polynomial bound on the number of scattering poles on montre que dans la diffusion par un potentiel infiniment differentiable a support compact les poles de l operateur de diffusion sont a distribution polynomiale

preference modeling experiments with surrogate weighting procedures for the promethee method abstract one of the main tasks in a multi criteria decision making process is to define weights for the evaluation criteria however in many situations the decision maker dm may not be confident about defining specific values for these weights and may prefer to use partial information to represent the values of such weights with surrogate weights although for the additive model the use of surrogate weighting procedures has been already explored in the literature there is a gap with regard to experimenting with such kind of preference modeling in outranking based methods such as promethee for which there already are applications with surrogate weights in the literature thus this paper presents an experimental study on preference modeling based on simulation so as to increase understanding and acceptance of a recommendation obtained when using surrogate weights within the promethee method the main approaches to surrogate weights in the literature ew rs rr and roc have been evaluated for choice and ranking problematics throughout statistical procedures including kendall s tau coefficient the surrogate weighting procedure that most faithfully represents a dm s value system according to this analysis is the roc procedure

multiple criteria decision making with interval stochastic variables a method based on interval stochastic dominance abstract a novel method based on interval stochastic dominance to solve the stochastic multiple criteria decision making smcdm problem with interval stochastic variables is proposed by analyzing the uncertainty of interval stochastic variables we propose the method of determining cumulative distribution function of interval stochastic variables then three types of interval stochastic dominance isd rules are investigated the definition of interval stochastic dominance degree isdd is presented and some interesting properties of isd and isdd are proved with respect to the smcdm problem with interval stochastic variables to begin with interval cumulative distribution functions of alternative criterion values are determined then the isd relations matrix associated with pairwise comparison of alternatives on each criterion is obtained based on isd rules and the isdd matrix on each criterion is calculated further based on promethee method the net flows of each alternative are derived so as to obtain the ranking result consequently examples are presented to illustrate the effectiveness of the proposed method

fuzzy flowsort an integration of the flowsort method and fuzzy set theory for decision making on the basis of inaccurate quantitative data nowadays most real life decision problems can be modeled as sorting problems although it is difficult to quantitatively express the evaluation criteria precisely or precise values are inadequate to model the criteria for these situations multicriteria methods can be extended by using fuzzy theory thereby providing mathematical methods able to deal with decision processes in a fuzzy environment in this context we propose a sorting method called fuzzy flowsort f flowsort based on fuzzy set theory and flowsort which is a promethee based sorting method to demonstrate the usefulness and applicability of this new method an illustrative numerical example is presented the result confirms the potential and the applicability of associating fuzzy logic with the flowsort method for processing imprecise data comparisons are made between the results provided by fuzzy flowsort and flowsort and also between fuzzy flowsort and another algorithm based on flowsort that deals with the imprecision of data when they are defined by intervals in addition the association between the results obtained with the f flowsort and flowsort methods and promethee and f promethee methods is investigated

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

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

scattering theory and the trace of the wave group in 9 lax and phillips discuss the analogue for classical scattering theories in odd space dimensions of the poisson summation formula as generalized to compact manifolds by chazarain 3 colin de verdi e 141 and duistermaat and guillemin 5 and further generalized to manifolds with boundary in 1 71 however in 9 this trace formula is only proved for comparatively large values of the time variable see also ralston 14 1 bardos el al 2 this note is devoted to the proof of the same formula for all positive time for the case of scattering by a smooth compactly supported potential if n a is the number of poles a 3 then for every e 0 there exists c 0 such that

stability analysis of tree structured decision functions in multicriteria decision problems many values must be assigned such as the importance of the different criteria and the values of the alternatives with respect to subjective criteria since these assignments are approximate it is very important to analyze the sensitivity of results when small modifications of the assignments are made when solving a multicriteria decision problem it is desirable to choose a decision function that leads to a solution as stable as possible we propose here a method based on genetic programming that produces better decision functions than the commonly used ones the theoretical expectations are validated by case studies

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

note on the distribution of poles of the scattering matrix abstract trapping obstacles having at least one isolated multiple reflecting trapping ray are considered it is proved that for every e 0 there are poles j of the scattering matrix such that 0 im j log j

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

fuzzy sets and decision analysis abstract this survey points out recent advances in multiple attribute decision making methods dealing with fuzzy or ill defined information fuzzy maut as well as fuzzy outranking methods are reviewed aggregation procedures choice problems and treatment of interactive attributes are covered trends in research and open problems are indicated

asymptotics of resonances for a schrodinger operator with vector values abstract we show that the resonance counting function for a schrodinger operator in dimension one has an asymptotic expansion and calculate an explicit expression for the leading term in some situations

complex scaling and the distribution of scattering poles the purpose of this paper is to establish sharp polynomial bounds on the number of scattering poles for a general class of compactly supported self adjoint perturbations of the laplacian in r n odd we also consider more general types of bounds that give sharper estimates in certain situations the general conclusion can be stated as follows the order of growth of the poles is the same as the order of growth of eigenvalues for corresponding compact problems from the few known cases however the exact asymptotics are expected to be different the scattering poles for compactly supported perturbations were rigorously defined by lax and phillips 13 in a more general setting they correspond to resonances the study of which has a long tradition in mathematical physics in the lax phillips theory they appear as the poles of the meromorphic continuation of the scattering matrix and coincide with the poles of the meromorphic continuation of the resolvent of the perturbed operator because of the latter characterization they can be considered as the analogue of the discrete spectral data for problems on noncompact domains the problem of estimating the counting function

multicriteria tools for the trade off analysis in rural planning between economic and environment objectives in this article a multicriteria approach combining several multiattribute methods is presented for the analysis of the trade offs between economic and environmental objectives in rural planning after separate aggregation of the economic and ecological criteria the pareto efficient solutions are identified these solutions are further analyzed using a discrete version of the compromise programming to test the sensitivity for changes in the weights the method is combined with a method calculating the best and worst score for the distance function used in the compromise technique for larger problems an integer programming version of the method has been developed allowing to extend the scope of applications

scattering asymptotics for riemann surfaces in this article we prove the optimal polynomial lower bound for the number of resonances of a surface with hyperbolic ends we also give weyl asymptotics for the relative scattering phase of such a surface the proofs are based on trace formulae analogous to those of the euclidean odd dimensional scattering the main technical ingredient is a new proof of the poisson formula theorem 5 7 which is applicable in the euclidean case as well our lower bound seems to be the first example of an optimal polynomial lower bound for the number of resonances holding for a general class of higher dimensional elliptic operators with no symmetries the previous general lower bounds or asymptotics were either nonoptimal 25 58 9 one dimensional or radial 65 67 and 54 41 1 or they required some degeneracy of the

sharp polynomial bounds on the number of scattering poles of radial potentials abstract it is shown that for scattering by a radially symmetric potential in r n n odd the number of poles in a disk of radius r satisfies an estimate n r c n r 1 n this bound is sharp as shown by the special case of potentials nonvanishing at the boundary where n r k n a n r n 1 o 1 a being the diameter of the support

preference ranking global frequencies in multicriterion analysis pragma abstract this paper presents an mcdm method known as pragma which provides the ranking frequencies of feasible actions the method is based on the comparison of the partial profiles of each alternative with reference to all the possible pairs of criteria considered the global frequencies are obtained as the weighted sum of the corresponding partial ranking frequencies the information supplied by this method is valuable in solving discrete multiple criteria choice problems and in particular in building complete and partial preoders of feasible actions pragma is a useful complement to the mappac method being instrumentally based on the same fundamental preference indices

a preference preserving projection technique for mcdm abstract the paper introduces a new method for the graphical representation of multicriteria decision problems with discrete sets of alternatives the approach proposed here extends projection techniques based on principal component analysis by incorporating information about preferences between alternatives in the graphical display the advantages of principal component projection which provides a clear view of data values and a projection orthogonal to indifference hyperplanes which provides preference information are both made available to the user through a linear combination of projection matrices with interactively changed weights the approach developed here can further be extended to more complex nonlinear preference structures and strategies for that extension are also discussed in the paper

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

resonances for non trapping time periodic perturbations for time periodic perturbations of the wave equation in given by a potential q t x we obtain an upper bound of the number of the resonances we establish for m n large enough a trace formula relating the iterations of the monodromy operator u mt 0 t 0 and the sum jzmj of all resonances counted with their multiplicities

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

existence of resonances in magnetic scattering the schrodinger operator with a compactly supported magnetic field is shown to produce infinitely many resonances in any odd dimension 3 the proof is based on the poisson formula for resonances and properties of the magnetic heat invariants

extra an expert system for multicriteria decision making abstract this paper presents an expert system approach to a classical decision making problem aiding in the selection of a preferred action from a list of alternatives evaluated on several criteria in outranking methods the non compensatory aggregation procedure uses an importance relation on criteria subsets in extra the decision maker s knowledge on this importance relation are treated purely formally without converting them into weights therefore each outranking relation may be explained in terms of the input informations and of some simple axioms finally the multicriteria analysis process is illustrated and studied on a real world problem the media selection

a new distance measure including the weak preference relation application to the multiple criteria aggregation procedure for mixed evaluations abstract we introduce a new distance measure between two preorders that captures indifference strict preference weak preference and incomparability relations this measure is the first to capture weak preference relations we illustrate how this distance measure affords decision makers greater modeling power to capture their preferences or uncertainty and ambiguity around them by using our proposed distance measure in a multiple criteria aggregation procedure for mixed evaluations

distribution of poles for scattering on the real line abstract the density of scattering poles is shown to be proportional to the length of the convex hull of the support of the potential in the case of a potential with finite singularities at the endpoints of the support asymptotic formulae for the poles are given while in the c 0 case an example of a potential with infinitely many scattering poles on i r is constructed the scattering amplitude of a compactly supported potential is also characterized

an inverse problem for the wave equation with first order perturbation pour l equation d onde sur r n avec perturbation du potentiel on montre que l on peut retrouver le potentiel a partir du comportement asymptotique de l amplitude de diffusion on montre qu un resultat semblable est vrai quand on ajoute des termes d ordre 1 a l equation

incremental elicitation of choquet capacities for multicriteria choice ranking and sorting problems this paper proposes incremental preference elicitation methods for multicriteria decision making with a choquet integral the choquet integral is an evaluation function that performs a weighted aggregation of criterion values using a capacity function assigning a weight to any coalition of criteria thus enabling positive and or negative interactions among them and covering an important range of possible decision behaviors however the specification of the capacity involves many parameters which raises challenging questions both in terms of elicitation burden and guarantee on the quality of the final recommendation in this paper we investigate the incremental elicitation of the capacity through a sequence of preference queries questions selected one by one using a minimax regret strategy so as to progressively reduce the set of possible capacities until the regret the worst case loss due to reasoning with only partially specified capacities is low enough we propose a new approach designed to efficiently compute minimax regret for the choquet model and we show how this approach can be used in different settings 1 the problem of recommending a single alternative 2 the problem of ranking alternatives from best to worst and 3 sorting several alternatives into ordered categories numerical experiments are provided to demonstrate the practical efficiency of our approach for each of these situations

a note on scale transformations in the promethee v method abstract as already noted by mavrotas et al 2006 the promethee v method for multi attribute analysis of portfolio problems will fail to include an item in a portfolio if it has a negative net flow with respect to other items although adding such an item might actually improve the entire portfolio however the model formulated by mavrotas et al introduces a bias in favor of large portfolios because the promethee v method is sensitive to scale transformations the present paper analyzes this effect and proposes a method to correct it

multiple criteria hierarchy process for electre tri methods abstract sorting methods in particular electre tri methods are widely used in multiple criteria decision aiding to deal with ordinal classification problems problems of this kind encountered in practice involve the evaluation of different alternatives actions on several evaluation criteria that are structured in a hierarchical way in order to deal with a hierarchical structure of criteria in decision problems multiple criteria hierarchy process mchp has been recently proposed in this paper we apply the mchp to the electre tri methods in particular we extend electre tri b electre tri c and electre tri nc methods we also adapt the mchp concept to the case where interaction among evaluation criteria has either strengthening or weakening or antagonistic effect finally we present an extension of the srf method to determine the weights of criteria in case they are hierarchically structured

multivariate gaussian criteria in smaa abstract we consider stochastic multicriteria decision making problems with multiple decision makers in such problems the uncertainty or inaccuracy of the criteria measurements and the partial or missing preference information can be represented through probability distributions in many real life problems the uncertainties of criteria measurements may be dependent however it is often difficult to quantify these dependencies also most of the existing methods are unable to handle such dependency information in this paper we develop a method for handling dependent uncertainties in stochastic multicriteria group decision making problems we measure the criteria their uncertainties and dependencies using a stochastic simulation model the model is based on decision variables and stochastic parameters with given distributions based on the simulation results we determine for the criteria measurements a joint probability distribution that quantifies the uncertainties and their dependencies we then use the smaa 2 stochastic multicriteria acceptability analysis method for comparing the alternatives based on the criteria distributions we demonstrate the use of the method in the context of a strategic decision support model for a retailer operating in the liberated european electricity market

a method for determining the weights of criteria the centralized weights abstract in multicriteria analysis many methods use weights to represent the relative importance of criteria the noncompensatory aggregation procedure used in outranking methods enables comparisons of subsets of criteria from this point of view an interactive method is presented which requests only ordinal comparisons from the decision maker the relation more important than is assumed to be a semiorder therefore the indifference part of this relation is not necessarily transitive the judgements can be formulated as linear inequalities which constrain the set of feasible weights and threshold values all vertices of this polyhedron are determined the threshold and the unknown real weights are estimated by the centroid some characteristics a possible refinement in the estimation and an illustrative example are also given

exponential sums on ⁿ ii we prove a vanishing theorem for the p adic cohomology of exponential sums on a n in particular we obtain new classes of exponential sums on an that have a single nonvanishing p adic cohomology group the dimension of this cohomology group equals a sum of milnor numbers

facilities location in a competitive environment a promethee based multiple criteria analysis abstract in this paper a methodology for locating facilities in a competitive environment is introduced in this methodology the multi criteria approach and the notion of efficiency are appropriately integrated the classic distance criterion is combined with a second one a quality criterion to produce a more realistic representation of a customer s decision process

methods for decision making with cardinal numbers and additive aggregation abstract for multi attribute decision making with cardinal numbers and additive aggregation the methods additive aggregation and outranking for crisp and fuzzy numbers are connected with the concept of linguistic variables preference ranking a generalization of outranking and preference ranking organization methods such as electre and promethee can be divided into three phases where each of them is defined completely by linguistic variables the derived method preference ranking with additive weighting and individual fuzziness has an improved selectivity or discrimination compared to conventional methods moreover the method fulfils four important requirements preference only for sufficiently large weights considering evaluation differences outside of thresholds and regarding aggregational and substitutional properties the simplified method preference ranking with additive weighting and general fuzziness allows a reduction of computational resources

hidden fuzzy information requirement specification and measurement of project provider performance using the best worst method abstract the requirement specification process is an important part of a project and has the potential to prevent problems that may last for years after a project is delivered previous studies on the requirement specification process have focused on clarifying stated fuzzy terms in software requirement engineering however in many projects there is information that is not stated but it is implied and can be inferred this hidden information is usually ignored due to the assumption that the provider understands what they mean need this assumption is not always true such information if extracted may include fuzzy terms namely hidden fuzzy terms hfts which need specification therefore these fuzzy terms have to be identified and then specified to avoid potential future consequences this study proposes an algorithm to extract the hidden fuzzy terms utilises a fuzzy inference system fis to specify them and applies the best worst multi criteria decision making method bwm to evaluate the delivered product and measure the performance of the provider the model is then used to examine a case from defence housing australia such evaluation and measurement enable the project owner manager to have a transparent basis to support decisions later in different phases of the project and to ultimately reduce the likelihood of conflict and the receipt of an unsatisfactory product

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

existence of resonances in three dimensions ifp is an elliptic self adjoint perturbation of the laplacian on 3 and the coefficients ofp decay super exponentially then we show thatp has infinitely many resonances the resonances are defined here as the poles of the meromorphic continuation of p 2 1

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

a method based on multiobjective optimization for deriving a ranking from a fuzzy preference relation abstract methods for deriving final ranking from a fuzzy preference relation do not perform well in presence of irrelevant alternatives or in case of complex graphs with numerous circuits a new method for improving the quality of their prescriptions is proposed here it rests on the idea of reducing differences between a global model of preferences and a final ranking via multiobjective optimization this proposal is also more robust than others in relation to irrelevant alternatives it can be seen as an intent of reconciling two schools of thought related to decision aid one approach accepts the fuzziness of preferences the other is based on a system of axioms that model a normative rationality

on the multilevel internal structure of the asymptotic distribution of resonances abstract we prove that the set of resonances h has a multilevel asymptotic structure for the following classes of hamiltonians h schrodinger operators with point interactions y j r 3 quantum graphs and 1 d photonic crystals in the case of n 2 point interactions h consists of a finite number of sequences with logarithmic asymptotics leading parameters n of these sequences are connected with the geometry of the family y y j j 1 n the minimal parameter min corresponds to sequences with more narrow and so more observable resonances the asymptotic density of narrow resonances is expressed via the multiplicity of min and is connected with symmetries of y in the cases of quantum graphs and 1 d photonic crystals the decomposition of h into asymptotic sequences is proved under commensurability conditions to address the general quantum graph we introduce asymptotic density functions for two classes of complex strips the obtained results and effects are compared with obstacle scattering

generating fuzzy membership functions a monotonic neural network model abstract a crucial issue in the practical applications of fuzzy sets is to find a fuzzy membership function this paper suggests that neural networks which use the back propagation learning algorithm under monotonic function constraints can be used in generating fuzzy membership functions

rough approximation of a preference relation by dominance relations an original methodology for using rough sets to preference modeling in multi criteria decision problems is presented this methodology operates on a pairwise comparison table pct including pairs of actions described by graded preference relations on particular criteria and by a comprehensive preference relation it builds up a rough approximation of a preference relation by graded dominance relations decision rules derived from the rough approximation of a preference relation can be used to obtain a recommendation in multi criteria choice and ranking problems the methodology is illustrated by an example of multi criteria programming of water supply systems

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

breit wigner approximation and the distribution of resonances for operators with a discrete spectrum j 2 the counting function of j s n trivially satisfies n n j j in scattering situations the natural analogue of the discrete spectrum is given by resonances j and of n by the scattering phase s the relation between the two is now non trivial and we prove that where is the harmonic measure of the upper of half plane and can be taken dependent on this provides a precise high energy version of the breit wigner approximation and relates the properties of s to the distribution of resonances close to the real axis

multiple criteria aggregation procedure for mixed evaluations most of the existing multiple criteria decision making methods handle one kind of the information imperfections at the same time stochastic methods and fuzzy methods constitute typical examples of these methods however several multiple criteria modelizations include simultaneously many kinds of the information imperfections in this work we propose a multiple criteria aggregation procedure which accepts mixed evaluations i e evaluations which contain different natures of imperfections it is based on an adaptation of the stochastic dominance results

ranking methods for valued preference relations abstract in this paper we study a particular method that builds a partial ranking on the basis of a valued preference relation this method which is used in the mcdm method promethee i is based on leaving and entering flows we show that this method is characterized by system of three independent axioms

an axiomatic analysis of concordance discordance relations outranking methods propose an original way to build a preference relation between alternatives evaluated on several attributes that has a denite ordinal avor indeed most of them appeal the concordance non discordance principle that leads to declaring that an alternative is superior to another if the coalition of attributes supporting this proposition is suciently important concordance condition and if there is no attribute that strongly rejects it non discordance condition such a way of comparing alternatives is rather natural however it is well known that it may produce binary relations that do not possess any remarkable property of transitivity or completeness this explains why the axiomatic foundations of outranking methods have not been much investigated which is often seen as one of their important weaknesses this paper uses conjoint measurement techniques to obtain an axiomatic characterization of preference relations that can be obtained on the basis of the concordance non discordance principle it emphasizes their main distinctive feature i e their very crude way to distinguish various levels of preference dierences on each attribute we focus on outranking methods such as electre i that produce a reexive relation interpreted as an at least as good as preference relation the results in this paper may be seen as an attempt to give such outranking methods a sound axiomatic foundation based on conjoint measurement

asymptotics on the number of scattering poles for degenerate perturbations of the laplacian abstract for a class of compactly supported hypoelliptic perturbations of the laplacian in r n n 3 odd we prove that an asymptotic on the number of the eigenvalues of the corresponding reference operator implies a similar asymptotic for the number of the scattering poles

distribution of scattering resonances for generic schrodinger operators abstract let v be the schrodinger operator acting on l 2 r d c with d 3 odd here v is a bounded real or complex valued function vanishing outside the closed ball of center 0 and radius a if v belongs to the class m a of potentials introduced by christiansen we show that when r the resonances of v scaled down by the factor r are asymptotically distributed with respect to an explicit probability distribution on the lower unit half disc of the complex plane the rate of convergence is also considered for subclasses of potentials

multicriteria fuzzy classification procedure procftn methodology and medical application in this paper we introduce a new classification procedure for assigning objects to predefined classes named procftn this procedure is based on a fuzzy scoring function for choosing a subset of prototypes which represent the closest resemblance with an object to be assigned it then applies the majority voting rule to assign an object to a class we also present a medical application of this procedure as an aid to assist the diagnosis of central nervous system tumours the results are compared with those obtained by other classification methods reported on the same data set including decision tree production rules neural network k nearest neighbor multilayer perceptron and logistic regression our results are very encouraging and show that the multicriteria decision analysis approach can be successfully used to help medical diagnosis

scattering phase asymptotics with fractal remainders for a riemannian manifold m g which is isometric to the euclidean space outside of a compact set and whose trapped set has liouville measure zero we prove weyl type asymptotics for the scattering phase with remainder depending on the classical escape rate and the maximal expansion rate for axiom a geodesic flows this gives a polynomial improvement over the known remainders we also show that the remainder can be bounded above by the number of resonances in some neighbourhoods of the real axis and provide similar asymptotics for hyperbolic quotients using the selberg zeta function

asymptotic number of scattering resonances for generic schrodinger operators let v be the schrodinger operator acting on l 2 mathbb r d mathbb c with d geq 3 odd here v is a bounded real or complex function vanishing outside the closed ball of center 0 and of radius a let n v r denote the number of resonances of v with modulus r we show that if the potential v is generic in a sense of pluripotential theory then n v r c d a dr d o r d 3 over 16 epsilon quad mbox as r to infty for any e 0 where c d is a dimensional constant

sharp bounds on the number of scattering poles for perturbations of the laplacian sharp bounds on the numbern r of the scattering poles in the disc z r for a large class of compactly supported perturbations not necessarily selfadjoint of the laplacian in n n 3 odd are obtained in particular in the elliptic case the estimaten r cr n c is proved

using box indices in supporting comparison in multiobjective optimization because of the conflicting nature of criteria or objectives solving a multiobjective optimization problem typically requires interaction with a decision maker who can specify preference information related to the objectives in the problem in question due to the difficulties of dealing with multiple objectives the way information is presented plays a very important role questions posed to the decision maker must be simple enough and information shown must be easy to understand for this purpose visualization and graphical representations can be useful and constitute one of the main tools used in the literature in this paper we propose to use box indices to represent information related to different solution alternatives of multiobjective optimization problems involving at least three objectives box indices are an intelligible and easy to handle way to represent data they are based on evaluating the solutions in a natural and rough enough scale in order to let the decision maker easily recognize the main characteristics of a solution at a glance and to facilitate comparison of two or more solutions in an easily understandable way

the selberg zeta function for convex co compact schottky groups we give a new upper bound on the selberg zeta function for a convex co compact schottky group acting on the hyperbolic space n 1 in strips parallel to the imaginary axis the zeta function is bounded by exp c s where is the dimension of the limit set of the group this bound is more precise than the optimal global bound exp c s n 1 and it gives new bounds on the number of resonances scattering poles of n 1 the proof of this result is based on the application of holomorphic l2 techniques to the study of the determinants of the ruelle transfer operators and on the quasi self similarity of limit sets we also study this problem numerically and provide evidence that the bound may be optimal our motivation comes from molecular dynamics and we consider n 1 as the simplest model of quantum chaotic scattering

sharp upper bounds on the number of the scattering poles abstract we study the scattering poles of a compactly supported black box perturbations of the laplacian in r n n odd we prove a sharp upper bound of the counting function n r modulo o r n in terms of the counting function of the reference operator in the smallest ball around the black box in the most interesting cases we prove a bound of the type n r a n r n o r n with an explicit a n we prove that this bound is sharp in a few special spherically symmetric cases where the bound turns into an asymptotic formula

purity of exponential sums on n ii we give a purity result for exponential sums of the type x2kn f x where k is a flnite fleld of characteristic p k c is a non trivial additive character and f 2 k x1 xn is a polynomial whose highest degree homogeneous form splits as a product of factors deflning a divisor with normal crossings in p ni1

scattering frequencies and gevrey 3 singularities on etudie les frequences de diffusion k pour le laplacien dans la region r n o exterieur a un obstacle analytique compact on suppose que n est impair et qu on impose des conditions de dirichlet sur

resonances in one dimension and fredholm determinants we discuss resonances for schrodinger operators in whole and half line problems one of our goals is to connect the fredholm determinant approach of froese to the fourier transform approach of zworski another is to prove a result on the number of antibound states namely in a half line problem there are an odd number of antibound states between any two bound states

multi criteria analysis with partial information about the weighting coefficients abstract in this paper we address the problem of ranking a set of alternatives with partial information about the weighting coefficients we introduce a family of quasiorders that are easily interpretable and manageable which includes among others the natural quasiorder in r n and other well known preference structures in the literature the enrichment of the preference structure with respect to the natural quasiorder is measured by means of an absolute measure we introduce

a local trace formula for resonances of perturbed periodic schrodinger operators abstract we give a local trace formula for the pair p 1 h p 0 w hy p 0 where p 0 is a periodic schrodinger operator w is a decreasing perturbation and h is a small positive parameter we apply this result to establish the existence of h n resonances near some energy of p 0

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

traceformula for resonances in small domains abstract traceformulas are useful in the study of resonances in this article we work in a semi classical black box framework and obtain a traceformula of the same type as that of the second author now for the resonances in h dependent domains of size h and under somewhat more restrictive assumptions as an application we extend to a long range situation a result by v petkov and m zworski on breit wigner peaks in the scattering phase

ordinal judgments in multiattribute decision analysis abstract the article discusses the contradiction between the ambiguity of human judgment in a multicriterion environment and the exactness of the assessments required in the majority of the decision making methods preferential information from the decision makers in the ordinal form e g more preferable less preferable etc is argued to be more stable and more reliable than cardinal input ways of obtaining and using ordinal judgments for rank ordering of multiattribute alternatives are discussed the effectiveness of the step wise procedure of using ordinal tradeoffs for comparison of alternatives is evaluated we introduce the notion of ordinal tradeoffs presentation of ordinal tradeoffs as a flexible three stage process a paired joint ordinal scale pjos and evaluation of the effectiveness of the three stage process simulation results examine the sensitivity of the number of pairwise comparisons required for given numbers of criteria and categories within criteria as well as the number of alternatives analyzed this simulation shows that ordinal pairwise comparisons provide sufficient power to discriminate between 75 and 80 of the alternatives compared while the proportional number of pairwise comparisons relative to the maximum possible decreases with the number of criteria and categories the method is relatively insensitive to the number of alternatives considered