extending yager s orness concept for the owa aggregators to other mean operators abstract in this paper we address the problem of defining the orness closeness to the maximum and andness closeness to the minimum of fuzzy aggregation operators in particular we center our study in fuzzy mean aggregators as defined by dubois prade and yager for this purpose we propose the introduction of the orness distribution function orness average value orness extension measure and orness sequence which we believe are valid concepts to characterize this type of aggregation operators we study their application to several well known mean operators and prove as well that in the case of yager s owa operators the orness average value that we propose coincides with yager s original orness definition we also introduce a method for the construction of mean operators from a predefined orness distribution function and make some considerations about the extension of these concepts to the cases of weighted aggregations or aggregations based on fuzzy measures

texture synthesis and nonparametric resampling of random fields this paper introduces a nonparametric algorithm for bootstrapping a stationary random field and proves certain consistency properties of the algorithm for the case of mixing random fields the motivation for this paper comes from relating a heuristic texture synthesis algorithm popular in computer vision to general nonparametric bootstrapping of stationary random fields we give a formal resampling scheme for the heuristic texture algorithm and prove that it produces a consistent estimate of the joint distribution of pixels in a window of certain size under mixing and regularity conditions on the random field the joint distribution of pixels is the quantity of interest here because theories of human perception of texture suggest that two textures with the same joint distribution of pixel values in a suitably chosen window will appear similar to a human thus we provide theoretical justification for an algorithm that has already been very successful in practice and suggest an explanation for its perceptually good results

nonlinear maps preserving the reduced minimum modulus of operators abstract let x and y be infinite dimensional complex banach spaces and let b x resp b y denote the algebra of all bounded linear operators on x resp on y we describe bijective bicontinuous maps from b x to b y satisfying s t s t for all s t b x where t is the reduced minimum modulus of an operator t an analogue result for the finite dimensional case is obtained

mappings that preserve pairs of operators with zero triple jordan product abstract let f be a field and n 3 suppose s 1 s 2 m n f contain all rank one idempotents the structure of surjections s 1 s 2 satisfying aba 0 a b a 0 is determined similar results are also obtained for a subsets of bounded operators acting on a complex or real banach space x b the space of hermitian matrices acting on n dimensional vectors over a skew field d c subsets of self adjoint bounded linear operators acting on an infinite dimensional complex hilbert space it is then illustrated that the results can be applied to characterize mappings on matrices or operators such that f aba f a b a for all a b for functions f such as the spectral norm schatten p norm numerical radius and numerical range etc

maps preserving the local spectrum of jordan product of matrices abstract let m n c be the algebra of all n n complex matrices and fix a nonzero vector x 0 c n we show that a map from m n c into itself satisfies t s s t x 0 t s s t x 0 t s m n c if and only if there exists an invertible matrix a m n c such that a x 0 x 0 and t a t a 1 for all t m n c

spectrum nonincreasing maps on matrices abstract maps which do not increase the spectrum on complex matrices in a sense that sp a b sp a b are classified

multivariate integration of functions depending explicitly on the minimum and the maximum of the variables abstract by using some basic calculus of multiple integration we provide an alternative expression of the integral a b n f x min x i max x i d x in which the minimum and the maximum are replaced with two single variables we demonstrate the usefulness of that expression in the computation of orness and andness average values of certain aggregation functions by generalizing our result to riemann stieltjes integrals we also provide a method for the calculation of certain expected values and distribution functions

equivalence of julesz ensembles and frame models in the past thirty years research on textures has been pursued along two different lines the first line of research pioneered by julesz 1962 ire transactions of information theory it 8 84 92 seeks essential ingredients in terms of features and statistics in human texture perception this leads us to a mathematical definition of textures in terms of julesz ensembles zhu et al ieee trans on pami vol 22 no 6 2000 a julesz ensemble is a set of images that share the same value of some basic feature statistics images in the julesz ensemble are defined on a large image lattice a mathematical idealization being z2 so that exact constraint on feature statistics makes sense the second line of research studies markov random field mrf models that characterize texture patterns on finite or small image lattice in a statistical way this leads us to a general class of mrf models called frame filter random field and maximum entropy zhu et al neural computation 9 1627 1660 in this article we bridge the two lines of research by the fundamental principle of equivalence of ensembles in statistical mechanics gibbs 1902 elementary principles of statistical mechanics yale university press we show that 1 as the size of the image lattice goes to infinity a frame model concentrates its probability mass uniformly on a corresponding julesz ensemble therefore the julesz ensemble characterizes the global statistical property of the frame models 2 for a large image randomly sampled from a julesz ensemble any local patch of the image given its environment follows the conditional distribution specified by a corresponding frame model therefore the frame model describes the local statistical property of the julesz ensemble and is an inevitable texture model on finite or small lattice if texture perception is decided by feature statistics the key to derive these results is the large deviation estimate of the volume of or the number of images in the julesz ensemble which we call the entropy function studying the equivalence of ensembles provides deep insights into questions such as the origin of mrf models typical images of statistical models and error rates in various texture related vision tasks yuille and coughlan ieee trans on pami vol 2 no 2 2000 the second thrust of this paper is to study texture distance based on the texture models of both small and large lattice systems we attempt to explain the asymmetry phenomenon observed in texture pop out experiments by the asymmetry of kullback leibler divergence our results generalize the traditional signal detection theory green and swets 1988 signal detection theory and psychophysics peninsula publishing for distance measures from iid cases to random fields our theories are verified by two groups of computer simulation experiments

the jackknife and the bootstrap for general stationary observations we extend the jackknife and the bootstrap method of estimating standard errors to the case where the observations form a general stationary sequence we do not attempt a reduction to i i d values the jackknife calculates the sample variance of replicates of the statistic obtained by omitting each block of l consecutive data once in the case of the arithmetic mean this is shown to be equivalent to a weighted covariance estimate of the spectral density of the observations at zero under appropriate conditions consistency is obtained if l l n rightarrow infty and l n n rightarrow 0 general statistics are approximated by an arithmetic mean in regular cases this approximation determines the asymptotic behavior bootstrap replicates are constructed by selecting blocks of length l randomly with replacement among the blocks of observations the procedures are illustrated by using the sunspot numbers and some simulated data

nonlinear maps preserving the minimum and surjectivity moduli abstract let x and y be infinite dimensional complex banach spaces and let b x resp b y denote the algebra of all bounded linear operators on x resp on y we describe maps from b x onto b y satisfying c s t c s t for all s t b x where c stands either for the minimum modulus or the surjectivity modulus or the maximum modulus we also obtain analog results for the finite dimensional case

construction of fuzzy σ algebras using triangular norms abstract generalizing the definitions given by the author fuzzy sets and systems4 1980 83 93 we introduce and study t fuzzy algebras t being any triangular norm the main result is that for a large class of triangular norms each t fuzzy algebra is generated i e consists of all functions x 0 1 being measurable with respect to some algebra on x

linear preserver problems a brief introduction and some special techniques abstract linear preserver problems concern the characterization of linear operators on matrix spaces that leave certain functions subsets relations etc invariant the earliest papers on linear preserver problems date back to 1897 and a great deal of effort has been devoted to the study of this type of question since then we present a brief picture of the subject aiming at giving a gentle introduction to the reader then we describe some techniques used in our recent papers on this type of problem

maps preserving peripheral spectrum of jordan semi triple products of operators abstract let a and b be not necessarily unital or closed standard operator algebras on complex banach spaces x and y respectively for a bounded linear operator a on x the peripheral spectrum a of a is the set a z a z max a where a denotes the spectrum of a assume that a b is a map the range of which contains all operators of rank at most two it is shown that the map satisfies the condition that bab b a b for all a b a if and only if there exists a scalar c with 3 1 and either there exists an invertible operator t b x y such that a tat 1 for every a a or there exists an invertible operator t b x y such that a ta t 1 for every a a if x h and y k are complex hilbert spaces the maps preserving the peripheral spectrum of the jordan skew semi triple product ba b are also characterized such maps are of the form a uau or a ua t u where u b h k is a unitary operator a t denotes the transpose of a in an arbitrary but fixed orthonormal basis of h

graded properties of unary and binary fuzzy connectives the paper studies basic graded properties of unary and binary fuzzy connectives i e unary and binary operations on the set of truth degrees of a background fuzzy logic extending the logic mtl of left continuous t norms the properties studied in this paper are graded generalizations of monotony lipschitz continuity null and unit elements idempotence commutativity and associativity the paper elaborates the initial study presented in previous papers and focuses mainly on parameterization of graded properties by conjunction multiplicities of subformulae in the defining formulae preservation of graded properties under compositions and slight variations of fuzzy connectives the values of graded properties for basic connectives of the ground logic and the dependence of the values on the ground logic the results are proved in the formal framework of higher order fuzzy logic mtl also known as fuzzy class theory fct general theorems provable in fct are illustrated on several semantic examples

generalized ordered modular averaging operator and its application to group decision making in this paper we propose a new class of operators called the ordered quasi modular averaging oqma operators based on the ordered modular averaging oma operators it is shown that the oqma operators are monotonic bounded idempotent commutative and quasi comonotone modular moreover we introduce the generalized ordered modular averaging goma operator which is a special case of the oqma operator some special cases of the goma operator are discussed an orness measure to reflect the or like degree of the goma operator is proposed we further extend the goma operator to the generalized ordered hybrid modular gohm operator which focuses not only on the degree of importance with respect to input arguments but also their serial positions finally a new method based on the gohm operator for multi attribute group decision making is presented and a numerical example shows that the developed approach is feasible

segmentation of natural images by texture and boundary compression we present a novel algorithm for segmentation of natural images that harnesses the principle of minimum description length mdl our method is based on observations that a homogeneously textured region of a natural image can be well modeled by a gaussian distribution and the region boundary can be effectively coded by an adaptive chain code the optimal segmentation of an image is the one that gives the shortest coding length for encoding all textures and boundaries in the image and is obtained via an agglomerative clustering process applied to a hierarchy of decreasing window sizes as multi scale texture features the optimal segmentation also provides an accurate estimate of the overall coding length and hence the true entropy of the image we test our algorithm on the publicly available berkeley segmentation dataset it achieves state of the art segmentation results compared to other existing methods

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

orthogonality preserving transformations on indefinite inner product spaces generalization of uhlhorn s version of wigner s theorem abstract we present an analogue of uhlhorn s version of wigner s theorem on symmetry transformations for the case of indefinite inner product spaces this significantly generalizes a result of van den broek the proof is based on our main theorem which describes the form of all bijective transformations on the set of all rank one idempotents of a banach space which preserve zero products in both directions

indicators for the characterization of discrete choquet integrals ordered weighted averaging owa operators and their extensions are powerful tools used in numerous decision making problems this class of operator belongs to a more general family of aggregation operators where each operator of this family is understood as a discrete choquet integral aggregation operators are usually characterized by indicators in this article four indicators usually associated with the owa operator are extended to the discrete choquet integral namely the degree of balance the divergence the variance indicator and renyi entropies all of these indicators are considered from a local and a global perspective linearity of indicators for linear combinations of capacities is investigated and to illustrate the usefulness of results indicators of the probabilistic ordered weighted averaging powa operator are derived finally a numerical example is provided to discuss the results in a specific context

condition spectra of special operators and condition spectra preservers abstract let h be a complex hilbert space and let l h be the algebra of all bounded linear operators on h descriptions of the condition spectra of various special classes of operators are established as application characterization is obtained for maps on l h leaving invariant the condition spectrum or the condition spectral radius of the product of operators analogous results are obtained for jordan triple product of operators

preservers of unitary similarity functions on lie products of matrices abstract denote by m n the set of n n complex matrices let f m n 0 be a continuous map such that f u a u f a for any complex unit a m n and unitary u m n f x 0 if and only if x 0 and the induced map t f t x is monotonically increasing on 0 for any rank one nilpotent x m n characterization is given for surjective maps on m n satisfying f a b b a f a b b a the general theorem is then used to deduce results on special cases when the function is the pseudo spectrum and the pseudo spectral radius

additive maps on standard operator algebras preserving parts of the spectrum let a and b be standard operator algebras on infinite dimensional complex banach spaces x and y respectively and let be a unital additive surjection from a onto b we introduce thirteen parts of the spectrum for elements in a and b and prove that if preserves any one of these parts of the spectrum then it is either an isomorphism or an anti isomorphism

properties and preservers of the pseudospectrum abstract the interplay between the algebraic and analytic properties of a matrix and the geometric properties of its pseudospectrum is investigated it is shown that one can characterize hermitian matrices positive semi definite matrices orthogonal projections unitary matrices etc in terms of the pseudospectrum also characterizations are given to maps on matrices leaving invariant the pseudospectrum of the sum difference or product of matrix pairs it is shown that such a map is always a unitary similarity transform followed by some simple operations such as adding a constant matrix taking the matrix transpose or multiplying by a scalar in 1 1

generalized medians distance aggregation operators are introduced in the case of singleton based distance a well known class of k medians is recovered for interval based distance characterization of p r distance aggregation operators is given in general as well as for idempotent operators based on the triangle of median factors medians are introduced owa operators are shown to be a linear convex combination of special j medians

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

pseudospectra of special operators and pseudospectrum preservers abstract denote by b h the banach algebra of all bounded linear operators on a complex hilbert space h let a b h and denote by a the spectrum of a for e 0 define the e pseudospectrum e a of a as e a z a e e b h e e in this paper the pseudospectra of several special classes of operators are characterized as an application complete descriptions are given of the maps of b h leaving invariant the pseudospectra of a b for different kinds of binary operations on operators such as the difference a b the operator product ab and the jordan product a b b a

preservers of local spectrum of matrix jordan triple products abstract let m n be the space of n n complex matrices and for a nonzero vector e c n and t m n let t e denote the local spectrum of t at e maps on m n which preserve the local spectrum of jordan triple product of matrices at e in a sense that t s t e t s t e t s m n are characterized with no surjectivity assumption on them

preservers of radial unitary similarity functions on products of operators abstract let s be a subset of the algebra l h of all bounded linear operators on an infinite dimensional complex hilbert space h and let f s 0 be a radial unitary similarity invariant function under some assumption on s and f characterizations are obtained for surjective maps on s satisfying f t s f t s t s s where the binary operation stands for the product or the jordan semi triple product on operators analogous descriptions are obtained for the finite dimensional case without the surjectivity assumption on

maps on matrix spaces it is well known that every automorphism of the full matrix algebra is inner we give a short proof of this statement and discuss several extensions of this theorem including structural results for multiplicative maps on matrix algebras characterizations of monotone and orthogonality preserving maps on idempotent matrices some nonlinear preserver results and some recent theorems concerning geometry of matrices we show that all these topics are closely related and point out the connections with physics and geometry several open problems are posed

markov random field texture models we consider a texture to be a stochastic possibly periodic two dimensional image field a texture model is a mathematical procedure capable of producing and describing a textured image we explore the use of markov random fields as texture models the binomial model where each point in the texture has a binomial distribution with parameter controlled by its neighbors and number of tries equal to the number of gray levels was taken to be the basic model for the analysis a method of generating samples from the binomial model is given followed by a theoretical and practical analysis of the method s convergence examples show how the parameters of the markov random field control the strength and direction of the clustering in the image the power of the binomial model to produce blurry sharp line like and blob like textures is demonstrated natural texture samples were digitized and their parameters were estimated under the markov random field model a hypothesis test was used for an objective assessment of goodness of fit under the markov random field model overall microtextures fit the model well the estimated parameters of the natural textures were used as input to the generation procedure the synthetic microtextures closely resembled their real counterparts while the regular and inhomogeneous textures did not

a parametric texture model based on joint statistics of complex wavelet coefficients we present a universal statistical model for texture images in the context of an overcomplete complex wavelet transform the model is parameterized by a set of statistics computed on pairs of coefficients corresponding to basis functions at adjacent spatial locations orientations and scales we develop an efficient algorithm for synthesizing random images subject to these constraints by iteratively projecting onto the set of images satisfying each constraint and we use this to test the perceptual validity of the model in particular we demonstrate the necessity of subgroups of the parameter set by showing examples of texture synthesis that fail when those parameters are removed from the set we also demonstrate the power of our model by successfully synthesizing examples drawn from a diverse collection of artificial and natural textures

graded dominance and related graded properties of fuzzy connectives graded properties of binary and unary fuzzy connectives valued in mtl algebras are studied including graded monotony a generalized lipschitz property commutativity associativity unit and null elements and the dominance relation between fuzzy connectives the apparatus of fuzzy class theory or higher order fuzzy logic is employed as a tool for easy derivation of graded theorems on the connectives

spectrum preserving linear maps abstract let x and y be banach spaces we show that a spectrum preserving surjective linear map from b x to b y is either of the form t ata 1 for an isomorphism a of x onto y or the form t bt b 1 for an isomorphism b of x onto y

maps leaving functional values of operator products invariant abstract let a be a standard operator algebra on a complex hilbert space h of dimension greater than 2 by invariants of certain functional values of operator products we characterize some surjective maps on a furthermore several kinds of general preserver problems on standard operator algebras are solved when we take respectively the functional as for example k numerical radius k 1 operator norm ky fan k norm schatten p norm 1 p and so on

parametric characterization of aggregation functions the aim of this contribution is to find a common framework for parametric characterization of aggregation functions exploiting the notions of unipolar and bipolar parametric characterization and also unify the ideas of global and local parametric characterization we revise the known approaches to classification of aggregation functions in special classes in this framework and also propose some new parameters in classes of averaging conjunctive and disjunctive aggregation functions

preservers of pseudo spectral radius of operator products abstract let h be an infinite dimensional complex hilbert space and let l h be the algebra of all bounded linear operators on h for e 0 and t l h let r e t denote the e pseudo spectral radius of t we characterize surjective maps on l h which satisfy r e t s r e t s for all t s l h we also obtain analogous result for the finite dimensional case without the surjectivity assumption on

jordan triple multiplicative surjective maps on b h abstract let h be a hilbert space and b h be the algebra of all bounded linear operators on h in this paper we obtain a structure theorem of maps preserving the jordan triple zero product on b h then this is applied to give a full characterization of a surjective map b h b h satisfying a b a a b a

preservers of local spectra of matrix sums abstract let m n c be the set of n n complex matrices and for a nonzero vector e c n and t m n c let t e denote the local spectrum of t at e we characterize surjective maps on m n c which satisfy t s e t s e for all matrices t and s we arrive at the same conclusion by supposing that t s e t s e for all matrices t and s without the surjectivity assumption on continuous maps from m n c onto itself that preserve the local spectral radius of the sum of matrices at a nonzero fixed vector are also characterized

importance weighting and andness control in de morgan dual power means and owa operators abstract importance weighted aggregation plays a central role in utilization of information resources for information retrieval and fusion pattern and object recognition decision making etc a class of aggregation operators of particular interest is formed by the aggregation operators between the min minimum and the max maximum the so called averaging operators two key issues in the choice of such an operator for a given application are the kind of importance weighting and the andness minness of the operator two main kinds of importance weighting for such operators namely multiplicative and implicative are proposed and discussed the purpose of this paper is to facilitate the choice and application of such operators through providing a systematization of their classes according to their behavior and equipping some classical averaging operators namely the power means and the owa operators with importance weighting schemes and direct parametric andness control for both kinds of importance weighting for increased efficacy and for symmetric behavior by andness and orness 1 andness at the same degree of both measures the two classes of averaging operators are applied in a de morgan dual form the main issue in the choice of underlying the classical averaging operator appears to be the computational cost of its application

maps preserving the spectrum of generalized jordan product of operators abstract let a 1 a 2 be standard operator algebras on complex banach spaces x 1 x 2 respectively for k 2 let i 1 i m be a sequence with terms chosen from 1 k and define the generalized jordan product t 1 t k t i 1 t i m t i m t i 1 on elements in a i this includes the usual jordan product a 1 a 2 a 1 a 2 a 2 a 1 and the triple a 1 a 2 a 3 a 1 a 2 a 3 a 3 a 2 a 1 assume that at least one of the terms in i 1 i m appears exactly once let a map a 1 a 2 satisfy that a 1 a k a 1 a k whenever any one of a 1 a k has rank at most one it is shown in this paper that if the range of contains all operators of rank at most three then must be a jordan isomorphism multiplied by an m th root of unity similar results for maps between self adjoint operators acting on hilbert spaces are also obtained

filters random fields and maximum entropy frame towards a unified theory for texture modeling this article presents a statistical theory for texture modeling this theory combines filtering theory and markov random field modeling through the maximum entropy principle and interprets and clarifies many previous concepts and methods for texture analysis and synthesis from a unified point of view our theory characterizes the ensemble of images i with the same texture appearance by a probability distribution f i on a random field and the objective of texture modeling is to make inference about f i given a set of observed texture examples in our theory texture modeling consists of two steps 1 a set of filters is selected from a general filter bank to capture features of the texture these filters are applied to observed texture images and the histograms of the filtered images are extracted these histograms are estimates of the marginal distributions of f i this step is called feature extraction 2 the maximum entropy principle is employed to derive a distribution p i which is restricted to have the same marginal distributions as those in 1 this p i is considered as an estimate of f i this step is called feature fusion a stepwise algorithm is proposed to choose filters from a general filter bank the resulting model called frame filters random fields and maximum entropy is a markov random field mrf model but with a much enriched vocabulary and hence much stronger descriptive ability than the previous mrf models used for texture modeling gibbs sampler is adopted to synthesize texture images by drawing typical samples from p i thus the model is verified by seeing whether the synthesized texture images have similar visual appearances to the texture images being modeled experiments on a variety of 1d and 2d textures are described to illustrate our theory and to show the performance of our algorithms these experiments demonstrate that many textures which are previously considered as from different categories can be modeled and synthesized in a common framework

on bootstrapping panel factor series this paper studies the asymptotic validity of sieve bootstrap for nonstationary panel factor series two main results are shown firstly a bootstrap invariance principle is derived pointwise in i obtaining an upper bound for the order of truncation of the ar polynomial that depends on n and t consistent estimation of the long run variances is also studied for n t secondly joint bootstrap asymptotics is also studied investigating the conditions under which the bootstrap is valid in particular the extent of cross sectional dependence which can be allowed for is investigated whilst we show that for general forms of cross dependence consistent estimation of the long run variance and therefore validity of the bootstrap is fraught with difficulties however we show that one cross sectional unit at a time resampling schemes yield valid bootstrap based inference under weak forms of cross sectional dependence