic and noncompensatory such a result theoretically justifies the weaknesses of certain indicators used at present as well as the noncomparability of certain social issues such as the quality of life etc

on weighted unbalanced linguistic aggregation operators in group decision making we generalize linguistic evaluation values and their weights in group decision making gdm problems based on unbalanced linguistic terms the gdm problems include two types of weights belief degrees of linguistic evaluation values and experts weights due to the time pressure and conflict of multi source of information etc experts may have various evaluations values on alternatives the belief degree is used to represent the confidence level of the values the experts weight is used to represent the differences among experts importance which caused by experts experience or knowledge distinction we propose the weighted unbalanced linguistic aggregation operators to synthesize linguistic evaluation value belief degree and experts weights some desired properties of the operator are then studied these properties show that the operator extends the linguistic weighted averaging operator lwa and the linguistic ordered weighted averaging lowa operator finally an illustrative example of human resource performance appraisal based on the linguistic aggregation operator is provided

on fuzzy tournaments and their solution concepts in group decision making abstract assuming as the point of departure a set of individual or collective fuzzy tournaments complete and reciprocal binary relations representing the preferences of the particular individuals or their group as a whole respectively we define some new solution concepts in group decision making as counterparts of the respective solution concepts in the case of nonfuzzy tournaments complete and asymmetric binary relations basically the new solution concepts are mainly counterparts of some sets of undominated options uncovered sets and banks sets we consider the cases of both the conventional nonfuzzy and fuzzy majorities

lattice boltzmann method and gas kinetic bgk scheme in the low mach number viscous flow simulations both lattice boltzmann method lbm and the gas kinetic bgk scheme are based on the numerical discretization of the boltzmann equation with collisional models such as the bhatnagar gross krook bgk model lbm tracks limited number of particles and the viscous flow behavior emerges automatically from the intrinsic particle stream and collisions process on the other hand the gas kinetic bgk scheme is a finite volume scheme where the time dependent gas distribution function with continuous particle velocity space is constructed and used in the evaluation of the numerical fluxes across cell interfaces currently lbm is mainly used for low mach number nearly incompressible flow simulation for the gas kinetic scheme the application is focusing on the high speed compressible flows in this paper we are going to compare both schemes in the isothermal low mach number flow simulations the methodology for developing both schemes will be clarified through the introduction of operator splitting boltzmann model and operator averaging boltzmann model from the operator splitting boltzmann model the error rooted in many kinetic schemes which are based on the decoupling of particle transport and collision can be easily understood as to the test case we choose to use the 2d cavity flow since it is one of the most extensively studied cases detailed simulation results with different reynolds numbers as well as the benchmark solutions are presented

managing non homogeneous information in group decision making within the frame of decision aid literature decision making problems with multiple sources of information have drawn the attention of researchers from a wide spectrum of disciplines in decision situations with multiple individuals each one has his own knowledge on the alternatives of the decision problem the use of information assessed in different domains is not a seldom situation this non homogeneous information can be represented as values belonging to domains with different nature as linguistic numerical and interval valued or can be values assessed in label sets with different granularity multi granular linguistic information decision processes for solving these problems are composed by two phases aggregation and exploitation the main problem to deal with non homogeneous contexts is how to aggregate the information assessed in these contexts in this paper taking as base the 2 tuple fuzzy linguistic representation model we shall develop an aggregation process for dealing with non homogeneous contexts in first place we shall develop an aggregation process for combining numerical interval valued and linguistic information afterwards we shall propose different extensions of this process to deal with contexts in which can appear other type of information as intuitionistic fuzzy sets or multi granular linguistic information

lattice boltzmann method for the compressible euler equations the lattice boltzmann model for the compressible euler equations is proposed together with its rigorous theoretical background the proposed model has completely overcome the defects of the previous model that the specific heat ratio cannot be chosen freely the macroscopic variables obtained from the solution are shown to satisfy in the limit of the small knudsen number the compressible euler equations if the variation of the solution is moderate this is the case where no shock waves or contact discontinuities appear in contrast when the solution makes steep variation at several localized regions due to the appearance of shock waves and contact discontinuities the corresponding macroscopic variables satisfy the weak form of the euler equations their derivation is carried out rigorously by taking into account the scale of variation of the solution correctly this is the first study that has laid the theoretical foundation of the lattice boltzmann model for the simulation of flows with shock waves and contact discontinuities numerical examples and the error estimates are also given which are consistent with the above theoretical arguments

aggregation of fuzzy opinions an axiomatic approach abstract the importance of fuzzy valuations in diagnostics is mentioned the problem of aggregation of fuzzy opinions obtained from a group of experts in answer to the question has an object the property labeled a and no property labeled 1a is formulated the set of fung and fu s 10 aggregation axioms is shortly described the idea of weighting expert s opinions is formalized then a new set of aggregation axioms is presented and an aggregating operator is introduced a posteriori weighting of opinions in aggregation is examined

implicit gas kinetic bhatnagar gross krook scheme for compressible flows a gas kinetic scheme based on the bhatnagar gross krook bgk model is developed for two dimensional compressible inviscid flowfields the bgk scheme is an approximate riemann solver that uses the collisional boltzmann equation as the governing equation for flow evolutions for efficient computations particle distribution functions in the general solution of the bgk model are simplified and used for the flow simulations high order accuracy is achieved via the reconstruction of flow variables using the muscl interpolation technique for steadystate problems the approximate factorization alternating direction implicit implicit time integration method is adopted which is preferable to a multistage runge kutta method to investigate the computational characteristics of bgk scheme in detail it has been applied to various two dimensional numerical experiments the results compared with some typical schemes such as the steger warming flux vector splitting and roe flux difference splitting as well as exact solutions are found to be robust and accurate and to have high resolution at discontinuities such as shock waves

solution of two dimensional riemann problems of gas dynamics by positive schemes the positivity principle and positive schemes to solve multidimensional hyperbolic systems of conservation laws have been introduced in x d liu and p d lax j fluid dynam 5 1996 pp 133 156 some numerical experiments presented there show how well the method works in this paper we use positive schemes to solve riemann problems for two dimensional gas dynamics

distributed recursive filtering for stochastic systems under uniform quantizations and deception attacks through sensor networks this paper is concerned with the distributed recursive filtering problem for a class of discrete time delayed stochastic systems subject to both uniform quantization and deception attack effects on the measurement outputs the target plant is disturbed by the multiplicative as well as additive white noises a novel distributed filter is designed where the available innovations are from not only the individual sensor but also its neighboring ones according to the given topology attention is focused on the design of a distributed recursive filter such that in the simultaneous presence of time delays deception attacks and uniform quantization effects an upper bound for the filtering error covariance is guaranteed and subsequently minimized by properly designing the filter parameters via a gradient based method at each sampling instant furthermore by utilizing the mathematical induction a sufficient condition is established to ensure the asymptotic boundedness of the sequence of the error covariance finally a simulation example is utilized to illustrate the usefulness of the proposed design scheme of distributed filters

linguistic multiperson decision making based on the use of multiple preference relations in multiperson decision making situations it is quite natural that different decision makers who may have different background and knowledge will provide their preferences by different kinds of preference relations this paper proposes a linguistic multiperson decision making model lmdmm based on linguistic preference relations integrating fuzzy preference relations different types of multiplicative preference relations and multigranular linguistic preference relations in the lmdmm several transformation functions are first obtained to relate fuzzy preference relations and different types of multiplicative preference relations with multigranular linguistic preference relations then we design the selection process of the lmdmm based on the use of the fuzzy majority and the extended ordered weighted averaging operator or the 2 tuple ordered weighted averaging operator and discuss conditions under which the proposed selection process satisfies the social choice axioms at last we analyze the internal consistency of the proposed transformation functions the results in this paper are helpful to complete chiclana et al s fuzzy decision model integrating three representation models in fuzzy multipurpose decision making based on fuzzy preference relations fuzzy sets and systems 97 1998 33 48

models to determine parameterized ordered weighted averaging operators using optimization criteria this paper proposes a general optimization model for determining ordered weighted averaging owa operators and three specific models for generating monotonic and symmetric owa operators as well as those with any function shape in these models entropy and variance concepts are generalized as general dispersion indices for use in the objective functions while the ordinary orness level constraints are used in the constraint equations as a special case we define an orness function for monotonic owa operators which measures the closeness of the aggregation value to the maximum value and a medianness function for symmetric owa operators which measures the closeness of the aggregation value to the median value we also extend the commonly used models for determining owa operators under given orness values to determine monotonic owa operators with given orness function values and symmetric owa operators with given medianness function values analytical solutions and properties of these models are discussed we also provide analytical solutions of the maximum entropy and minimum variance problems with given linear medianness values by setting different forms of the objective function and constraints the parameterized owa operator family elements can achieve various distributions in any desired shape two examples are given to show the owa operator elements distributed in quadratic and gaussian distribution function shapes

finite horizon h_ infty state estimation for periodic neural networks over fading channels the problem of finite horizon h infty state estimator design for periodic neural networks over multiple fading channels is studied in this paper to characterize the measurement signals transmitted through different channels experiencing channel fading a multiple fading channels model is considered for investigating the situation of correlated fading channels a set of correlated random variables is introduced specifically the channel coefficients are described by white noise processes and are assumed to be correlated two sufficient criteria are provided by utilizing a stochastic analysis approach to guarantee that the estimation error system is stochastically stable and achieves the prescribed h infty performance then the parameters of the estimator are derived by solving recursive linear matrix inequalities finally some simulation results are shown to illustrate the effectiveness of the proposed method

robust mathscr h _ infty filtering for a class of two dimensional uncertain fuzzy systems with randomly occurring mixed delays this paper is concerned with the robust mathscr h infty filtering problem for a class of 2 d uncertain fuzzy systems with randomly occurring mixed delays romds the underlying 2 d systems are described by the fornasini marchesini model and the uncertainty is expressed in a linear fraction form an improved takagi sugeno t s fuzzy model corresponding to the spatial promise variables is adopted to represent the complicated 2 d nonlinear system the mixed delays consisting of both discrete and distributed delays are allowed to appear in a random manner governed by two sets of bernoulli distributed white sequences with known probability a full order fuzzy filter is constructed to estimate the output signal such that in the presence of parameter uncertainties and romds the dynamics of the estimation errors is asymptotically stable with a prescribed mathscr h infty disturbance attenuation level based on the stochastic analysis technique and the lyapunov like functional sufficient conditions are established to ensure the existence of the desired filters and the explicit expressions of such filters are derived by means of the solution to a class of convex optimization problems that can be solved via standard software packages a numerical example is provided to demonstrate the effectiveness of the developed filter design algorithms and the filter performances with and without fuzzy rules are also compared

state estimation for coupled uncertain stochastic networks with missing measurements and time varying delays the discrete time case this paper is concerned with the problem of state estimation for a class of discrete time coupled uncertain stochastic complex networks with missing measurements and time varying delay the parameter uncertainties are assumed to be norm bounded and enter into both the network state and the network output the stochastic brownian motions affect not only the coupling term of the network but also the overall network dynamics the nonlinear terms that satisfy the usual lipschitz conditions exist in both the state and measurement equations through available output measurements described by a binary switching sequence that obeys a conditional probability distribution we aim to design a state estimator to estimate the network states such that for all admissible parameter uncertainties and time varying delays the dynamics of the estimation error is guaranteed to be globally exponentially stable in the mean square by employing the lyapunov functional method combined with the stochastic analysis approach several delay dependent criteria are established that ensure the existence of the desired estimator gains and then the explicit expression of such estimator gains is characterized in terms of the solution to certain linear matrix inequalities lmis two numerical examples are exploited to illustrate the effectiveness of the proposed estimator design schemes

modeling rationality in a linguistic framework in classical decision theory there exists a large class of rationality models which try to capture different kinds of behavior when individuals compare by pairs a set of alternatives all these models assume that decision makers have dichotomous preferences however in real decisions individuals feel different degrees of preference in this paper we have checked the mentioned models in a real case where different kinds of linguistic preferences are allowed after the empirical analysis the main conclusion is that the fulfillment of rational conditions decreases when individuals have non extreme preferences based on the obtained empirical evidences we propose some classes of transitivity conditions in the framework of linguistic preferences

on godunov type methods near low densities abstract when the energy of a flow is largely kinetic many conservative differencing schemes may fail by predicting non physical states with negative density or internal energy we describe as positively conservative the subclass of schemes that by contrast always generate physical solutions from physical data and show that the godunov method is positively conservative it is also shown that no scheme whose interface flux derives from a linearised riemann solution can be positively conservative classes of data that will bring about the failure of such schemes are described however the harten lax van leer hlle scheme is positively conservative under certain conditions on the numerical wavespeeds and this observation allows the linearised schemes to be rescued by modifying the wavespeeds employed

delay dependent state estimation for delayed neural networks in this letter the delay dependent state estimation problem for neural networks with time varying delay is investigated a delay dependent criterion is established to estimate the neuron states through available output measurements such that the dynamics of the estimation error is globally exponentially stable the proposed method is based on the free weighting matrix approach and is applicable to the case that the derivative of a time varying delay takes any value an algorithm is presented to compute the state estimator finally a numerical example is given to demonstrate the effectiveness of this approach and the improvement over existing ones

modeled lattice boltzmann equation and the constant density assumption c sound speed d flow dimension 2 for two dimensional flow and 3 for three dimensional flow f particle distribution function f equilibrium particle distribution function h half width of the channel upstream of the expansion in a sudden expansion geometry kn knudsen number l characteristic length m mach number p static pressure re reynolds number t time u velocity vector u velocity component along x axis v velocity component along y axis x y cartesian coordinates xj position vector index for the lattice velocity fluid viscosity particle velocity vector particle velocity along lattice fluid density relaxation time ij viscous stress tensor o reference relaxation time vorticity

direct approach processes in group decision making using linguistic owa operators abstract in a linguistic framework several group decision making processes by direct approach are presented these processes are designed using the linguistic ordered weighted averaging lowa operator to do so first a study is made of the properties and the axiomatic of lowa operator showing the rationality of its aggregation way and secondly we present the use of lowa operator to solve group decision making problems from individuals linguistic preference relations

rarefied flow computations using nonlinear model boltzmann equations high resolution finite difference schemes for solving the nonlinear model boltzmann equations are presented for the computations of rarefied gas flows the discrete ordinate method is first applied to remove the velocity space dependency of the distribution function which renders the model boltzmann equation in phase space to a set of hyperbolic conservation laws with source terms in physical space then a high order essentially nonoscillatory method due to harten et al j comput phys 71 231 1987 is adapted and extended to solve them explicit methods using operator splitting and implicit methods using the lower upper factorization are described to treat multidimensional problems the methods are tested for both steady and unsteady rarefied gas flows to illustrate its potential use the computed results using model boltzmann equations are found to compare well both with those using the direct simulation monte carlo results in the transitional regime flows and those with the continuum navier stokes calculations in near continuum regime flows

finite difference lattice boltzmann method applied to acoustic scattering problems this paper reports on an attempt to simulate acoustic waves scattering using a finite difference lattice boltzmann method based on an alternative lattice equilibrium particle distribution function constructed for compressible thermal fluids the studies focus on acoustics scattering by a zero circulation vortex and by an isolated thermal source with no heat gain loss two limiting cases of each type of scattering are examined one is the case of an incoming acoustic wave with a short wavelength and the other has a relatively long wavelength compared with the characteristic dimension of the obstacle these scattering problems have been treated previously using a conventional lattice boltzmann method and a gas kinetic scheme the results showed that these methods were only able to simulate the short wavelength limit case with fair accuracy for the two types of acoustics scattering considered because the present approach is able to recover the compressible navier stokes equations with correct fluid properties the finite difference solution of the proposed alternative modeled lattice boltzmann equation allows the limiting cases of the acoustics scattering problems to be calculated without numerical instability the results thus obtained are in agreement either with analysis or with results obtained from direct aeroacoustics simulations employing the compressible navier stokes equations

probability density functions based weights for ordered weighted averaging owa operators an example of water quality indices abstract this paper explores the application of ordered weighted averaging owa operators to develop water quality index which incorporates an attitudinal dimension in the aggregation process the major thrust behind selecting the owa operator for aggregation of multi criteria is its capability to encompass a range of operators bounded between minimum and maximum a new approach for generating owa weight distributions using probability density functions pdfs is proposed in this paper the basic parameters mean and standard deviation of the probability density functions can be determined using the number of criteria e g water quality indicators in the aggregation process the proposed approach is demonstrated using data provided in a study by swamee and tyagi swamee p k tyagi a 2000 describing water quality with aggregate index asce journal of environmental engineering 126 5 451 455 for establishing water quality indices the normal distribution and its inverse form were found suitable for compromising or normative decisions whereas the exponential and its inverse form were found suitable for pro risk and risk averse decisions respectively the proposed owa weight distributions are also compared with the commonly used regular increasing monotone rim functions for generating owa weights sensitivity analyses are carried out to highlight the utility of the proposed approach for multi criteria decision making and establishing water quality indices

a novel approach to probability distribution aggregation today s business world is highly competitive and unpredictable so effective decision making is of primary importance however it is difficult to make effective decisions when sufficient information is not available and decision making in such situations involves a high risk of error conventional statistics based approaches to such problems are not effective because in such situations decision making is usually in the hands of a small panel of experts however the expert opinions can be represented by probability distribution functions thus such a problem reduces to the aggregation of a set of probability distribution functions to an aggregated or consensus distribution in this paper we propose a new approach to address this problem the novelties of the proposed approach include 1 the problem is formulated as an optimization problem and 2 the overlapping area between an individual expert s distribution and an aggregated distribution is taken to measure the expertise level of that expert and subsequently to determine the weight of the expert the proposed approach in this paper is illustrated by an example reported in literature handled with the delphi method which also shows the effectiveness of our approach

social choice axioms for fuzzy set aggregation the problem of aggregating n fuzzy sets f1 f2 fn on a set is viewed as one of merging the opinions of n individuals e g experts that rate objects belonging to this approach contrasts with the pure set theoretic point of view and leads to interpreting already known axioms underlying fuzzy connectives in a way different from that of multiple criteria aggregation various natural properties of a voting procedure including the ones proposed by arrow are expressed in the fuzzy set setting a number of conditions limiting the choice of fuzzy set operations are proposed and classified according to whether they are imperative mainly technical or facultative families of solutions are obtained that include those proposed in earlier works the case of non homogeneous groups is briefly examined lastly the application of the voting paradigm to the management of antagonistic local decision rules in knowledge based systems is outlined

a fuzzy linguistic methodology to deal with unbalanced linguistic term sets many real problems dealing with qualitative aspects use linguistic approaches to assess such aspects in most of these problems a uniform and symmetrical distribution of the linguistic term sets for linguistic modeling is assumed however there exist problems whose assessments need to be represented by means of unbalanced linguistic term sets i e using term sets that are not uniformly and symmetrically distributed the use of linguistic variables implies processes of computing with words cw different computational approaches can be found in the literature to accomplish those processes the 2 tuple fuzzy linguistic representation introduces a computational model that allows the possibility of dealing with linguistic terms in a precise way whenever the linguistic term set is uniformly and symmetrically distributed in this paper we present a fuzzy linguistic methodology in order to deal with unbalanced linguistic term sets to do so we first develop a representation model for unbalanced linguistic information that uses the concept of linguistic hierarchy as representation basis and afterwards an unbalanced linguistic computational model that uses the 2 tuple fuzzy linguistic computational model to accomplish processes of cw with unbalanced term sets in a precise way and without loss of information

modeled boltzmann equation and its application to direct aeroacoustics simulation the bhatnagar gross and krook modeled boltzmann equation has been applied to simulate different fluid dynamics problems with varying degrees of success however its application to direct aeroacoustic computation is less successful one possible reason could be its inability to recover the state equation correctly for a diatomic gas and hence an inaccurate determination of the speed of sound the present study reports on the development of an improved modeled boltzmann equation for aeroacoustics simulation the approach is to modify the maxwellian distribution normally assumed for the equilibrium particle distribution function constraints imposed are the exact recovery of the state equation for a diatomic gas and the euler equations without invoking the small mach number assumption thus formulated a distribution function consisting of the maxwellian distribution plus three other terms that attempt to account for particle particle collisions is obtained a velocity lattice method is used to solve the improved modeled boltzmann equation using an equivalent lattice equilibrium distribution function the simulations are validated against benchmark aeroacoustic problems whose solutions are deduced from a direct numerical simulation of the euler equations the results of the improved modeled boltzmann equation obtained using a smaller computational domain are in excellent agreement with those deduced from direct numerical simulation using a larger computational domain thus verifying the viability and correctness of the modified equilibrium distribution function

one step aeroacoustics simulation using lattice boltzmann method the lattice boltzmann method lbm is a numerical simplification of the boltzmann equation of the kinetic theory of gases that describes fluid motions by tracking the evolution of the particle velocity distribution function based on linear streaming with nonlinear collision if the bhatnagar gross krook bgk collision model is invoked the velocity distribution function in this mesoscopic description of nonlinear fluid motions is essentially linear this intrinsic feature of lbm can be exploited for convenient parallel programming which makes itself particularly attractive for one step aeroacoustics simulations it is shown that the compressible navier stokes equations and the ideal gas equation of state can be correctly recovered by considering the translational and rotational degrees of freedom of diatomic gases in the internal energy and using a multiscale chapman enskog expansion assuming two relaxation times in the bgk model allows the temperature dependence of the first coefficient of viscosity of diatomic gases to be replicated the modified lbm model is solved using a two dimensional 9 discretized and a twodimensional 13 discretized velocity lattices three cases are selected to validate the one step lbm aeroacoustics simulation they are the one dimensional acoustic pulse propagation the circular acoustic pulse propagation and the propagation of acoustic vorticity and entropy pulses in a uniform stream the accuracy of the lbm is established by comparing with direct numerical simulation dns results obtained by solving the governing equations using a finite difference scheme the tests show that the proposed lbm and the dns give identical results thus suggesting that the lbm can be used to simulate aeroacoustics problems correctly

exponential stability and stabilization of delayed memristive neural networks based on quadratic convex combination method this paper is concerned with the exponential stability and stabilization of memristive neural networks mnns with delays first we present some generalized double integral inequalities which include some existing inequalities as their special cases second combining with quadratic convex combination method these double integral inequalities are employed to formulate a delay dependent stability condition for mnns with delays third a state dependent switching control law is obtained for mnns with delays based on the proposed stability conditions the desired feedback gain matrices are accomplished by solving a set of linear matrix inequalities finally the feasibility and effectiveness of the proposed results are tested by two numerical examples

defining the borda count in a linguistic decision making context different kinds of decision rules have been successfully implemented under a linguistic approach this paper aims the same goal for the borda count a well known procedure with some interesting features in order to this two ways of extension from the borda rule to a linguistic framework are proposed taking into account all the agents opinions or only the favorable ones for each alternative when compared with each other in the two cases both individual and collective borda counts are analyzed asking for properties as good as those of the original patterns

global exponential stability of memristive neural networks with mixed time varying delays this article investigates the lagrange exponential stability and the lyapunov exponential stability of memristive neural networks with discrete and distributed time varying delays dmnns by means of inequality techniques theories of the m matrix and the comparison strategy the lagrange exponential stability of the underlying dmnns is considered in the sense of filippov and the globally exponentially attractive set is estimated through employing the m matrix and external input especially when the external input is not concerned the lyapunov exponential stability of the corresponding dmnns is developed immediately in the form of an m matrix which contains some published outcomes as special cases furthermore by constructing an m matrix based differential system the lyapunov exponential stability of the dmnns is studied which is less conservative than some existing ones finally three simulation examples are carried out to examine the validness of the theories

aggregation functions means this two part state of the art overview on aggregation theory summarizes the essential information concerning aggregation issues an overview of aggregation properties is given including the basic classification on aggregation functions in this first part the stress is put on means i e averaging aggregation functions both with fixed arity n ary means and with multiple arities extended means

a tool for aggregation with words the need of computing with words has become an important topic in many areas dealing with vague information the aim of this paper is to present different tools which support computing with words especially we are concerned with the weighted aggregation of linguistic term sets whose results are just the words themselves without using the fuzzy numbers that represent the semantics of their linguistic terms we propose a new aggregation operator referred to as the symbolic weighted median that computes the most representative element from an ordered collection of weighted linguistic terms this operator aggregates the linguistic labels such that its result is expressed in terms of the initial linguistic term set though is modified by using dedicated tools called the generalized symbolic modifiers one advantage of this proposal is that the expression domain does not change we increase or decrease the granularity only where it becomes necessary additionally this new operator exhibits several interesting mathematical properties

simulations of compressible flows with strong shocks by an adaptive lattice boltzmann model an adaptive lattice boltzmann model for compressible flows is presented the particle velocity set is so large that the mean flow may have a high velocity the support set of the equilibrium distribution function is quite small and varies with the mean velocity and internal energy the adaptive nature of this support set permits the mean flows to have high mach number meanwhile it makes the model simple and practicable the model is suitable for perfect gases with an arbitrary specific heat ratio navier stokes equations are derived by the chapman enskog method from the bgk boltzmann equation when the viscous terms and the diffusion terms are considered as a discretion error this system becomes an inviscid euler system several simulations of flows with strong shocks including the forward facing step test double mach reflection test and a strong shock of mach number 5 09 diffracting around a corner were carried out on hexagonal lattices showing the model s capability of simulating the propagation of strong shock waves

a sequential selection process in group decision making with a linguistic assessment approach in this paper a sequential selection process in group decision making under linguistic assessments is presented where a set of linguistic preference relations represents individuals preferences a collective linguistic preference is obtained by means of a defined linguistic ordered weighted averaging operator whose weights are chosen according to the concept of fuzzy majority specified by a fuzzy linguistic quantifier then we define the concepts of linguistic non dominance linguistic dominance and strict dominance degrees as parts of the sequential selection process the solution alternative s is obtained by applying these concepts

modeled boltzmann equation and its application to shock capturing simulation a modified equilibrium distribution function for the bhatnagar gross krook type modeled boltzmann equation has recently been proposed the function was deduced using acoustics scaling to normalize the equation and allowed a correct recovery of similarly normalized euler equations it is a combination of a maxwellian distribution plus three other terms that are moments of particle velocity the lattice counterpart of the modified equilibrium distribution function also led to an exact recovery of the euler equations therefore there is no mach number limitation in the entire approach this lattice counterpart was able to replicate aeroacoustics problems involving vorticity acoustic and entropy acoustic interactions correctly and the simulations were carried out using a finite difference lattice boltzmann method employing only a two dimensional nine velocity lattice thus formulated the numerical scheme has no arbitrary constants and all calculations were carried out using one single relaxation time and a set of constants derived from the analysis this paper investigates the validity and extent of the formulation to capture shocks and resolve contact discontinuity and expansion waves in one and two dimensional riemann problems the simulations are carried out using the same two dimensional nine velocity lattice and identical set of constants and relaxation time they are compared with theoretical results and those obtained by solving the euler equations directly using harten s first order numerical scheme good agreement is obtained for all test cases however the modified equilibrium distribution function is not suitable for shock structure simulation for that an exact recovery of the navier stokes equations is required

robust state estimation for uncertain neural networks with time varying delay the robust state estimation problem for a class of uncertain neural networks with time varying delay is studied in this paper the parameter uncertainties are assumed to be norm bounded based on a new bounding technique a sufficient condition is presented to guarantee the existence of the desired state estimator for the uncertain delayed neural networks the criterion is dependent on the size of the time varying delay and on the size of the time derivative of the time varying delay it is shown that the design of the robust state estimator for such neural networks can be achieved by solving a linear matrix inequality lmi which can be easily facilitated by using some standard numerical packages finally two simulation examples are given to demonstrate the effectiveness of the developed approach

exponential stability of complex valued memristive recurrent neural networks in this brief we establish a novel complex valued memristive recurrent neural network cvmrnn to study its stability as a generalization of real valued memristive neural networks cvmrnn can be separated into real and imaginary parts by means of m matrix and lyapunov function the existence uniqueness and exponential stability of the equilibrium point for cvmrnns are investigated and sufficient conditions are presented finally the effectiveness of obtained results is illustrated by two numerical examples

event triggered h_ infty state estimation for delayed stochastic memristive neural networks with missing measurements the discrete time case in this paper the event triggered h infty state estimation problem is investigated for a class of discrete time stochastic memristive neural networks dsmnns with time varying delays and missing measurements the dsmnn is subject to both the additive deterministic disturbances and the multiplicative stochastic noises the missing measurements are governed by a sequence of random variables obeying the bernoulli distribution for the purpose of energy saving an event triggered communication scheme is used for dsmnns to determine whether the measurement output is transmitted to the estimator or not the problem addressed is to design an event triggered h infty estimator such that the dynamics of the estimation error is exponentially mean square stable and the prespecified h infty disturbance rejection attenuation level is also guaranteed by utilizing a lyapunov krasovskii functional and stochastic analysis techniques sufficient conditions are derived to guarantee the existence of the desired estimator and then the estimator gains are characterized in terms of the solution to certain matrix inequalities finally a numerical example is used to demonstrate the usefulness of the proposed event triggered state estimation scheme

h state estimation for neural networks with general activation function and mixed time varying delays this article deals with h state estimation of neural networks with mixed delays in order to make full use of delay information novel delay product lyapunov krasovskii functional lkf by using parameterized delay interval is first constructed then generalized free weighting matrix integral inequality is used to estimate the derivative of lkf to reduce the conservatism also a more general activation function is further applied by combining with parameterized delay interval in order to obtain a more accurate estimator model finally sufficient conditions are derived to confirm that the estimation error system is asymptotically stable with a prescribed h performance numerical examples are simulated to show the benefits of our proposed method