some universal properties for restricted trace gaussian orthogonal unitary and symplectic ensembles consider fixed and bounded trace gaussian orthogonal unitary and symplectic ensembles closely related to gaussian ensembles without any constraint for three restricted trace gaussian ensembles we prove universal limits of correlation functions at zero and at the edge of the spectrum edge our argument also applies to restricted trace ensembles with monomial potentials in addition by using the universal result in the bulk for fixed trace gaussian unitary ensemble which has been obtained by gotze and gordin we also prove the universal limits of correlation functions everywhere in the bulk for bounded trace gaussian unitary ensemble

character expansion method for supergroups and extended superversions of the leutwyler smilga and berezin karpelevich integrals we introduce an extension of the character expansion method to the case of supergroups this method allows us to calculate a superversion of the leutwyler smilga integral which to the best of our knowledge has not been calculated before we also use the method to generalize a previously calculated superversion of the berezin karpelevich integral our character expansion method should also allow for the calculation of other supergroup integrals

an axiomatic approach to the measurement of the amount of interaction among criteria or players in the framework of multicriteria decision making based on fuzzy measures or cooperative game theory an axiomatization of the concept of amount of interaction index is given it is based on four axioms a natural property called absence of interaction a boundary condition for which the index reduces to the shapley or banzhaf interaction index a pseudo additivity axiom and a recursivity property the resulting index which can be interpreted as a measure of the average degree of independence among criteria or players takes a particularly simple and natural form for supermodular or submodular measures the approach to the notion of interaction adopted in this paper can be seen as complementary to that recently adopted by grabisch and roubens

estimation of the weights of interacting criteria from the set of profiles by means of information theoretic functionals abstract following the recent work of marichal and roubens eur j operat res 124 2000 641 on fuzzy measure identification in multicriteria decision problems we propose an alternative unsupervised identification method based on the estimation of the fuzzy measure coefficients by means of information theoretic functionals

an axiomatic approach to the definition of the entropy of a discrete choquet capacity to extend the classical shannon entropy to nonadditive measures marichal recently introduced the concept of generalized entropy for discrete choquet capacities we provide a first axiomatization of this new concept on the basis of three axioms the symmetry property a boundary condition for which the entropy reduces to the shannon entropy and a generalized version of the well known recursivity property we also show that this generalized entropy fulfills several properties considered as requisites for defining an entropy like measure lastly we provide an interpretation of it in the framework of aggregation by the discrete choquet integral

angular gelfand tzetlin coordinates for the supergroup uosp k 1 2k 2 we construct gelfand tzetlin coordinates for the unitary orthosymplectic supergroup uosp k1 2k2 this extends a previous construction for the unitary supergroup u k1 k2 we focus on the angular gelfand tzetlin coordinates i e our coordinates stay in the space of the supergroup we also present a generalized gelfand pattern for the supergroup uosp k1 2k2 and discuss various implications for representation theory

classical and quantum superintegrability with applications a superintegrable system is roughly speaking a system that allows more integrals of motion than degrees of freedom this review is devoted to finite dimensional classical and quantum superintegrable systems with scalar potentials and integrals of motion that are polynomials in the momenta we present a classification of second order superintegrable systems in two dimensional riemannian and pseudo riemannian spaces it is based on the study of the quadratic algebras of the integrals of motion and on the equivalence of different systems under coupling constant metamorphosis the determining equations for the existence of integrals of motion of arbitrary order in real euclidean space e2 are presented and partially solved for the case of third order integrals a systematic exposition is given of systems in two and higher dimensional space that allow integrals of arbitrary order the algebras of integrals of motions are not necessarily quadratic but close polynomially or rationally the relation between superintegrability and the classification of orthogonal polynomials is analyzed

determination of weights of interacting criteria from a reference set abstract in this paper we present a model allowing to determine the weights related to interacting criteria this is done on the basis of the knowledge of a partial ranking over a reference set of alternatives prototypes a partial ranking over the set of criteria and a partial ranking over the set of interactions between pairs of criteria

on the efetov wegner terms by diagonalizing a hermitian supermatrix the diagonalization of hermitian supermatrices is studied such a change of coordinates is inevitable if one wishes to find certain structures in random matrix theory however it still poses serious problems since until now the calculation of all rothstein contributions known as efetov wegner terms in physics was quite cumbersome we derive the supermatrix bessel function with all efetov wegner terms for an arbitrary rotation invariant probability density function as applications we consider representations of generating functions for hermitian random matrices with and without an external field as integrals over eigenvalues of hermitian supermatrices all results are obtained with all efetov wegner terms which were previously unknown in such an explicit and compact representation

sharp regularity for the degenerate doubly nonlinear parabolic equation abstract the aim of this paper is to provide sharp regularity estimates for locally bounded solutions of the degenerate doubly nonlinear parabolic equation u t div m u m 1 d u p 2 d u f where m 1 p 2 and f l q r more precisely we show that solutions are locally of class c 0 where depends explicitly only on the optimal holder exponent for solutions of the homogeneous case the integrability of f in space and time and the nonlinearity parameters p and m

gelfand tzetlin coordinates for the unitary supergroup the gelfand tzetlin method provides explicit coordinates on the parameter space of the unitary groupu k which make direct evaluations of group integrals possible it is closely related to the gelfand construction of finite dimensional irreducible representations we generalize the gelfand tzetlin method to the unitary supergroupu k1 k2 the coordinates on the parameter space for supergroup integrals and the invariant haar measure are evaluated as an example the supersymmetric harish chandra itzykson zuber integral is calculated a generalized gelfand pattern containing anticommuting variables is introduced which determines the representation

recursive construction for a class of radial functions ii superspace we extend the recursion formula for matrix bessel functions which we obtained previously to superspace it is sufficient to do this for the unitary orthosymplectic supergroup by direct computations we show that fairly explicit results can be obtained at least up to dimension 8 8 for the supermatrices since we introduce a new technique we discuss various of its aspects in some detail

derivation of determinantal structures for random matrix ensembles in a new way there are several methods to treat ensembles of random matrices in symmetric spaces circular matrices chiral matrices and others orthogonal polynomials and the supersymmetry method are particular powerful techniques here we present a new approach to calculate averages over ratios of characteristic polynomials at first sight paradoxically one can call our approach supersymmetry without supersymmetry because we use structures from supersymmetry without actually mapping onto superspaces we address two kinds of integrals which cover a wide range of applications for random matrix ensembles for probability densities factorizing in the eigenvalues we find determinantal structures in a unifying way as a new application we derive an expression for the k point correlation function of an arbitrary rotation invariant probability density over the hermitian matrices in the presence of an external field

a comparison of the superbosonization formula and the generalized hubbard stratonovich transformation recently two different approaches were put forward to extend the supersymmetry method in random matrix theory from gaussian ensembles to general rotation invariant ensembles these approaches are the generalized hubbard stratonovich transformation and the superbosonization formula here we prove the equivalence of both approaches to this end we reduce integrals over functions of supersymmetric wishart matrices to integrals over quadratic supermatrices of certain symmetries

mixing of orthogonal and skew orthogonal polynomials and its relation to wilson rmt the unitary wilson random matrix theory is an interpolation between the chiral gaussian unitary ensemble and the gaussian unitary ensemble this new way of interpolation is also reflected in the orthogonal polynomials corresponding to such a random matrix ensemble although the chiral gaussian unitary ensemble and the gaussian unitary ensemble are associated with the dyson index 2 the intermediate ensembles exhibit a mixing of orthogonal polynomials and skew orthogonal polynomials we consider the hermitian and the non hermitian wilson random matrix and derive the corresponding polynomials their recursion relations christoffel darboux like formulas rodrigues formulas and representations as random matrix averages in a unifying way with the help of these results we derive the unquenched k point correlation function of the hermitian and the non hermitian wilson random matrix in terms of two flavor partition functions only this representation is due to a pfaffian factorization it drastically simplifies the expressions which can be easily numerically evaluated it also serves as a good starting point for studying the wilson dirac operator in the regime of lattice quantum chromodynamics

family of solvable generalized random matrix ensembles with unitary symmetry we construct a very general family of characteristic functions describing random matrix ensembles rme having a global unitary invariance and containing an arbitrary one variable probability measure which we characterize by a spread function various choices of the spread function lead to a variety of possible generalized rmes which show deviations from the well known gaussian rme originally proposed by wigner we obtain the correlation functions of such generalized ensembles exactly and show examples of how particular choices of the spread function can describe ensembles with arbitrary eigenvalue densities as well as critical ensembles with multifractality

on the issue of obtaining owa operator weights we first investigate the issue of obtaining the weights associated with the owa aggregation in the situation when we have observed data on the arguments and the aggregated value we next introduce a family of owa operators called exponential owa operators finally we look at a simple procedure for generating the weights given a required degree of orness

distribution of the smallest eigenvalue in complex and real correlated wishart ensembles for the correlated gaussian wishart ensemble we compute the distribution of the smallest eigenvalue and a related gap probability we obtain exact results for the complex 2 and for the real case 1 for a particular set of empirical correlation matrices we find universality in the spectral density for both real and complex ensembles and all kinds of rectangularity we calculate the asymptotic and universal results for the gap probability and the distribution of the smallest eigenvalue we use the supersymmetry method in particular the generalized hubbard stratonovich transformation and superbosonization

boundedness of the gradient for a doubly nonlinear parabolic equation we prove the local boundedness of the gradient for positive solutions to a doubly nonlinear parabolic equation in the case when the standard lebesgue measure has been replaced by a doubling measure which supports a weak poincare inequality

arbitrary rotation invariant random matrix ensembles and supersymmetry orthogonal and unitary symplectic case recently the supersymmetry method was extended from gaussian ensembles to arbitrary unitarily invariant matrix ensembles by generalizing the hubbard stratonovich transformation here we complete this extension by including arbitrary orthogonally and unitary symplectically invariant matrix ensembles the results are equivalent to but the approach is different from the superbosonization formula we express our results in a unifying way we also give explicit expressions for all one point functions and discuss features of the higher order correlations

k intolerant capacities and choquet integrals we define an aggregation function to be at most k intolerant if it is bounded from above by its kth lowest input value applying this definition to the discrete choquet integral and its underlying capacity we introduce the concept of k intolerant capacities which when varying k from 1 to n cover all the possible capacities on n objects just as the concepts of k additive capacities and p symmetric capacities have been previously introduced essentially to overcome the problem of computational complexity of capacities k intolerant capacities are proposed here for the same purpose but also for dealing with intolerant or tolerant behaviors of aggregation we also introduce axiomatically indices to appraise the extent to which a given capacity is k intolerant and we apply them on a particular recruiting problem

new correlation functions for random matrices and integrals over supergroups the averages of ratios of characteristic polynomials det x of n n random matrices x are investigated in the large n limit for the gue goe and gse ensembles the density of states and the two point correlation function are derived from these ratios the method relies on an extension of the harish chandra itzykson zuber integrals to the goe ensemble and to supergroups which are explicitly computed through heat kernel differential equations an external matrix source linearly coupled to the random matrices may also be added to the gaussian distribution and allows for a discussion of the universality of the goe results in the large n limit

fourier bessel analysis for ordinary and graded 2 2 hermitian matrices chainlike integrals in matrix spaces play an important part in high energy and solid state physics and in general random matrix theory in the special case of ordinary and graded 2 2 hermitian matrices a method is proposed to integrate out all angular variables the essence of this method is a fourier bessel analysis in these matrix spaces which is formulated in this paper close formal similarities are found between the ordinary and the graded case the main differences arise from the fact that the ordinary case can be reduced to the study of a vector space whereas no analogous feature is present in the graded case

existence of weak solutions of doubly nonlinear parabolic equations abstract we deal with a cauchy dirichlet problem with homogeneous boundary conditions on the parabolic boundary of a space time cylinder for doubly nonlinear parabolic equations whose prototype is t u div u m 1 d u p 2 d u f with a non negative lebesgue function f on the right hand side where p 2 n n 2 and m 0 the central objective is to establish the existence of weak solutions under the optimal integrability assumption on the inhomogeneity f the constructed solution is obtained by a limit of approximations i e we use solutions of regularized cauchy dirichlet problems and pass to the limit to receive a solution for the original cauchy dirichlet problem

entropy of bi capacities in the context of multicriteria decision making whose aggregation process is based on the choquet integral bi capacities can be regarded as a natural extension of capacities when the underlying evaluation scale is bipolar the notion of entropy recently generalized to capacities to measure their uniformity is now extended to bi capacities we show that the resulting entropy measure has a very natural interpretation in terms of the choquet integral and satisfies many natural properties that one would expect from an entropy measure

surprising pfaffian factorizations in random matrix theory with dyson index β 2 in recent decades determinants and pfaffians were found for eigenvalue correlations of various random matrix ensembles these structures simplify the average over a large number of ratios of characteristic polynomials to integrations over one and two characteristic polynomials only up to now it was thought that determinants occur for ensembles with dyson index 2 whereas pfaffians only for ensembles with 1 4 we derive a non trivial pfaffian determinant for 2 random matrix ensembles which is similar to the one for 1 4 thus it unveils a hidden universality of this structure we also give a general relation between the orthogonal polynomials related to the determinantal structure and the skew orthogonal polynomials corresponding to the pfaffian as a particular example we consider the chiral unitary ensembles in great detail

minimum variance capacity identification abstract in the framework of multi criteria decision making whose aggregation process is based on the choquet integral we present a maximum entropy like method enabling to determine if it exists the least specific capacity compatible with the initial preferences of the decision maker the proposed approach consists in solving a strictly convex quadratic program whose objective function is equivalently either the opposite of a generalized entropy measure or the variance of the capacity the application of the proposed approach is illustrated on two examples

integration of grassmann variables over invariant functions on flat superspaces we study integration over functions on superspaces these functions are invariant under a transformation which maps the whole superspace onto the part of the superspace which only comprises purely commuting variables we get a compact expression for the differential operator with respect to the commuting variables which results from berezin integration over all grassmann variables also we derive cauchy like integral theorems for invariant functions on supervectors and symmetric supermatrices this extends theorems partly derived by other authors as a physical application we calculate the generating function of the one point correlation function in random matrix theory furthermore we give another derivation of supermatrix bessel functions for u k1 k2

local behaviour of solutions to doubly nonlinear parabolic equations we give a relatively simple and transparent proof for harnack s inequality for certain degenerate doubly nonlinear parabolic equations we consider the case where the lebesgue measure is replaced with a doubling borel measure which supports a poincare inequality

estimates of optimal storage conditions in neural network memories based on random matrix theory the authors formulate a method for estimating the critical conditions for storage of sets of data in neural network memory this variational method is based on random matrix theory and calculating the average spectrum of a matrix whose elements are given by overlaps of the stored patterns several generic cases of random overlap matrices are considered they investigate the cases of simply uncorrelated random patterns and spatially and semantically correlated ones they obtain bounds of the critical curve in the control parameters space which determine the stability of the stored data sets

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

tolerant or intolerant character of interacting criteria in aggregation by the choquet integral abstract in many multi criteria decision making problems the decision criteria present some interaction whose nature may vary from one situation to another for example some criteria may be statistically correlated thus making them somewhat redundant or opposed some others may be somewhat substitutive or complementary depending on the behavior of the decision maker some others may be decisive in the sense that the global score of any alternative obtained by aggregation is bounded by the partial score along one of them in this paper we analyze this latter form of interaction when a criterion bounds the global score from above it is called a blocker or a veto due to its rather intolerant character when it bounds the global score from below it is then called a pusher or a favor we thus investigate the tolerance of criteria or equivalently the tolerance of the weighted aggregation operator here the choquet integral that is used to aggregate criteria more specifically we propose axiomatically indices to appraise the extent to which each criterion behaves like a veto or a favor in the aggregation by the choquet integral previous to this we also propose global tolerance degrees measuring the extent to which the choquet integral is conjunctive or disjunctive

general random matrix approach to account for the effect of static disorder on the spectral properties of light harvesting systems we develop a random matrix model approach to study static disorder in pigment protein complexes in photosynthetic organisms as a case study we examine the ring of b850 bacteriochlorophylls in the peripheral light harvesting complex of rhodospirillum molischianum formulated in terms of an effective hamiltonian describing the collective electronic excitations of the system we numerically examine and compare various models of disorder and observe that both the density of states and the absorption spectrum of the model show remarkable spectral universality for the case of unitary disorder we develop a method to analytically evaluate the density of states of the ensemble using the supersymmetric formulation of random matrix theory succinct formulas that can be readily applied in future studies are provided in an appendix

superbosonization of invariant random matrix ensembles superbosonization is a new variant of the method of commuting and anti commuting variables as used in studying random matrix models of disordered and chaotic quantum systems we here give a concise mathematical exposition of the key formulas of superbosonization conceived by analogy with the bosonization technique for dirac fermions the new method differs from the traditional one in that the superbosonization field is dual to the usual hubbard stratonovich field the present paper addresses invariant random matrix ensembles with symmetry group un on or uspn giving precise definitions and conditions of validity in each case the method is illustrated at the example of wegner s n orbital model superbosonization promises to become a powerful tool for investigating the universality of spectral correlation functions for a broad class of random matrix ensembles of non gaussian and or non invariant type

determining the fuzzy measures in multiple criteria decision aiding from the tolerance perspective abstract we consider multiple criteria decision aiding mcda in the case of interactions between criteria in dealing with interactions between criteria fuzzy measures and integrals have demonstrated great advantages nevertheless the determination of fuzzy measures has proven difficult because the capacities of not only single criterion but also all subsets of criteria need to be identified due to the value judgment essence of mcda the attitudes of the decision maker dm are typically modeled to identify fuzzy measures in this paper the tolerance attitudes of the dm which implies a direct requirement instead of partial preference are modeled with regard to the determination of fuzzy measures for the first time with two scales developed in this paper the dm can directly express the tolerance attitudes to certain criteria other than providing partial preference through pairwise comparison as a result it requires less prior knowledge and is more efficient to some extent further the inherent interacting mechanism of criteria under different tolerance attitudes is explored at last the tolerance attitudes are applied to the process of multiple criteria analysis using a choquet integral a classic student evaluation problem is given as an example the evaluation results are compared with additive models this paper not only provides a new inspiration to the determination of fuzzy measures but also improves the descriptive capacity of fuzzy measures to the real world

asymptotic coincidence of the statistics for degenerate and non degenerate correlated real wishart ensembles the correlated wishart model provides the standard benchmark when analyzing time series of any kind unfortunately the real case which is the most relevant one in applications poses serious challenges for analytical calculations often these challenges are due to square root singularities which cannot be handled using common random matrix techniques we present a new way to tackle this issue using supersymmetry we carry out an anlaytical study which we support by numerical simulations for large but finite matrix dimensions we show that statistical properties of the fully correlated real wishart model generically approach those of a correlated real wishart model with doubled matrix dimensions and doubly degenerate empirical eigenvalues this holds for the local and global spectral statistics with monte carlo simulations we show that this is even approximately true for small matrix dimensions we explicitly investigate the k point correlation function as well as the distribution of the largest eigenvalue for which we find a surprisingly compact formula in the doubly degenerate case moreover we show that on the local scale the k point correlation function exhibits the sine and the airy kernel in the bulk and at the soft edges respectively we also address the positions and the fluctuations of the possible outliers in the data

entropy of discrete choquet capacities we introduce a measure of entropy for any discrete choquet capacity and we interpret it in the setting of aggregation by the choquet integral

a holder estimate for nonlinear parabolic systems of p laplacian type abstract we extend the holder regularity results for weak solutions of the p laplacian systems originally obtained by dibenedetto to a larger class of right hand side terms by appropriately arranging two scale parameters on the sizes of a local parabolic cylinder and of the gradient of the solutions we get the same holder exponent as in the scalar case our method can also recover the classical parabolic case p 2

the integral theorem for supersymmetric invariants a supersymmetric integral theorem that extends results of parisi sourlas efetov wegner and others is rigorously proved in particular arbitrary generators are allowed in the integrand instead of canonical ones and the invariance condition is very much relaxed the connection with cauchy s integral formula is made transparent in passing the unitary lie supergroup is studied by using elementary methods applications in the theory of disordered systems are discussed

character expansions for the orthogonal and symplectic groups formulas for the expansion of arbitrary invariant group functions in terms of the characters for the sp 2n so 2n 1 and so 2n groups are derived using a combinatorial method the method is similar to one used by balantekin to expand group functions over the characters of the u n group all three expansions have been checked for all n by using them to calculate the known expansions of the generating function of the homogeneous symmetric functions an expansion of the exponential of the traces of group elements appearing in the finite volume gauge field partition functions is worked out for the orthogonal and symplectic groups

2 additive capacity identification methods from multicriteria correlation preference information the essential role of the particular families of capacities and the capacity identification methods is to help the decision maker to deal with the exponential complexity inherent in the construction process of the capacity the 2 additive capacities appear to be the most popular among the particular families of capacities since they permit to model interactions between criteria while preserving simplicity besides the preference with respect to the decision criteria most of the capacity identification methods also need to provide the desired overall evaluations of the decision alternatives in the learning set which is a time consuming task for the decision maker in this paper we propose some models to identify 2 additive capacities only from a kind of refined preference information with respect to the decision criteria called the multicriteria correlation preference information mccpi the mccpi is a group of 2 d preference information which can be described and obtained by the refined diamond diagram the common principle of the proposed models is to minimize the different kinds of deviations between the mccpi and the most desired 2 additive capacity ies a multicriteria decision making example is presented to show the feasibility of the proposed methods and a 2 d scale of the mccpi is also introduced in the further discussion of the illustrative example

distribution of the smallest eigenvalue in the correlated wishart model wishart random matrix theory is of major importance for the analysis of correlated time series the distribution of the smallest eigenvalue for wishart correlation matrices is particularly interesting in many applications in the complex and in the real case we calculate it exactly for arbitrary empirical eigenvalues i e for fully correlated gaussian wishart ensembles to this end we derive certain dualities of matrix models in ordinary space we thereby completely avoid the otherwise unsurmountable problem of computing a highly nontrivial group integral our results are compact and much easier to handle than previous ones furthermore we obtain a new universality for the distribution of the smallest eigenvalue on the proper local scale

arbitrary unitarily invariant random matrix ensembles and supersymmetry we generalize the supersymmetry method in random matrix theory to ensembles which are unitarily invariant but otherwise arbitrary our exact approach extends a previous contribution in which we constructed a supersymmetric representation for the class of norm dependent random matrix ensembles here we derive a supersymmetric formulation under very general circumstances a reduced probability density and a projector are identified that map the probability density from ordinary to superspace furthermore it is demonstrated that setting up the theory in fourier superspace has considerable advantages general and exact expressions for the correlation functions are given we also show how the use of hyperbolic symmetry can be circumvented in the present context in which the nonlinear model is not used we construct exact supersymmetric integral representations of the correlation functions for arbitrary positions of the imaginary increments in the green s functions

replica method for wide correlators in gaussian orthogonal unitary and symplectic random matrix ensembles we calculate connected correlators in gaussian orthogonal unitary and symplectic random matrix ensembles by the replica method in the 1 n expansion we obtain averaged one point green s functions up to the next to leading order wide two level correlators up to the first non trivial order and wide three level correlators up to the first non trivial order by carefully treating fluctuations in saddle point evaluation

a numerically stable dual method for solving strictly convex quadratic programs an efficient and numerically stable dual algorithm for positive definite quadratic programming is described which takes advantage of the fact that the unconstrained minimum of the objective function can be used as a starting point its implementation utilizes the cholesky and qr factorizations and procedures for updating them the performance of the dual algorithm is compared against that of primal algorithms when used to solve randomly generated test problems and quadratic programs generated in the course of solving nonlinear programming problems by a successive quadratic programming code the principal motivation for the development of the algorithm these computational results indicate that the dual algorithm is superior to primal algorithms when a primal feasible point is not readily available the algorithm is also compared theoretically to the modified simplex type dual methods of lemke and van de panne and whinston and it is illustrated by a numerical example

holder estimates for local solutions of some doubly nonlinear degenerate parabolic equations abstract we prove interior and boundary holder continuity for bounded weak soluttions of a class of quasilinear parabolic equations whose prototype is u t div u m 1 du p 2 du

harnack type inequalities for solutions of certain doubly nonlinear parabolic equations abstract here we prove an intrinsic version of the harnack inequality for locally bounded nonnegative weak solutions of nonlinear parabolic equations of the type u t div u m 1 du p 2 du in d t where p 1 m p 2 m p p n 3

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

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

an axiomatic approach of the discrete choquet integral as a tool to aggregate interacting criteria the most often used operator to aggregate criteria in decision making problems is the classical weighted arithmetic mean however in many problems the criteria considered interact and a substitute to the weighted arithmetic mean has to be adopted we show that under rather natural conditions the discrete choquet integral is an adequate aggregation operator that extends the weighted arithmetic mean by taking into consideration of the interaction among criteria the axiomatic that supports the choquet integral is presented and an intuitive approach is proposed as well

a supersymmetry approach to billiards with randomly distributed scatterers ii correlations in a previous contribution stockmann h j 2002 j phys a math gen 35 5165 the density of states was calculated for a billiard with randomly distributed delta like scatterers doubly averaged over the positions of the impurities and the billiard shape this result is now extended to the k point correlation function using supersymmetric methods we show that the correlations in the bulk are always identical to those of the gaussian unitary ensemble gue of random matrices in passing from the band centre to the tail states the density of states is depleted considerably and the two point correlation function shows a gradual change from the gue behaviour to that found for completely uncorrelated eigenvalues this can be viewed as similar to a mobility edge

the choquet integral for the aggregation of interval scales in multicriteria decision making this paper addresses the question of which models fit with information concerning the preferences of the decision maker over each attribute and his preferences about aggregation of criteria interacting criteria we show that the conditions induced by these information plus some intuitive conditions lead to a unique possible aggregation operator the choquet integral

the supersymmetry method for chiral random matrix theory with arbitrary rotation invariant weights in the past few years the supersymmetry method has been generalized to real symmetric hermitian and hermitian self dual random matrices drawn from ensembles invariant under the orthogonal unitary and unitary symplectic groups respectively we extend this supersymmetry approach to chiral random matrix theory invariant under the three chiral unitary groups in a unifying way thereby we generalize a projection formula providing a direct link and hence a short cut between the probability density in ordinary space and that in superspace we emphasize that this point was one of the main problems and shortcomings of the supersymmetry method since only implicit dualities between ordinary space and superspace were known before to provide examples we apply this approach to the calculation of the supersymmetric analogue of a lorentzian cauchy ensemble and an ensemble with a quartic potential moreover we consider the partially quenched partition function of the three chiral gaussian ensembles corresponding to four dimensional continuum quantum chromodynamics we identify a natural splitting of the chiral lagrangian in its lowest order into a part for the physical mesons and a part associated with source terms generating the observables e g the level density of the dirac operator

robust optimization of the choquet integral we study the problem of the choquet integral maximization for the case when preferences of the decision maker do not define a unique capacity but rather some convex set we introduce a robust version of the problem based on the minimax regret criterion and construct a global optimization algorithm it is shown that the decision rule based on regret minimization over a set of capacities is equivalent to maximization of the choquet integral with respect to a certain capacity belonging to this set we compare our method to various capacity identification approaches developed in the literature and provide a semantic interpretation in terms of information value

a method of integration over matrix variables the integral over twon n hermitan matricesz g c dadbexp tr a 2 b 2 2cab g n a 4 b 4 is evaluated in the limit of largen for this purpose use is made of the theory of diffusion equation and that of orthogonal polynomials with a non local weight the above integral arises in the study of the planar approximation to quantum field theory

on the graded group u 1 1 a noncanonical parametrization for the graded group u 1 1 is introduced similar to the euler angles for the ordinary group su 2 two differential representations for the underlying algebra of u 1 1 are constructed on the full and the restricted i e coset parameter space respectively a space of functions living on the latter is found exhibiting close formal similarities to a hilbert space remarkably the indices of those functions and thus the orthogonality and completeness relations involve anticommuting variables using this hilbert space a representation of u 1 1 is evaluated which shows analogies to the wigner functions for su 2

dyson s correlation functions and graded symmetry a new derivation of dyson s k level correlation functions of the gaussian unitary ensemble gue is given the method uses matrices with graded symmetry the number of integrations needed for the ensemble average becomes independent of the level number n for arbitrary level number n the k level correlation function is expressed as an integral involving the eigenvalues of a 2k 2k graded matrix the limit of infinitely many levels n is calculated by a simple saddle point approximation of this integral avoiding the introduction of hermite polynomials and oscillator wave functions

the smallest eigenvalue distribution in the real wishart laguerre ensemble with even topology we consider rectangular random matrices of size p times n belonging to thereal wishart laguerre ensemble also known as the chiral gaussian orthogonalensemble this ensemble appears in many applications like qcd mesoscopicphysics and time series analysis we are particularly interested in thedistribution of the smallest non zero eigenvalue and the gap probability tofind no eigenvalue in an interval 0 t while for odd topology nu n p explicit closed results are known for finite and infinite matrix size for even nu 2 only recursive expressions in p are available the smallest eigenvaluedistribution as well as the gap probability for general even nu isequivalent to expectation values of characteristic polynomials raised to ahalf integer the computation of such averages is done via a combination ofskew orthogonal polynomials and bosonisation methods the results are given interms of pfaffian determinants both at finite p and in the hard edge scalinglimit p to infty and nu fixed for an arbitrary even topology nu numerical simulations for the correlated wishart ensemble illustrate theuniversality of our results in this particular limit these simulations pointto a validity of the hard edge scaling limit beyond the invariant case

norm dependent random matrix ensembles in external field and supersymmetry the class of norm dependent random matrix ensembles is studied in the presence of an external field the probability density of the ensemble depends on the trace of the squared random matrices but is otherwise arbitrary an exact mapping to superspace is performed a transformation formula is derived which gives the probability density in superspace as a single integral over the probability density in ordinary space this is done for orthogonal unitary and symplectic symmetries in the case of unitary symmetry some explicit results for the correlation functions are derived

wigner dyson statistics from the replica method we compute the correlation functions of the eigenvalues in the gaussian unitary ensemble using the fermionic replica method we show that non trivial saddle points which break replica symmetry must be included in the calculation in order to correctly reproduce the exact asymptotic behaviour of the correlation functions at a large distance

compromise principle based methods of identifying capacities in the framework of multicriteria decision analysis abstract the basic aim of the compromise principle employed in this paper is to seek the capacity by which each alternative has a relatively equal chance to reach as close as possible to its highest reachable overall evaluation according to the compromise principle three types of capacity identification methods the simple arithmetic average based compromise method the least squares based compromise method and the linear programming based compromise method are proposed the input information required for the compromise principle based identification methods consists of the preference information with respect to the decision criteria and the partial evaluations of the alternatives provided by the decision maker an illustrative example is given to show the processes of the proposed methods and a comparison analysis with the maximum entropy principle based identification method is also presented

supersymmetry approach to wishart correlation matrices exact results we calculate the one point function meaning the marginal probability density function for any single eigenvalue of real and complex wishart correlation matrices no ex plicit expression had been obtained for the real case so far we succeed in doing so by using supersymmetry techniques to express the one point function of real wishart correlation ma trices as a twofold integral the result can be viewed as a resummation of a series of jack polynomials in a non trivial case we illustrate our formula by numerical simulations we also rederive a known expression for the one point function of complex wishart correlation matrices