bootstrapping nonparametric estimators of the volatility function we prove that the bootstrap works in a quite general sense for nonparametric estimators of the trend and volatility functions in nonlinear ar arch models we illustrate the implications of this result by constructing uniform confidence bands for those functions based on localized nonparametric function estimates as an application we study the trend and volatility of a time series of high frequency foreign exchange rate returns

fuzzy geometry perpendicular to fuzzy line segment abstract in this study we define the perpendicular to fuzzy line segment pfls which intersects a given fuzzy line segment fls normally at a specified fuzzy point in order to construct pfls some spatial transformations of fuzzy points such as translation rotation expansion contraction and reflection trecore are needed and have also been defined here the concept of pfls has been justified and formulated in three different ways with the help of same and inverse point theory of fuzzy points their properties and interrelations are also investigated the area of a fuzzy triangle has been calculated with the proposed methodology

comparing images using the hausdorff distance the hausdorff distance measures the extent to which each point of a model set lies near some point of an image set and vice versa thus this distance can be used to determine the degree of resemblance between two objects that are superimposed on one another efficient algorithms for computing the hausdorff distance between all possible relative positions of a binary image and a model are presented the focus is primarily on the case in which the model is only allowed to translate with respect to the image the techniques are extended to rigid motion the hausdorff distance computation differs from many other shape comparison methods in that no correspondence between the model and the image is derived the method is quite tolerant of small position errors such as those that occur with edge detectors and other feature extraction methods it is shown that the method extends naturally to the problem of comparing a portion of a model against an image

the use of quadratic finite element methods and irregular grids in the solution of hyperbolic problems abstract the galerkin method for first order hyperbolics using most higher order finite elements on any mesh or using any type of element on an irregular mesh is known to give a low order of accuracy this is because the exact solutions become distorted though the propagation speeds are handled to a higher order of accuracy the distortion comes about because the method makes no smoothness assumptions in its formulation computations with these methods can show rapid growth of small scale noise the algorithms can be improved by making smoothness assumptions many other techniques for obtaining higher order accuracy with such elements ignore the structure of the error and give worse results than standard galerkin methods this paper presents analysis and computational examples to support these statements

fuzzy spatial relation ontology for image interpretation the semantic interpretation of images can benefit from representations of useful concepts and the links between them as ontologies in this paper we propose an ontology of spatial relations in order to guide image interpretation and the recognition of the structures it contains using structural information on the spatial arrangement of these structures as an original theoretical contribution this ontology is then enriched by fuzzy representations of concepts which define their semantics and allow establishing the link between these concepts which are often expressed in linguistic terms and the information that can be extracted from images this contributes to reducing the semantic gap and it constitutes a new methodological approach to guide semantic image interpretation this methodological approach is illustrated on a medical example dealing with knowledge based recognition of brain structures in 3d magnetic resonance images using the proposed fuzzy spatial relation ontology

linear time distances between fuzzy sets with applications to pattern matching and classification we present four novel point to set distances defined for fuzzy or gray level image data two based on integration over cuts and two based on the fuzzy distance transform we explore their theoretical properties inserting the proposed point to set distances in existing definitions of set to set distances among which are the hausdorff distance and the sum of minimal distances we define a number of distances between fuzzy sets these set distances are directly applicable for comparing gray level images or fuzzy segmented objects but also for detecting patterns and matching parts of images the distance measures integrate shape and intensity membership of observed entities providing a highly applicable tool for image processing and analysis performance evaluation of derived set distances in real image processing tasks is conducted and presented it is shown that the considered distances have a number of appealing theoretical properties and exhibit very good performance in template matching and object classification for fuzzy segmented images as well as when applied directly on gray level intensity images examples include recognition of hand written digits and identification of virus particles the proposed set distances perform excellently on the mnist digit classification task achieving the best reported error rate for classification using only rigid body transformations and a knn classifier

a douglas wang finite element approach for transient advection diffusion problems abstract the paper presents an effective finite element method for approximating the two dimensional unsteady advection diffusion transport the new scheme is a direct generalization of the douglas wang finite element method applied to steady advection diffusion and stokes problems higher order spatial derivatives in the new formulation necessitate higher degree polynomial shape function quadratic finite element approximation quadrilateral q9 and triangular t6 are used the finite difference weighting formulation is used for a time discretization a stability analysis using the von neumann method shows that the formulation based on the implicit crank nicholson scheme reduces dissipation and dispersion errors when both advective and diffusive problems are considered also numerical results demonstrate that the accuracy achieved with the present model is excellent even with irregular element grids the results of this work strongly suggest further use and testing of this robust model in engineering practice especially for environmental problems related to pollution transport

a generalized galerkin method for steady convection diffusion problems with application to quadratic shape function elements abstract a generalization of the standard galerkin finite element method is considered to enable it to deal successfully with steady convection diffusion problems the proposed method employs a generalized governing equation which is obtained by subtracting from the original differential equation the scalar product of its gradient by a vector of free parameters associated with each of the coordinate directions the generalized equation is successively discretized by the standard bubnov galerkin finite element method the effectiveness of the method is illustrated for the case of quadratic local interpolations in one and two space dimensions

self organizing maps for imprecise data self organizing maps soms consist of a set of neurons arranged in such a way that there are neighbourhood relationships among neurons following an unsupervised learning procedure the input space is divided into regions with common nearest neuron vector quantization allowing clustering of the input vectors in this paper we propose an extension of the soms for data imprecisely observed self organizing maps for imprecise data soms id the learning algorithm is based on two distances for imprecise data in order to illustrate the main features and to compare the performances of the proposed method we provide a simulation study and different substantive applications

symmetric difference operators based on thresholds abstract here we study two formulas that define the symmetric difference operators of fuzzy sets in fuzzy logic we call this an exclusive or operator an interesting open problem was to find a certain class of operator systems where the two well known definitions of the symmetric difference operator are equivalent and it is associative here we state a functional equation which characterizes the equivalence of these two forms we present a general class of operators which fulfills the associativity requirement and we show that the two definitions are equivalent we generalize the symmetric difference operator to the n variable case and based on the latter the weighted form can be obtained we will give concrete forms of these operators and we will also show that they have different types of transitivity properties

on similarity relations in fuzzy relational databases abstract a characterization of a certain type of similarity relation is presented this characterization is conceptually very easy and may be used to provide easier proofs of already established theorems we use this characterization to show that if only a few similarity values of a similarity relation are known then the others may be computed this results in efficient storage of similarity relations associated with fuzzy relational databases in addition we use our characterization to show that there is only one type of similarity relation that provides a non redundant decomposition of data in a fuzzy relational data base

an introduction to finite element methods for transient advection problems abstract an introduction is presented to time accurate finite element methods recently developed for solving unsteady problems governed by linear and nonlinear advection equations this includes methods making an explicit use of the characteristic curves methods based on the taylor series in time and least squares methods

an analysis of time discretization in the finite element solution of hyperbolic problems abstract the problem of the time discretization of hyperbolic equations when finite elements are used to represent the spatial dependence is critically examined a modified equation analysis reveals that the classical second order accurate time stepping algorithms i e the lax wendroff leap frog and crank nicolson methods properly combine with piecewise linear finite elements in advection problems only for small values of the time step on the contrary as the courant number increases the numerical phase error does not decrease uniformly at all wavelengths so that the optimal stability limit and the unit cfl property are not achieved these fundamental numerical properties can however be recovered while still remaining in the standard galerkin finite element setting by increasing the order of accuracy of the time discretization this is accomplished by exploiting the taylor series expansion in the time increment up to the third order before performing the galerkin spatial discretization using piecewise linear interpolations as a result it appears that the proper finite element equivalents of second order finite difference schemes are implicit methods of incremental type having third and fourth order global accuracy on uniform meshes taylor galerkin methods numerical results for several linear examples are presented to illustrate the properties of the taylor galerkin schemes in one and two dimensional calculations

analysis of time varying errors in quadratic finite element approximation of hyperbolic problems a methodology for analysing the numerical errors generated by schemes using high order approximation is presented based on fourier analysis this methodology is illustrated through the study of the weighting taylor galerkin finite element model applied to an unsteady one dimension advection problem with quadratic elements results show that the dissipation and dispersion errors may be computed by considering simultaneously the so called physical and computational modes and then contrarily to what is shown when linear approximation is considered these errors present a transient behaviour moreover it appears that the errors computed at the end node and at the middle node present in general a different behaviour which in some cases may be opposed to one another numerical tests are presented to support the validity of the proposed strategy we recommend strongly the use of this method for studying the behaviour of numerical schemes based on high order approximations

quantitative analysis of properties and spatial relations of fuzzy image regions properties of objects and spatial relations between objects play an important role in rule based approaches for high level vision the partial presence or absence of such properties and relationships can supply both positive and negative evidence for region labeling hypotheses similarly fuzzy labeling of a region can generate new hypotheses pertaining to the properties of the region its relation to the neighboring regions and finally hypotheses pertaining to the labels of the neighboring regions a unified methodology that can be used to characterize both properties and spatial relationships of object regions in a digital image is presented the methods proposed for computing the properties and relations of image regions can be used to arrive at more meaningful decisions about the contents of the scene

differentials of fuzzy functions abstract in this paper the radstrom embedding theorem proc amer math soc 3 1952 165 is generalized and is used to define the concept of the differential of a fuzzy function

analysis of spurious eigenmodes in finite element equations numerical analysis of difference schemes often reveals the presence of eigenmodes which do not feature in the continuum solution an examination of the dispersion relation shows how the spurious and physical modes interact the behaviour of certain wave profiles was predicted using this analysis and the results confirmed by numerical experiment

analytical fuzzy plane geometry iii in this study we attempt to construct fuzzy circles in a fuzzy geometrical plane we provide a comprehensive study where we find a fuzzy number with a predetermined fuzzy distance from a given fuzzy number we formulate fuzzy circles using the conventional basic definitions of crisp circles two different formulations of fuzzy circles are proposed which depend on the information known about a fuzzy circle the interrelations between the evaluated fuzzy circles are investigated we show that the center of a fuzzy circle may not be a fuzzy point however the radius of a fuzzy circle that passes through three given fuzzy points is always a fuzzy number the concepts of same and inverse points and a fuzzy number along a line are used to define and analyze the proposed ideas our discussions and studies are supported by suitable numerical and pictorial examples

on fuzzy distances and their use in image processing under imprecision abstract this paper proposesa classification of fuzzy distances with respect to the requirements needed for applications in image processing under imprecision we distinguish on the one hand distances that basically compare only the membership functions representing the concerned fuzzy objects and on the other hand distances that combine spatial distance between objects and membership functions to our point of view the second class of methods finds more general applications in image processing since these methods take into account both spatial information and information related to the imprecision attached to the image objects new distances based on mathematical morphology are proposed in this second class

fuzzy proximities induced by functional fuzzy separation abstract mashhour and morsi introduced an axiom of n complete regularity to characterize the lowen fuzzy uniformizable fuzzy neighbourhood spaces fns s guided by that axiom we supply a sierpinski object for the artico moresco category fp of fuzzy proximity spaces which katsaras has shown to be a topological category we define the degree of functional fuzzy separatedness of a pair of subsets of a fns we use that notion to define the cech fuzzy proximity of an n completely regular fns x we establish that it is the finest fuzzy proximity that induces the fns x we study in some detail the cech fuzzy proximities obtained from n normal fns s

adaptive generalized metrics distance maps and nearest neighbor transforms on gray tone images this paper aims to introduce and study two novel metrics on gray tone images these metrics are based on the general adaptive neighborhood image processing ganip framework that enables to represent an image by spatial neighborhoods named general adaptive neighborhoods gan that fit to their local context these metrics are generalized in the sense that they do not satisfy all the axioms of a standard mathematical metric this notion of adaptive generalized metrics leads to the definition of relevant gan distance maps and gan nearest neighbor transforms used for image segmentation

approximate reflectional symmetries of fuzzy objects with an application in model based object recognition this paper is devoted to the study of reflectional symmetries of fuzzy objects we introduce a symmetry measure which defines the degree of symmetry of an object with respect to a given plane it is computed by measuring the similarity between the original object and its reflection the choice of an appropriate measure of comparison is based on the desired properties of the symmetry measure then an algorithm for computing the symmetry plane of fuzzy objects is proposed this is done using an optimization technique in the space of plane parameters finally we illustrate our approach with an application where the symmetry measure is used as an attribute in graph matching for model based object recognition

an experimental study on fuzzy distances for skull face overlay in craniofacial superimposition abstract skull face overlay is the most time consuming and error prone stage in craniofacial superimposition an important skeleton based forensic identification technique this task focuses on achieving the best possible overlay of an unknown skull found and a single ante mortem image of a candidate missing person the process is influenced by some sources of uncertainty since two objects of different nature are involved i e a skull and a face in previous works we have developed a computer aided craniofacial superimposition system aimed to assist forensic anthropologists in obtaining the best possible skull and face overlay the system has successfully allowed us to reduce the processing time simplify the forensic anthropologists work and make the process more objective and reproducible our approach is based on automatically overlaying a skull three dimensional model onto a facial photograph by minimizing the distance between two subsets of corresponding cranial and facial landmarks the proposed method properly deals with the inherent uncertainty sources to the skull face overlay process by considering fuzzy sets to model imprecise landmark location and imprecise cranial and facial landmarks spatial correspondence resulting from the presence of soft tissues in the face accordingly our methodology requires computing two kinds of distance metrics between a point and a fuzzy set and between two fuzzy sets this contribution is devoted to study the performance and influence of the most significant and suitable fuzzy distances proposed in the specialized literature as well as other new ones proposed on our skull face overlay system in particular we have tested the behavior of our automatic method when considering eight different distance measurements the system performance has been objectively evaluated considering 18 case studies resulting from a ground truth dataset following a rigorous statistical experimental setup the fact that the choice of a good distance metric is crucial to our method has been demonstrated since it significantly affects the quality of the final solutions it has been shown that our skull face overlay approach presents the best performance using the weighted mean distance in most of the cases and that the results are both more accurate and robust than the other studied metrics

fuzzy relative position between objects in image processing a morphological approach in order to cope with the ambiguity of spatial relative position concepts we propose a new definition of the relative position between two objects in a fuzzy set framework this definition is based on a morphological and fuzzy pattern matching approach and consists of comparing an object to a fuzzy landscape representing the degree of satisfaction of a directional relationship to a reference object it has good formal properties it is flexible it fits the intuition and it can be used for structural pattern recognition under imprecision moreover it also applies in 3d and for fuzzy objects issued from images

fuzzy pyramid based invariant object recognition abstract a new fuzzy decision based invariant pattern recognition method for object recognition is presented blending the well known image pyramid data structure with fuzzy mathematics the new method sets out to show how fuzzy concepts such as membership grade are used in fuzzifying the features and building up a fuzzy feature pyramid this is supported by a new segmentation technique using annular and sector windows inspired by the human visual system a fuzzy pyramid technique is then naturally introduced to make the recognition decision this new fuzzy decision approach is shown to have all the essential invariant properties and robustness against noise and uncertainty the recognition system was applied to the problem of tool recognition and good results were obtained a comparative study reveals many important advantages of our method over other techniques

fuzzy skeleton by influence zones application to interpolation between fuzzy sets this paper introduces a definition of influence zones for fuzzy sets the notion of fuzzy skeleton by influence zones skiz or fuzzy generalized voronoi diagram is derived these definitions are based on fuzzy dilations and their interpretations in terms of distances as another contribution we show how this notion can be used to define a fuzzy median set and a series of fuzzy sets interpolating between two fuzzy sets

weighted fuzzy pattern matching the fuzzy pattern matching technique has been developed in the framework of fuzzy set and possibility theory in order to take into account the imprecision and the uncertainty pervading values which have to be compared in a matching process this technique has proved very useful for implementing patterns of approximate reasoning in expert system inference engines and for designing retrieval systems capable of managing incomplete and fuzzy information data bases and vague queries in this paper the fuzzy pattern matching procedure is improved by introducing weights assessing the relative importance of atoms in the pattern matching indices are obtained using weighted versions of the minimum and maximum operations of fuzzy set theory this approach is extended to the case of variable weights and is related to aggregation schemes proposed by yager when modeling soft quantified statements such as most of the criteria must be met a notion of soft partial matching is thus modelled

fuzzy partitions a way to integrate expert knowledge into distance calculations this work proposes a new pseudo metric based on fuzzy partitions fps this pseudo metric allows for the introduction of expert knowledge into distance computations performed on numerical data and can be used in various types of statistical clustering or other applications the knowledge is formalized by a fp in which each fuzzy set represents a linguistic concept the pseudo metric is designed to respect the fp semantics the univariate case is first studied and the pseudo metric behavior is discussed using synthetic experiments then a multivariate version is proposed as a minkowski like combination of univariate distances or semi distances the value of the proposal is illustrated with two real world case studies in the fields of biology and precision agriculture

fuzzy clustering of fuzzy data based on robust loss functions and ordered weighted averaging abstract in many real cases the data are not expressed in term of single values but are imprecise in all these cases standard clustering methods for single valued data are unable to properly take into account the imprecise nature of the data in this paper by considering the partitioning around medoids pam approach in a fuzzy framework we propose a fuzzy clustering method for imprecise data formalized in a fuzzy manner in particular in order to neutralize the negative effects of possible outlier fuzzy data in the clustering process we proposed a robust fuzzy c medoids clustering method for fuzzy data based on the combination of huber s m estimators and yager s owa ordered weighted averaging operators the proposed method is able to smooth the influence of anomalous data by means of a suitable parameter the so called typicality parameter capable to tune the influence of the outliers the performance of the proposed method has been shown by means of a simulation study composed of experiments on i simple two dimensional dataset ii benchmark datasets and iii the fuzzy art outliers dataset the comparison made with the robust clustering methods known from the literature indicates the competitiveness of the introduced method to others an application of the suggested method to a real dataset is also provided and the results of the method has been compared with other clustering methods suggested in the literature in the application the comparative assessment has shown the informational gain in term of additional information of the proposed method vs the other robust methods