stationary velocity distributions in traffic flows we introduce a traffic flow model that incorporates clustering and passing we obtain analytically the steady state characteristics of the flow from a boltzmann like equation a single dimensionless parameter r c 0v 0t 0 with c 0 the concentration v 0 the velocity range and 1 t 0 the passing rate determines the nature of the steady state when r 1 large clusters with average mass r alpha form and the flux is j r gamma the initial distribution of slow cars governs the statistics when p 0 v v mu as v 0 the scaling exponents are gamma 1 mu 2 alpha 1 2 when mu 0 and alpha mu 1 mu 2 when mu 0

interactive group decision making procedure under incomplete information this paper deals with multiple criteria decision making problem with incomplete information when multiple decision makers multiple criteria group decision making mcgdm are involved usually decision makers dms are willing or able to provide only incomplete information because of time pressure lack of knowledge or data and their limited expertise related with problem domain there have been just a few studies considering incomplete information in group settings this incompletely specified information constructs region of linear constraints and therefore pairwise dominance relationship between alternatives reduces to intractable nonlinear programmings hence to handle this difficulty we suggest a method utilizing individual decision results to form group consensus final group consensus ranking toward more agreement of participants can be built through solving a series of linear programmings using individual decision results under group members possibly different weight constraints

applications of field theoretic renormalization group methods to reaction diffusion problems we review the application of field theoretic renormalization group rg methods to the study of fluctuations in reaction diffusion problems we first investigate the physical origin of universality in these systems before comparing rg methods to other available analytic techniques including exact solutions and smoluchowski type approximations starting from the microscopic reaction diffusion master equation we then pedagogically detail the mapping to a field theory for the single species reaction ka a k we employ this particularly simple but non trivial system to introduce the field theoretic rg tools including the diagrammatic perturbation expansion renormalization and callan symanzik rg flow equation we demonstrate how these techniques permit the calculation of universal quantities such as density decay exponents and amplitudes via perturbative dc d expansions with respect to the upper critical dimension dc with these basics established we then provide an overview of more sophisticated applications to multiple species reactions disorder effects l evy flights persistence problems and the influence of spatial boundaries we also analyse field theoretic approaches to non equilibrium phase transitions separating active from absorbing states we focus particularly on the generic directed percolation universality class as well as on the most prominent exception to this class even offspring branching and annihilating random walks finally we summarize the state of the field and present our perspective on outstanding problems for the future

linear response theory applied to stochastic resonance in models of ensembles of oscillators we apply linear response theory to a parallel ensemble of stochastic resonators we show that for a large number of elements the system can be used to process broadband signals without frequency distortions both conventional stochastic resonance and aperiodic stochastic resonance are studied

persistence properties of a system of coagulating and annihilating random walkers we study a d dimensional system of diffusing particles that on contact either annihilate with probability 1 q ensuremath 1 or coagulate with probability q ensuremath 2 q ensuremath 1 in one dimension the system models the zero temperature glauber dynamics of domain walls in the q state potts model we calculate overline p m t the probability that a randomly chosen lattice site contains a particle whose ancestors have undergone exactly m ensuremath 1 coagulations using perturbative renormalization group analysis for dl2 we show that if the number of coagulations m is much less than the typical number m t then overline p m t ensuremath sim m ensuremath zeta d t ensuremath ensuremath theta with ensuremath theta dq q q ensuremath 1 2 ensuremath epsilon o ensuremath epsilon 2 ensuremath zeta 2q ensuremath 1 ensuremath epsilon 2q ensuremath 1 q ensuremath 1 1 2 aq ensuremath epsilon 2 o ensuremath epsilon 3 where q q ensuremath 1 q ensuremath epsilon 2 ensuremath d and a ensuremath 0 006 dots m t is shown to scale as m t ensuremath sim t d 2 ensuremath ensuremath delta where ensuremath delta d 1 ensuremath q q ensuremath 1 q ensuremath 1 2 ensuremath epsilon o ensuremath epsilon 2 in two dimensions we show that overline p m t ensuremath sim mathrm ln t q 3 ensuremath 2q mathrm ln m 2q ensuremath 1 2 t ensuremath 2q for m ensuremath ll t 2q ensuremath 1 we also derive an exact nonperturbative relation between the exponents namely ensuremath delta q ensuremath theta 1 ensuremath q the one dimensional results corresponding to ensuremath epsilon 1 are compared with results from monte carlo simulations

survival probability of a mobile particle in a fluctuating field we study the the survival probability p t upto time t of a test particle moving in a fluctuating external field the particle moves according to some prescribed deterministic or stochastic rules and survives as long as the external field that it sees at its own location does not change sign this is a natural generalization of the static persistence when the particle is at rest that has generated considerable recent interests two types of motions of the particle are considered in one case the particle adopts a strategy to live longer and in the other it just diffuses randomly three different external fields were considered i the solution of diffusion equation ii the colour profile of the q state potts model undergoing zero temperature coarsening dynamics and iii spatially uncorrelated brownian signals in most cases studied p t sim t theta m for large t the exponent theta m is calculated via numerically analytically by approximate methods and in some cases exactly it is shown in some special cases that the survival probability of the mobile particle is related to the persistence of special patterns present in the initial configuration of a phase ordering system

an approach for finding the most preferred alternative in the presence of multiple criteria abstract an interactive approach for discrete multiple criteria decision making problems is developed the approach requires the decision maker to compare pairs of presented alternatives these alternatives may be existing alternatives or dummy alternatives created from existing alternatives inferior alternatives are sequentially eliminated by either using the responses of the decision maker directly or by constructing cones of inferior solutions based on these responses the approach converges to the most preferred solution so long as the decision maker has a nondecreasing quasiconcave value function the aim is to keep the number of pairwise comparisons required of the decision maker as small as possible computational experience on randomly generated problems is reported and the results are compared with the results of similar approaches

finite size fluctuations and stochastic resonance in globally coupled bistable systems the dynamics of a system formed by a finite number n of globally coupled bistable oscillators and driven by external forces is studied focusing on a global variable defined as the arithmetic mean of each oscillator variable several models based on truncation schemes of a hierarchy of stochastic equations for a set of fluctuating cumulant variables are presented this hierarchy is derived using it o stochastic calculus and the noise terms in it are treated using an asymptotic approximation valid for large n in addition a simplified one variable model based on an effective potential is also considered these models are tested in the framework of the phenomenon of stochastic resonance in turn they are used to explain in simple terms the very large gains recently observed in these finite systems

a comparison of multiple criteria analysis techniques for water resource management multiple criteria analysis mca is a framework for evaluating decision options against multiple criteria numerous techniques for solving an mca problem are available this paper applies mca to six water management decision problems the mca methods tested include weighted summation range of value promthee ii evamix and compromise programming we show that different mca methods were in strong agreement with high correlations amongst rankings in the few cases where strong disagreement between mca methods did occur it was due to presence of mixed ordinal cardinal data in the evaluation matrix the results suggest that whilst selection of the mca technique is important more emphasis is needed on the initial structuring of the decision problem which involves choosing criteria and decision options

mappac as a compromise between outranking methods and maut abstract this article shows that the bicriteria preference indices of the mappac method may be classified in two categories those of a compensatory type in cases of discordant evaluations methodologically in line with the maut approach and those which underline partial dominance relations in cases of concordant evaluations in analogy with noncompensatory outranking methods and with the electre methods in particular mappac may therefore be considered a mixed or intermediate method a sort of compromise between the approaches mentioned above it will also be shown that the aggregated index of mappac is a function not only of the weight of the criteria and of the entity of the difference in evaluation but also all other conditions remaining unvaried of the number of criteria according to which one action is preferred or indifferent with respect to another it is possible to note a number of similarities and differences between the indices of this method and the concordance indices of the electre methods

noisy fitzhugh nagumo model from single elements to globally coupled networks we study the noisy fitzhugh nagumo model representative of the dynamics of excitable neural elements and derive a fokker planck equation for both a single element and for a network of globally coupled elements we introduce an efficient way to numerically solve this fokker planck equation especially for large noise levels we show that contrary to the single element the network can undergo a hopf bifurcation as the coupling strength is increased furthermore we show that an external sinusoidal driving force leads to a classical resonance when its frequency matches the underlying system frequency this resonance is also investigated analytically by exploiting the different time scales in the problem

the greek banking system reanalysis of performance abstract zopounidis et al used an ordinal regression analysis to assess an additive utility model and to obtain final ranking of a representative sample of commercial greek banks c zopounidis d k despotis e stavropoulou multiattribute evaluation of greek banking performance applied stochastic models and data analysis 11 1995 97 107 in this paper we reanalyze their data by means of a new multivariate analysis method called co plot a two dimensional graphic display technique designed to analyze observations e g 16 banks and attributes e g 7 attributes simultaneously the method produces three results 1 similarity among the banks by the composite of all attributes involved five clusters are obtained 2 the structure of correlations among the attributes three clusters are obtained and 3 the mutual relationships between the banks and the attributes the banks are mapped into a partial order according to their increased performance to obtain their rating the final ranking obtained by the co plot method differed from that obtained by zopounidis et al

gain in stochastic resonance precise numerics versus linear response theory beyond the two mode approximation in the context of the phenomenon of stochastic resonance sr we study the correlation function the signal to noise ratio snr and the ratio of output over input snr i e the gain which is associated to the nonlinear response of a bistable system driven by time periodic forces and white gaussian noise these quantifiers for sr are evaluated using the techniques of linear response theory lrt beyond the usually employed two mode approximation scheme we analytically demonstrate within such an extended lrt description that the gain can indeed not exceed unity we implement an efficient algorithm based on work by greenside and helfand detailed in the appendix to integrate the driven langevin equation over a wide range of parameter values the predictions of lrt are carefully tested against the results obtained from numerical solutions of the corresponding langevin equation over a wide range of parameter values we further present an accurate procedure to evaluate the distinct contributions of the coherent and incoherent parts of the correlation function to the snr and the gain as a main result we show for subthreshold driving that both the correlation function and the snr can deviate substantially from the predictions of lrt and yet the gain can be either larger or smaller than unity in particular we find that the gain can exceed unity in the strongly nonlinear regime which is characterized by weak noise and very slow multifrequency subthreshold input signals with a small duty cycle this latter result is in agreement with recent analog simulation results by gingl et al icnf 2001 edited by g bosman world scientific singapore 2002 pp 545 548 fluct noise lett 1 l181 2001

how to select and how to rank projects the promethee method abstract in this paper we present the promethee methods a new class of outranking methods in multicriteria analysis their main features are simplicity clearness and stability the notion of generalized criterion is used to construct a valued outranking relation all the parameters to be defined have an economic signification so that the decision maker can easily fix them two ways of treatment are proposed it is possible to obtain either a partial preorder promethee i or a complete one promethee ii both on a finite set of feasible actions a comparison is made with the electre iii method the stability of the results given by the two methods is analysed numerical applications are given in order to illustrate the properties of the new methods and some further problems are discussed

dynamical critical behaviours of the ising spin chain swendsen wang and wolff algorithms we study the zero temperature ising chain evolving according to the swendsen wang dynamics we determine analytically the domain length distribution and various historical characteristics e g the density of unreacted domains is shown to scale with the average domain length as l with 3 2 for the q state potts model 1 q 1 we also compute the domain length distribution for the ising chain endowed with the zero temperature wolff dynamics

canonical fuzzy bags and bag fuzzy measures as a basis for madm with mixed non cardinal data abstract this contribution introduces what will be called sine analysis a new approach to multiple attribute decision making madm with mixed noncardinal data this approach is based upon the notion of canonical fuzzy bags and their scalar evaluations by bag fuzzy measures

geometrical representations for mcda abstract in this paper geometrical representations for multicriteria decision problems are proposed this new approach provides assistance to understand the conflictual aspects of the criteria and to tackle the problem of the weights associated to them a generalized criterion including a preference function is first generated for each criterion this allows to define unicriterion preference flows for which a geometrical representation can be obtained by using the principal components analysis the actions are represented by points and criteria by axes in the pca plane a decision axis taking into account the weights associated to the criteria can be defined this technique provides the decision maker with a considerable enrichment for the understanding of his problem clusters of actions can be considered the importance of the criteria can be evaluated conflictual criteria are immediately detected incomparability between actions is emphasized and explained best compromise actions are easily selected new decision axes representing possible clusters of criteria can be considered undesirable actions can be eliminated the technique consists in a powerful new qualitative decision tool it is illustrated in the paper on some examples treated by the promethee i and ii methods a didactic and user friendly microcomputer code is available

promethee md 2t method for project selection abstract project selection is a real problem of multicriteria group decision making mcgdm where each decision maker expresses his her preferences depending on the nature of the alternatives and on his her own knowledge over them thus information as much quantitative as qualitative coexists the traditional methods of mcgdm developed for project selection usually discriminates in favour of quantitative information at the expense of qualitative information and this is due to the capability to integrate this first type of information inside their procedure in this article two new multicriteria 2 tuple group decision methods called preference ranking organisation method for enrichment evaluation multi decision maker 2 tuple i and ii promethee md 2t i and ii are presented they are able to integrate inside their procedure both quantitative and qualitative information in an uncertain context this has been performed by integrating a 2 tuple linguistic representation model dealing with non homogeneous and imprecise information data made up by valued intervals numerical and linguistic values into the aggregation operators of promethee methods although they have been developed for project selection problems these proposed methods can be applied to all kinds of decision making problems with heterogeneous and multigranular information therefore the application of these methods to real problems will lead to better results in mcgdm it offers to the decision makers simpler and wider application of the aggregation operators of the promethee multicriteria method without sacrificing any of its advantageous properties and by taking into account the imprecision of data a numerical simulation of the proposed method is carried out to show its possibilities

construction of global fuzzy preference structures from two parameter single criterion fuzzy outranking relations in this paper we deal with the construction of global fuzzy preference structures from two parameter single criterion fuzzy outranking relations proposed in 10 and which are based on the aggregation of outranking indices associated with a cuts we consider two ways of constructing global fuzzy preference structures i aggregate the two parameter single criterion fuzzy outranking relations and then construct the global fuzzy preference structures and ii construct global fuzzy preference structures and then aggregate the single criterion fuzzy preference indifference and incomparability relations we also investigate the case where these two ways of proceeding lead to the same results

cardinal ranking of alternative actions extension of the promethee method abstract the method presented in this paper is an extension of the promethee one of the most known multicriteria outranking methods this extension consists in a more detailed investigation of the differences existing among the performances of the actions examined achieved through the notion of ideal and anti ideal alternative hence the state of strict preference relating various pairs of actions can be differentiated with reference to the extreme performances attained by the alternatives under consideration the more accurate description of the reality leads to a relatively more reliable ranking of the available solutions and allows the exploitation of the results for the construction of a cardinal scale assigning to each action a numerical value between 0 and 1 the quantitative differentiation of the alternatives thus achieved gives another dimension of information which is extremely useful for the decision making process a comparative study of the two methods shows the greater sensitivity of exprom and its ability to reflect in the quantitative results any probable deviation in the initial data of a problem this sensitivity is accompanied with a greater stability due to the smoothing of the discontinuities characterizing most preference functions in promethee

system size resonance in a binary attractor neural network system size resonance ssr is a phenomenon in which the response of a system is optimal for a certain finite size but poorer as the size goes to zero or infinity in order to show ssr effects in binary attractor neural networks we study the response of a network in the ferromagnetic phase to an external time dependent stimulus under the presence of such a stimulus the network shows ssr as is demonstrated by the measure of the signal amplification both analytically and by simulation

decision making in multiobjective optimization aided by the multicriteria tournament decision method abstract this paper proposes a new method for multicriteria analysis named multicriteria tournament decision mtd it provides the ranking of alternatives from best to worst according to the preferences of a human decision maker dm it has some positive aspects such as it has a simple algorithm with intuitive appeal it involves few input parameters just the importance weight of each criterion the helpfulness of mtd is demonstrated by using it to select the final solution of multiobjective optimization problems in an a posteriori decision making approach having at hand a discrete approximation of the pareto front provided by a multiobjective evolutionary search algorithm the choice of the preferred pareto optimal solution is performed using mtd a simple method named gain analysis method gam for verifying the existence of a better solution a solution associated to higher marginal rates of return than the one originally chosen by the dm is also introduced here the usefulness of mtd and gam methods is confirmed by the suitable results shown in this paper

coarsening in the q state potts model and the ising model with globally conserved magnetization we study the nonequilibrium dynamics of the q state potts model following a quench from the high temperature disordered phase to zero temperature the time dependent two point correlation functions of the order parameter field satisfy dynamic scaling with a length scale l t t 1 2 in particular the autocorrelation function decays as l t q we illustrate these properties by solving exactly the kinetic potts model in d 1 we then analyze a langevin equation of an appropriate field theory to compute these correlation functions for general q and d we establish a correspondence between the two point correlations of the q state potts model and those of a kinetic ising model evolving with a fixed magnetization 2 q 1 the dynamics of this ising model is solved exactly in the large q limit and in the limit of a large number of components n for the order parameter for general q and in any dimension we introduce a gaussian closure approximation and calculate within this approximation the scaling functions and the exponent q these are in good agreement with the direct numerical simulations of the potts model as well as the kinetic ising model with fixed magnetization we also discuss the existing and possible experimental realizations of these models

the mechanism of stochastic resonance it is shown that a dynamical system subject to both periodic forcing and random perturbation may show a resonance peak in the power spectrum which is absent when either the forcing or the perturbation is absent

novel types of sensitivity analysis for additive mcdm methods three novel types of sensitivity analysis are presented they determine the following 1 the sensitivity of a ranking to specific changes in the evaluations of all alternatives on certain criteria 2 the influence of specific changes in certain criterion scores of an alternative 3 the minimum modification of the weights required to make an alternative ranked first the use of these instruments is demonstrated by the results of a simulation experiment results show that the first and second type of sensitivity analysis enable to apply multiple criteria decision making mcdm methods in dynamic circumstances the third type of sensitivity analysis is demonstrated to be a tool to analyze the total weight space

extensions of the prudence principle to exploit a valued outranking relation abstract in many outranking methods the alternatives are first compared pairwise to build a valued outranking relation which is then exploited to derive a recommendation for the decision maker this paper proposes extensions of arrow and raynaud s prudence principle to exploit a valued outranking relation even in cases where the outranking values have an ordinal interpretation the idea is to build a ranking that maximizes the weakest support for its implicit pairwise comparisons we present a family of exploitation models providing three types of solutions depending on the decision maker s request a linear order a weak order or a partial preorder an algorithm is provided which solves the exploitation models relations between these models and some of their properties are also discussed

validity of basic concepts in nonlinear cooperative fokker planck models the stochastic amplification of a periodic signal in a truly nonlinear fokker planck model whose drift coefficient exhibits a functional dependence on the distribution function is analyzed numerically by means of a finite difference method our aim is to check the validity of basic concepts widely used in studying linear and or undriven systems a perturbation approach to numerically evaluate the generalized susceptibility of the model by means of the linear response theory is tested and found to be adequate for weak driving fields we also check the validity of the floquet theory and the h theorem for which no extension to the case of truly nonlinear driven systems exists the influence of the functional nonlinearity on the typical stochastic resonance effects is pointed out textcopyright 1996 the american physical society

a promethee based classification method using concordance and discordance relations and its application to bankruptcy prediction outranking relation theory has been widely used to study pattern classification here we propose a classification method with concepts from the flows used in promethee methods which are extensively applied in multi criteria decision aids promethee uses a flow generated on the basis of a preference index and measured by various preference functions for each criterion to represent the preference intensity for one pattern over another pattern however only criteria that are concordant with the preference contribute to a preference index in the present study the opinions from discordant criteria are also taken into account the proposed method newly defines an overall preference index using both concordance and discordance relations for ordinal sorting problems the final classification decision for a new pattern depends on its net flow the criteria weights are determined using a genetic algorithm based approach empirical results obtained for a real world problem regarding bankruptcy prediction demonstrate that the proposed method performs well compared to other well known classification methods

statistics of small clusters in system with rare aggregation centers abstract an integral equation describing the statistics of small clusters in a system with rare aggregation centers is considered in this paper this equation is obtained from the probabilistic consideration of transition to cluster cluster aggregation in the small cluster system several different dependences for the characteristic probability are used a new form of dependence for the cluster size distribution is obtained the fluctuation character of used model is discussed in the case of poisson s statistics of growth centers the levy cluster size distribution is obtained

complementarity of phase transition and stochastic resonance in spatially restricted systems we study the linear response in a soft potential the landau type temperature dependence of which is responsible for the monostable to bistable transformation the system can be considered as a model of a sample with internal noise where a second order phase transition takes place in the bulk limit the intensity of noise influencing the order parameter is supposed to be a function of the volume we demonstrate that the anomaly of susceptibility at the phase transition point described by the landau phase transition theory transforms into the maximal response caused by stochastic resonance if the volume of the system decreases the phenomenon can be treated also as an increase in the diffuseness of a phase transition with lowering of the critical temperature we suggest that it is this crossover that contributes to the mechanism of dielectric peculiarities in ceramic and relaxor ferroelectrics

stochastic resonance in a mean field model of cooperative behavior we study the long time response of a stochastic system formed by very many interacting subsystems coupled by a mean field interaction and subject to a time periodic external field in the absence of a driving field the system shows an order disorder phase transition and its time evolution is well described by a fokker planck equation which is nonlinear in the probability density we carry out an analysis of the dynamics in the case of a weak driving field by means of a perturbation analysis linear response theory the response of the system is then given in terms of a generalized susceptibility its evaluation shows that the phenomenon of stochastic resonance typical of driven bistable systems is greatly enhanced by the dynamical feedback induced by mean field coupling

role of fluctuations in the response of coupled bistable units to weak time periodic driving forces we analyze the stochastic response of a finite set of globally coupled noisy bistable units driven by rather weak time periodic forces we focus on the stochastic resonance and phase frequency synchronization of the collective variable defined as the arithmetic mean of the variable characterizing each element of the array for single unit systems stochastic resonance can be understood with the powerful tools of linear response theory proper noise induced phase frequency synchronization for a single unit system in this linear response regime does not exist for coupled arrays our numerical simulations indicate an enhancement of the stochastic resonance effects leading to gains larger than unity as well as genuine phase frequency synchronization the nonmonotonicity of the response with the strength of the coupling strength is investigated comparison with simplifying schemes proposed in the literature to describe the random response of the collective variable is carried out

rim reference ideal method in multicriteria decision making abstract multiple criteria decision making methods provide a useful tool to support decision making to date different methods have been developed using different approaches in particular the conception used by the topsis and vikor methods identifies the best alternative based on the positive and the negative ideal solutions in this paper a new method based on the concept of ideal solution is presented as a possible variant of the aforementioned however in our case these values can vary between the maximum value and the minimum value this does not occur in the vikor and topsis methods in which these values are the extreme values moreover our method is characterized to be independent of the type of data moreover rim does not present rank reversal an aspect that is not present in other multiple criteria decision making methods

convergence properties and practical estimation of the probability of rank reversal in pairwise comparisons for multi criteria decision making problems abstract in this paper we address the impact of uncertainty introduced when the experts complete pairwise comparison matrices in the context of multi criteria decision making we first discuss how uncertainty can be quantified and modeled and then show how the probability of rank reversal scales with the number of experts we consider the impact of various aspects which may affect the estimation of probability of rank reversal in the context of pairwise comparisons such as the uncertainty level alternative preference scales and different weight estimation methods we also consider the case where the comparisons are carried out in a fuzzy manner it is shown that in most circumstances augmenting the size of the expert group beyond 15 produces a small change in the probability of rank reversal we next address the issue of how this probability can be estimated in practice from information gathered simply from the comparison matrices of a single expert group we propose and validate a scheme which yields an estimate for the probability of rank reversal and test the applicability of this scheme under various conditions the framework discussed in the paper can allow decision makers to correctly choose the number of experts participating in a pairwise comparison and obtain an estimate of the credibility of the outcome

note a preference ranking organisation method the promethee method for multiple criteria decision making principles for a new family of outranking methods are given the main aim of the proposed promethee approach is to be as easily understood as possible by the decision maker it is based on extensions of the notion of criterion six possible extensions are considered these extensions can easily be identified by the decision maker because the parameters to be defined at most 2 have an economic significance a valued outranking graph is constructed by using a preference index two possibilities are considered to solve the ranking problem by using this valued graph promethee i provides a partial preorder and promethee ii a total preorder on the set of the possible actions

construction of a two parameters fuzzy outranking relation from fuzzy evaluations at the early stages of design process several design concepts are proposed as potential solutions the selection of the most appropriate one is based on their evaluation with respect to several conflicting criteria in this paper we consider the case where the evaluations of design concepts with respect to different criteria are represented by means of fuzzy numbers we deal with the construction of a two parameters fuzzy outranking relation from fuzzy evaluations it is based on the aggregation of outranking indices associated with alpha cuts this fuzzy outranking index allows the decision maker to adopt different strategies by choosing a degree of optimism and a degree of aggressiveness

fraction of uninfected walkers in the one dimensional potts model the dynamics of the one dimensional q state potts model in the zero temperature limit can be formulated through the motion of random walkers which either annihilate a a phi or coalesce a a a with a q dependent probability we consider all of the walkers in this model to be mutually infectious whenever two walkers meet they experience mutual contamination walkers which avoid an encounter with another random walker up to time t remain uninfected the fraction of uninfected walkers is known to obey a power law decay u t approximately t phi q with a nontrivial exponent phi q c monthus phys rev e 54 4844 1996 s n majumdar and s j cornell ibid 57 3757 1998 we probe the numerical values of phi q to a higher degree of accuracy than previous simulations and relate the exponent phi q to the persistence exponent theta q b derrida v hakim and v pasquier phys rev lett 75 751 1995 through the relation phi q gamma q theta q where gamma is an exponent introduced in s j o donoghue and a j bray preceding paper phys rev e 65 051113 2002 our study is extended to include the coupled diffusion limited reaction a a b b b a in one dimension with equal initial densities of a and b particles we find that the density of walkers decays in this model as rho t approximately t 1 2 the fraction of sites unvisited by either an a or a b particle is found to obey a power law p t approximately t theta with theta approximately 1 33 we discuss these exponents within the context of the q state potts model and present numerical evidence that the fraction of walkers which remain uninfected decays as u t approximately t phi where phi approximately 1 13 when infection occurs between like particles only and phi approximately 1 93 when we also include cross species contamination we find that the relation between phi and theta in this model can also be characterized by an exponent gamma where similarly phi gamma theta

sigma mu efficiency analysis a methodology for evaluating units through composite indicators abstract we propose a methodology to employ composite indicators for performance analysis of units of interest using and extending the family of stochastic multiattribute acceptability analysis we start evaluating each unit by means of weighted sums of their elementary indicators in the whole set of admissible weights for each unit we compute the mean and the standard deviation of its evaluations clearly the former has to be maximized while the latter has to be minimized as it denotes instability in the evaluations with respect to the variability of weights we consider a unit to be pareto koopmans efficient with respect to and if there is no convex combination of and of the rest of the units with a value of that is not smaller and a value of that is not greater with at least one strict inequality the set of all pareto koopmans efficient units constitutes the first pareto koopmans frontier in the spirit of context dependent data envelopment analysis we assign each unit to one of the sequence of pareto koopmans frontiers we measure the local efficiency of each unit with respect to each frontier but also its global efficiency taking into account all frontiers in the plane thus enhancing the explicative power of the proposed approach to illustrate its potential we present a case study of world happiness based on the data of the homonymous report that is annually produced by the united nations sustainable development solutions network

a multiple criteria ranking procedure based on distance between partial preorders abstract in this paper a multiple criteria ranking procedure based on distance between partial preorders is proposed this method consists of two phases in the first phase the decision maker is asked to rank alternatives with a preorder complete or partial for each criterion and provide complete or partial linear information about the relative importance weights of the criteria in the second phase we introduce a distance procedure to aggregate the above individual rankings into a global ranking a partial preorder an algorithm for the aggregation procedure is proposed followed by a numerical illustration

environmental impact assessment using the evidential reasoning approach environmental impact assessment eia problems are often characterised by a large number of identified environmental factors that are qualitative in nature and can only be assessed on the basis of human judgments which inevitably involve various types of uncertainties such as ignorance and fuzziness so eia problems need to be modelled and analysed using methods that can handle uncertainties the evidential reasoning er approach provides such a modelling framework and analysis method in this paper the er approach will be applied to conduct eia analysis for the first time the environmental impact consequences are characterized by a set of assessment grades that are assumed to be collectively exhaustive and mutually exclusive all assessment information quantitative or qualitative complete or incomplete and precise or imprecise is modelled using a unified framework of a belief structure the original er approach with a recursive er algorithm will be introduced and a new analytical er algorithm will be investigated which provides a means for using the er approach in decision situations where an explicit er aggregation function is needed such as in optimisation problems the er approach will be used to aggregate multiple environmental factors resulting in an aggregated distributed assessment for each alternative policy a numerical example and its modified version are studied to illustrate the detailed implementation process of the er approach and demonstrate its potential applications in eia

the reunions of three dissimilar vicious walkers we study the behavior of three vicious random walkers which diffuse freely in one dimension witharbitrary diffusivitiesb 1 2 b 2 2 b 3 2 except that their paths may not cross the full distribution function is calculated exactly in the continuum limit the exponent 3 governing the decay of the probability r n 3 sim 1 n psi 3 of a simultaneousreunion of all three walkers aftern steps is found to varycontinuously according to psi 3 1 pi cos 1 left b 2 2 left b 1 2 b 2 2 b 2 2 b 3 2 right 1 2 right this variation has consequences for various interfacial wetting transitions in 1 1 dimensions it may also be related heuristically to the marginality of direct interface wall interactions decaying asw0 l2 in the intermediate fluctuation regime of 1 1 dimensional wetting where exponents varying continuously withw0 have recently been found

the use of domains in multicriteria decision making abstract this paper describes a domain criterion for a multicriteria problem given decision maker it then outlines possibilities for aggregating individual preference structures in the case of multiple decision makers

project prioritization under policy restrictions a combination of mcda with 0 1 programming abstract multiple criteria decision aid methods are increasingly used in financial decision making in order to capture the multifaceted character of modern enterprises activated in a complex and versatile market environment this paper presents a multiple criteria approach for the selection of firms applying for financial support from public funds besides the budget constraint the specific decision situation imposes the consideration of additional policy constraints that prevent from directly exploiting rankings provided by a multiple criteria method in such a case the problem solution is to find a set of alternatives satisfying the constraints and at the same time maximizing a measure of global performance the proposed procedure relies on the promethee v method which belongs to the well known promethee family of multiple criteria outranking methods and is combined with an integer programming formulation capable to effectively deal with the problem s combinatorial character this method is modified in order to avoid any bias in the selection of the optimal set that may arrive because of the apparent contradiction between the rate of resources consumption and the coefficients of the alternatives in the additive objective function

electre methods in prioritized mcdm environment abstract in most cases electre methods just apply to traditional multicriteria decision making mcdm problems with independent criteria however there exist more or less interdependences among criteria in actual situations a special case is mcdm with prioritizations among criteria called prioritized mcdm in recent years how to deal with mcdm problems in the environment of prioritized criteria becomes hot topic increasingly lots of existing methods including promethee are modified for the prioritized mcdm but the advantages of electre have not been exploited to the prioritized mcdm in my opinion design specific electre methods for prioritized mcdm problems will benefit the developments of both electre and prioritized mcdm in this paper we firstly reformulate the expressions of concordance and discordance indices for use in the mcdm problems with dependent criteria especially prioritized criteria based on the concepts of fuzzy measures and digraphs respectively after replacing the fuzzy measure by a prioritized measure we successfully validate the concordance of an assertion under prioritized criteria furthermore we design an approach to validate the discordance of the assertion based on a digraph constructed by the criteria and their prioritizations finally we design three procedures to construct outranking relations in the prioritized mcdm environment according to the ideas of electre i electre iv and electre is respectively it is meaningful of this paper to provide a new idea to solve the prioritized mcdm problems and widen the application scope of electre methods by means of the reformulations of concordance and discordance

an outranking method under uncertainty abstract the uncertainty of consequences and the imprecision of data often imply in multicriteria decision problems the use of probability distributions to characterize the evaluation of each action with respect to eacg criterion to keep as much information as possible the analysis should treat directly these probability distributions instead of reducing them to single values such as mean or median in this context the paper proposes a multicriteria procedure which transforms these distributive evaluations of actions according to decisionmaker s preferences in order to progress to a ranking of these actions the procedure consists for each couple of actions to construct a distributive preference degree with respect to each criterion and a distributive outranking degree over all criteria these distributive outranking degrees are then explored in order to rank the actions totally or partially

recommendation using neighborhood methods with preference relation based similarity abstract selecting appropriate items from a list consisting of a large number of items provided by a product website can be difficult and time consuming for the potential customers the development of recommender systems should be an important solution that will help users to select items easily according to their preferences for recommender systems the main aim of the popular collaborative filtering approaches is to recommend items that users with similar preferences have liked in the past because there is a certain degree to which one alternative is not worse than another in decision making it would be interesting to make further use of the preference relation to design a similarity measure by measuring the overall strength of one user s preference over that of another the proposed similarity of one user to another user is therefore dependent on the strength of the preference of the former over the latter in contrast to traditional similarity measures for neighborhood methods in collaborative filtering the proposed preference relation based similarity is not symmetric for any two users experimental results have demonstrated that the generalization ability of the proposed multi criteria neighborhood method performs well in comparison to other single criterion and multi criteria neighborhood methods

co plot a graphic display method for geometrical representations of mcdm abstract a relatively new multivariate analysis method called co plot is shown to be highly efficient for the geometrical representation of multicriteria decision problems co plot a two dimensional graphic display technique is designed for multicriteria analysis its main feature is the simultaneous analysis of actions e g observations and criteria e g variables in a simple way the method produces three results 1 similarity among actions by the composite of all criteria involved 2 the structure of correlations among the criteria and 3 the mutual relationships between the actions and the criteria the method is demonstrated on two numerical applications previously analyzed by mareschal and brans b mareschal j p brans european journal of operational research 34 1988 69 77 using the promethee methods and principal component analysis

ranking alternatives using fuzzy numbers we investigate the problem of employing expert opinion to rank alternatives across a set of criteria the experts use fuzzy numbers to express their preferences and we employ fuzzy arithmetic to compute an issue s fuzzy ranking this leads to a partition of the alternatives into sets h1 h2 where h1 contains the highest ranked issues h2 has all the second highest ranked alternatives etc the total ranking process is shown to possess a number of important properties an example is presented to illustrate the method

persistence of non markovian gaussian stationary processes in discrete time the persistence of a stochastic variable is the probability that it does not cross a given level during a fixed time interval although persistence is a simple concept to understand it is in gener

a generalized stochastic goal programming model in this paper we show how one can get stochastic solutions of stochastic multi objective problem smop using goal programming models in literature it is well known that one can reduce a smop to deterministic equivalent problems and reduce the analysis of a stochastic problem to a collection of deterministic problems the first sections of this paper will be devoted to the introduction of deterministic equivalent problems when the feasible set is a random set and we show how to solve them using goal programming technique in the second part we try to go more in depth on notion of smop solution and we suppose that it has to be a random variable we will present stochastic goal programming model for finding stochastic solutions of smop our approach requires more computational time than the one based on deterministic equivalent problems due to the fact that several optimization programs which depend on the number of experiments to be run needed to be solved on the other hand since in our approach we suppose that a smop solution is a random variable according to the central limit theorem the larger will be the sample size and the more precise will be the estimation of the statistical moments of a smop solution the developed model will be illustrated through numerical examples

the sir method a superiority and inferiority ranking method for multiple criteria decision making abstract in this paper a superiority and inferiority ranking sir method is proposed this new method uses two types of information the superiority and the inferiority information to derive two types of flows the superiority flow and the inferiority flow by which the set of alternatives are ranked partially or completely relationships between the sir method and some of the classical multiple criteria decision making mcdm methods such as saw topsis and promethee are explored it is proved that the sir method is a significant extension of the well known promethee method

bbtopsis a bag based technique for order preference by similarity to ideal solution abstract this contribution explores the way of accomplishing a topsis ranking of various submitted variants taking into account a our newly developed notions of variant superiority inferiority and noninferiority multiattribute canonical fuzzy bags defined on attributes and b making use of bag metrics to compute the relative closeness of the different variants to an ideal solution in particular we prove the existence and the uniqueness of a bag metric fulfilling a number of interesting properties

input output gain of collective response in an uncoupled parallel array of saturating dynamical subsystems abstract we explore the collective response of an uncoupled parallel array of saturating dynamical subsystems to a noisy periodic or random signal numerical simulation results show that a parallel array of nonlinear saturating subsystems can enhance the signal transmission via tuning the internal noise intensity and increasing the array size the input output gain larger than unity described by the signal to noise ratio for a periodic signal or the correlation coefficient for a random signal is observed in a form of array stochastic resonance this stochastic resonance phenomenon can be useful for practical information processing systems

multicriterion decision making in river basin planning and development five multicriterion decision making mcdm methods namely electre 2 promethee 2 analytic hierarchy process ahp compromise programming cp and exprom 2 are employed to select the best reservoir configuration for the case study of chaliyar river basin kerala india spearman rank correlation coefficient is used to assess the correlation between the ranks obtained by the above mcdm methods although these methods follow different approaches the analysis has shown that the same preference strategy is reached by all the methods comparative evaluation of mcdm methods revealed that compromise programming is best suited for the present case study

exponents appearing in the zero temperature dynamics of the 1d potts model for the glauber dynamics of the one dimensional q state potts model at zero temperature the fraction of spins which have never flipped up to time t decreases as t theta q where the exponent theta q varies continuously with q the calculation of the q dependence of this exponent can be reduced to the study of a simple reaction diffusion model using finite size scaling this allows one to obtain accurate estimates of b q for all values of q one can also show that for 1 1 epsilon the expansion of theta y is given by theta 1 2 pi epsilon o epsilon 2

multicriteria analysis survey and new directions abstract before the advent of multicriteria analysis decision problems often took the form of the optimization of an objective function or a utility function this approach has the advantage of resulting in well defined mathematical problems but is not always representative of reality in fact the comparison of several possible decisions is rarely made according to a single point of view and the preferences on a point of view are in many cases only modelled with difficulty by a function the aim of this paper is to survey the different directions in which multicriteria analysis has developed multiattribute utility theory outranking relations interactive methods the methodology recently proposed by b roy is also presented

domain statistics in coarsening systems we study the domain number and size distributions in the one dimensional ising and q state potts models subject to zero temperature glauber dynamics the survival probability of a domain s t t 2c and an unreacted domain q1 t t 2d are characterized by two independent nontrivial exponents for the ising case we find c50 126 and d51 27 using numerical simulations we develop an independent interval approximation that predicts the qualitative behavior of the domain distribution and provides good estimates for the exponents exact results for the domain distribution are also obtained in several solvable cases s1063 651x 97 00110 4

renormalisation of fluctuation effects in the a a to a reaction the field theoretical description of the a a to a reaction is exactly renormalised to all orders in perturbation theory it is confirmed that it belong to the same universality class as the a a to oe reaction and that the concentration decay like t d 2 for space dimensionality d smaller than two and like ln t t for d 2 are exact results

stochastic resonance of collective variables in finite sets of interacting identical subsystems we explore stochastic resonance effects in the response of a complex stochastic system formed by a finite number of interacting identical subunits driven by a time periodic force the driving force alone cannot induce sustained oscillations between the different attractors of the dynamics in the absence of noise we focus on a global stochastic variable defined as the arithmetic mean of the relevant stochastic variable of each subunit we construct numerical approximations to its first two long time cumulant moments and its long time correlation function we also compute the output signal to noise ratio and the stochastic resonance gain for a wide range of parameter values and several types of driving forces the coupling between the subsystems leads within adequate ranges of the parameter values to global outputs with very large signal to noise ratios we have also observed gains larger than unity in the global response to subthreshold sinusoidal driving forces

approximating promethee ii s net flow scores by piecewise linear value functions abstract p romethee ii is a prominent method for multi criteria decision aid mcda that builds a complete ranking on a set of potential actions by assigning each of them a so called net flow score however to calculate these scores each pair of actions has to be compared causing the computational load to increase quadratically with the number of actions eventually leading to prohibitive execution times for large decision problems for some problems however a trade off between the ranking s accuracy and the required evaluation time may be acceptable therefore we propose a piecewise linear model that approximates p romethee ii s net flow scores and reduces the computational complexity with respect to the number of actions from quadratic to linear at the cost of some wrongly ranked actions simulations on artificial problem instances allow us to quantify this time quality trade off and to provide probabilistic bounds on the problem size above which our model satisfyingly approximates p romethee ii s rankings they show for instance that for decision problems of 10 000 actions evaluated on 7 criteria the pearson correlation coefficient between the original scores and our approximation is of at least 0 97 when put in balance with computation times that are more than 7000 times faster than for the p romethee ii model the proposed approximation model represents an interesting alternative for large problem instances

families of vicious walkers we consider a generalization of the vicious walker problem in which n random walkers in rd are grouped into p families using field theoretic renormalization group methods we calculate the asymptotic behaviour of the probability that no pairs of walkers from different families have met up to time t for d 2 this is constant but for d 2 it decays as a power t which we compute to e2 in an expansion in e 2 d the second order term depends on the ratios of the diffusivities of the different families in two dimensions we find a logarithmic decay ln t and compute exactly

introduction to a new weighting method hierarchy consistency analysis abstract this paper proposes a new methodology hierarchy consistency analysis hca the approach to this methodology was developed owing to the fact that in the analysis of large scale problems a different viewpoint or specific points emphasis will result in different hierarchy structures on the basis of different structures being created the methodology is designed to combine these different structures and estimate their compromised criterion weights so that all different hierarchy structures will have the same aggregated index the hca methodology will thus provide us with a comprehensive framework for solving hierarchy evaluation problems its merits include amongst others providing a simpler method for calculating the weight of criteria providing a consistency index for monitoring dm judgment consistency and delivering more types of hierarchy structure schemata to aid the decision maker in understanding and auditing the performance status of systems

multi objective optimization for prestress design of cable strut structures abstract stiffness of a cable strut structure is dependent on the level and distribution of prestress although a higher prestress level enhances overall stiffness of the structure this condition may demand larger member sectional areas and material cost the effect of fabrication and installation error should also be incorporated in the prestress design this paper presents a new optimization method for prestress design of cable strut structures a multi objective optimization problem is formulated and solved to obtain preferred coefficient vectors of prestress modes with the following four objective functions 1 minimize average area of members 2 maximize minimum eigenvalue of stiffness matrix 3 minimize prestress variance of cables and 4 minimize maximum eigenvalue of error sensitivity matrix pareto optimal solutions are obtained by nsga ii among the pareto optimal solutions the most preferred solution is selected using promethee ii two examples are presented to illustrate the proposed process the results are compared with those by existing methods of optimization with a single objective function significance of each objective function is also evaluated by the number of remaining pareto optimal solutions after removal of the objective function

kang redner small mass anomaly in cluster cluster aggregation the large time small mass asymptotic behavior of the average mass distribution p m t is studied in a d dimensional system of diffusing aggregating particles for 1 or d or 2 by means of both a renormalization group computation as well as a direct resummation of leading terms in the small reaction rate expansion of the average mass distribution it is shown that p m t approximately 1 t d m 1 d sqrt t e kr for m t d 2 where e kr epsilon o epsilon 2 and epsilon 2 d in two dimensions it is shown that p m t approximately ln m ln t t 2 for m t ln t numerical simulations in two dimensions supporting the analytical results are also presented

fuzzy outranking for environmental assessment case study iron and steel making industry recent years have seen a world wide change in the environmental policy towards integrated pollution prevention taking into account all environmental media consequently the environmental assessment of production techniques has to consider multiple criteria which cannot be aggregated to one single index the concepts of multi criteria decision making mcdm seem a suitable means in order to implement life cycle assessment lca into integrated decision processes the outranking methods as a special subgroup of mcdm methods are particularly suitable for integral decision making through the notion of weak preference and incomparability which better represent the real decision situation as demonstrated in this paper especially the outranking method promethee brings together flexibility and simplicity for the user and is therefore chosen for the enhancement towards the evaluation of fuzzy data on preferences scores and weights

distribution of domain sizes in the zero temperature glauber dynamics of the one dimensional potts model for the zero temperature glauber dynamics of the q state potts model we calculate the exact distribution of domain sizes by mapping the problem on an exactly soluble one species coagulation model a1a a in the long time limit this distribution is universal and from its complicated exact expression we extract its behavior in various regimes our results are tested in a simulation and compared to the predictions of a simple approximation proposed recently considering the dynamics of domain walls as a reaction diffusion model a1a a with probability q22 q21 and a1a f with probability 1 q21 we calculate the pair correlation function in the long time regime s1063 651x 96 12809 9

an extension of the promethee method for decision making in fuzzy environment ranking of alternative energy exploitation projects abstract in the decision making process for the development of local resources a number of factors sometimes conflicting have to be considered multicriteria decision making procedures are widely applied today to ensure a rigorous analysis in this presentation a multicriteria method of ranking alternative projects promethee is extended to deal with fuzzy input data the method is applied for the evaluation and ranking of alternative energy exploitation schemes of a low temperature geothermal field it is demonstrated that this approach is more realistic and produces a more reliable ranking for problems such as the evaluation of alternative energy exploitation scenarios where the input data are not well defined

preference relations on actions and criteria in multicriteria decision making abstract let a be a finite set of feasible actions which are judged following several criteria an outranking relation is defined on a by considering preference of the decision maker as a weak order on each criterion and the relation among criteria as a semi order on the given set of criteria several ways of constructing outranking relations have been proposed one of the most popular introduced by b roy for instance electre s is based on the use of weights related to criteria in our approach the knowledge of weights is replaced by the existence of a semi order a case study is developed it deals with a computer selection problem

persistence in cluster cluster aggregation persistence is considered in one dimensional diffusion limited cluster cluster aggregation when the diffusion coefficient of a cluster depends on its size s as d s approximately s gamma the probabilities that a site has been either empty or covered by a cluster all the time define the empty and filled site persistences the cluster persistence gives the probability of a cluster remaining intact the empty site and cluster persistences are universal whereas the filled site depends on the initial concentration for gamma 0 the universal persistences decay algebraically with the exponent 2 2 gamma for the empty site case the exponent remains the same for gamma 0 but the cluster persistence shows a stretched exponential behavior as it is related to the small s behavior of the cluster size distribution the scaling of the intervals between persistent regions demonstrates the presence of two length scales the one related to the distances between clusters and that between the persistent regions

coarsening and persistence in the voter model the voter model is a simple model for coarsening with a nonconserved scalar order parameter we investigate coarsening and persistence in the voter model by introducing the quantity pn t defined as the fraction of voters who changed their opinion n times up to time t we show that pn t exhibits scaling behavior that strongly depends on the dimension as well as on the initial opinion concentrations exact results are obtained for the average number of opinion changes n and the autocorrelation function a t 21 n pn t 2d 2 in arbitrary dimension d these exact results are complemented by a mean field theory heuristic arguments and numerical simulations for dimensions d 2 the system does not coarsen and the opinion changes follow a nearly poissonian distribution in agreement with mean field theory for dimensions d 2 the distribution is given by a different scaling form which is characterized by nontrivial scaling exponents for unequal opinion concentrations an unusual situation occurs where different scaling functions correspond to the majority and the minority as well as for even and odd n

noise enhanced fisher information in parallel arrays of sensors with saturation this paper investigates stochastic resonance in parallel arrays of uncoupled saturating devices the fisher information is used to demonstrate the possibility of noise improved parameter estimation for arbitrary parametric signals especially it is shown that improvement by noise always occurs in these arrays for any configuration of the input signal even in optimal configuration the results contribute to establish stochastic resonance in parallel uncoupled arrays as a general mechanism of enhancement by noise which can occur in wide classes of nonlinearities and for various information processing tasks it can supplement other mechanisms of stochastic resonance that take place in isolated nonlinearities but generally in restricted configurations of the input signal

a multiplicative version of promethee ii applied to multiobjective optimization problems the method promethee ii has produced attractive results in the choice of the most satisfactory optimal solution of convex multiobjective problems however according to the current literature it may not work properly with nonconvex problems a modified version of this method called multiplicative promethee is proposed in this paper both versions are applied to some analytical problems previously optimized by an evolutionary algorithm the multiplicative promethee got much better results than the original promethee ii being capable of solving convex and nonconvex problems with continuous and discontinuous pareto fronts

exponents appearing in heterogeneous reaction diffusion models in one dimension we study the following 1d two species reaction diffusion model there is a small concentration of b particles with diffusion constant d b in an homogenous background of w particles with diffusion constant d w two w particles of the majority species either coagulate w w longrightarrow w or annihilate w w longrightarrow emptyset with the respective probabilities p c q 2 q 1 and p a 1 q 1 a b particle and a w particle annihilate w b longrightarrow emptyset with probability 1 the exponent theta q lambda d b d w describing the asymptotic time decay of the minority b species concentration can be viewed as a generalization of the exponent of persistent spins in the zero temperature glauber dynamics of the 1d q state potts model starting from a random initial condition the w particles represent domain walls and the exponent theta q lambda characterizes the time decay of the probability that a diffusive spectator does not meet a domain wall up to time t we extend the methods introduced by derrida hakim and pasquier em phys rev lett bf 75 751 1995 saclay preprint t96 013 to appear in em j stat phys 1996 for the problem of persistent spins to compute the exponent theta q lambda in perturbation at first order in q 1 for arbitrary lambda and at first order in lambda for arbitrary q