are grades of membership probabilities abstract a small sample is given of the difficulties with present day fuzzy set theory with respect to the requirements of a scientific theory and a summary of some probabilistic interpretations of grades of membership to be found in the literature the tee model for grades of membership is then suggested instead of starting out from mathematical postulates such as the assumed max and min operations for or and and the tee model uses a semantic physio logical psycho logical starting point by investigating the possibilities which a person has for assigning linguistic labels and partial grades of membership in a meaningful way the assignment of partial grades of membership is explained by the assumption that humans have the ability to take errors of observation and intersubject differences into consideration a membership value uex is identified with the subject s estimate of the probability that the label e g tall would be assigned to an object of exact attribute value uex in a natural language situation this situation being a labeling or a yes no one in which at least one of three possible sources of uncertainty is present almost all the accepted formulas of fuzzy set theory as well as the shapes of the grade of membership curves are then derived instead of having to be postulated however the derived formulas for or and and reduce to the max and min operations only in a number of special cases in another special case they reduce to the summation and the zero operation respectively the generally valid formulas are presented

a geometrical fuzzy clustering based solution to glottal wave estimation accurate estimation of the glottal waveform gw is required for purposes such as natural speech synthesis speaker recognition physiological speech processing etc most methods available for gw estimation are based on inverse filtering of the speech signal through the vocal tract and they all suffer from inaccuracies due to incorrect assumptions the method for gw estimation developed in the present study is based on fuzzy clustering of quasi linear geometrical substructures represented within the signal shifts hyperspace algorithms for estimation of the driving function to the vocal tract are presented and evaluated on simulated and real data comparison of the fuzzy clustering based method with the psiaif and wong s closed phase algorithms shows that the present method is superior with respect to both the gw estimation and determination of gw event time instants

fast and robust fuzzy c means clustering algorithms incorporating local information for image segmentation fuzzy c means fcm algorithms with spatial constraints fcm s have been proven effective for image segmentation however they still have the following disadvantages 1 although the introduction of local spatial information to the corresponding objective functions enhances their insensitiveness to noise to some extent they still lack enough robustness to noise and outliers especially in absence of prior knowledge of the noise 2 in their objective functions there exists a crucial parameter a used to balance between robustness to noise and effectiveness of preserving the details of the image it is selected generally through experience and 3 the time of segmenting an image is dependent on the image size and hence the larger the size of the image the more the segmentation time in this paper by incorporating local spatial and gray information together a novel fast and robust fcm framework for image segmentation i e fast generalized fuzzy c means fgfcm clustering algorithms is proposed fgfcm can mitigate the disadvantages of fcm s and at the same time enhances the clustering performance furthermore fgfcm not only includes many existing algorithms such as fast fcm and enhanced fcm as its special cases but also can derive other new algorithms such as fgfcm s1 and fgfcm s2 proposed in the rest of this paper the major characteristics of fgfcm are 1 to use a new factor s i j as a local both spatial and gray similarity measure aiming to guarantee both noise immunity and detail preserving for image and meanwhile remove the empirically adjusted parameter a 2 fast clustering or segmenting image the segmenting time is only dependent on the number of the gray levels q rather than the size n q of the image and consequently its computational complexity is reduced from o nci 1 to o qci 2 where c is the number of the clusters i 1 and i 2

some groups generated by transvection subgroups in the 1960 s j e mclaughlin lo 111 determined all irreducible finite dimensional linear groups generated by transvection subgroups a trans section of a k vector space v is linear map t cp x v t given by vt cp x 2 vqj y for all t e v where xe vand pe v are non zero and xcp 0 v is the dual space of v a k transvection subgroup t cp x consists of the identity and all r cp x where q and x range over the l dimensional subspaces spanned by cp and x respectively it is isomorphic to the additive group of k mclaughlin showed that the only such groups are the special linear and symplectic groups and in the case when k is f the field with two elements the orthogonal and symmetric groups it is our purpose to give a new proof of a result which includes mclaughlin s we discard the assumptions of finiteness of the dimension of v over k and also to some extent the irreducibility of the group while still obtaining a result which is recognizably like mclaughlin s our result for irreducible groups is the following unexplained terminol ogy will be defined after the statement of the theorem the more com plicated result under a weaker hypothesis is stated near the end of the introduction

a study of parameter values for a mahalanobis distance fuzzy classifier a supervised mahalanobis distance fuzzy classifier and the related fuzzy c means clustering algorithm requires the a priori selection of a weighting parameter called the fuzzy exponent guidance in the existing literature on an appropriate value is not definitive this paper attempts to rigorously justify previous experimental findings on suitable values for this fuzzy exponent using the criterion that fuzzy set memberships reflect class proportions in the mixed pixels of a remotely sensed image

a modified fuzzy c means algorithm for bias field estimation and segmentation of mri data we present a novel algorithm for fuzzy segmentation of magnetic resonance imaging mri data and estimation of intensity inhomogeneities using fuzzy logic mri intensity inhomogeneities can be attributed to imperfections in the radio frequency coils or to problems associated with the acquisition sequences the result is a slowly varying shading artifact over the image that can produce errors with conventional intensity based classification our algorithm is formulated by modifying the objective function of the standard fuzzy c means fcm algorithm to compensate for such inhomogeneities and to allow the labeling of a pixel voxel to be influenced by the labels in its immediate neighborhood the neighborhood effect acts as a regularizer and biases the solution toward piecewise homogeneous labelings such a regularization is useful in segmenting scans corrupted by salt and pepper noise experimental results on both synthetic images and mr data are given to demonstrate the effectiveness and efficiency of the proposed algorithm

technical communique identification of dynamical systems with a robust interval fuzzy model in this paper we present a new method of interval fuzzy model identification the method combines a fuzzy identification methodology with some ideas from linear programming theory on a finite set of measured data an optimality criterion that minimizes the maximal estimation error between the data and the proposed fuzzy model output is used the idea is then extended to modelling the optimal lower and upper bound functions that define the band that contains all the measurement values this results in a lower and an upper fuzzy model or a fuzzy model with a set of lower and upper parameters the model is called the interval fuzzy model infumo the method can be used when describing a family of uncertain nonlinear functions or when the systems with uncertain physical parameters are observed we believe that the fuzzy interval model can be very efficiently used especially in fault detection and in robust control design

fuzzy shell clustering algorithms in image processing fuzzy c rectangular and 2 rectangular shells objective function based clustering has been generalized recently to detect contours of circles and ellipses or even hyperbolas in a set of binary data vectors although there are special algorithms to discover lines the detection of rectangles needs further treatment a simple line detection algorithm is not sufficient for rectangles since for identifying four lines as one rectangle additional information such as the length of the lines and whether they are parallel or meet at a right angle is necessary in this paper a special fuzzy shell clustering algorithm for rectangular contours is developed the principal idea behind it can be generalized for other polygons so we also derive an algorithm that is capable of detecting rectangles and other polygons as well as approximating circles ellipses and lines

a parametric model for fusing heterogeneous fuzzy data presented is a model that integrates three data types numbers intervals and linguistic assessments data of these three types come from a variety of sensors one objective of sensor fusion models is to provide a common framework for data integration processing and interpretation that is what our model does we use a small set of artificial data to illustrate how problems as diverse as feature analysis clustering cluster validity and prototype classifier design can all be formulated and attacked with standard methods once the data are converted to the generalized coordinates of our model the effects of reparameterization on computational outputs are discussed numerical examples illustrate that the proposed model affords a natural way to approach problems which involve mixed data types

unsupervised optimal fuzzy clustering this study reports on a method for carrying out fuzzy classification without a priori assumptions on the number of clusters in the data set assessment of cluster validity is based on performance measures using hypervolume and density criteria an algorithm is derived from a combination of the fuzzy k means algorithm and fuzzy maximum likelihood estimation the unsupervised fuzzy partition optimal number of classes algorithm performs well in situations of large variability of cluster shapes densities and number of data points in each cluster the algorithm was tested on different classes of simulated data and on a real data set derived from sleep eeg signal

adaptive fuzzy c shells clustering and detection of ellipses several generalizations of the fuzzy c shells fcs algorithm are presented for characterizing and detecting clusters that are hyperellipsoidal shells an earlier generalization the adaptive fuzzy c shells afcs algorithm is examined in detail and is found to have global convergence problems when the shapes to be detected are partial new formulations are considered wherein the norm inducing matrix in the distance metric is unconstrained in contrast to the afcs algorithm the resulting algorithm called the afcs u algorithm performs better for partial shapes another formulation based on the second order quadrics equation is considered these algorithms can detect ellipses and circles in 2d data they are compared with the hough transform ht based methods for ellipse detection existing ht based methods for ellipse detection are evaluated and a multistage method incorporating the good features of all the methods is used for comparison numerical examples of real image data show that the afcs algorithm requires less memory than the ht based methods and it is at least an order of magnitude faster than the ht approach

eden growth on fractal media abstract simulations are presented for two dimensional eden growth into fractal networks we find that the fractal dimension of the eden cluster d e does not have a simple behavior when the cluster grows into the structure of a fractal network we also find that d e depends strongly on the minimal path between two arbitrary points in the network backbone and on the number of paths that appear between these two points at each scale

generalized fuzzy c shells clustering and detection of circular and elliptical boundaries abstract the fuzzy c shells fcs algorithm and its adaptive generalization called the adaptive fuzzy c shells afcs algorithm are considered for detection of curved boundaries specifically circular and elliptical the fcs algorithms utilize hyper spherical shells as cluster prototypes thus in two dimensions the prototypes are circles the afcs algorithms consider hyper ellipsoidal shells as prototypes hence the ability to characterize elliptical boundaries the generalization is achieved by allowing the distances to be measured through a norm inducing matrix that is symmetric positive definite each cluster is allowed to have a different matrix which is made a variable of optimization the ability of the algorithms to detect circular and elliptical boundaries in two dimensional data is illustrated through several examples

linear transvection groups and embedded polar spaces most classical groups arising from anti hermitian forms or pseudo quadratic forms contain so called isotropic transvections the isotropic transvection subgroups of these classical groups i e the subgroups generated by all isotropic transvections with a fixed axis form a class of abelian subgroups which is a class of abstract transvection groups in the sense of timmesfeld 24 in this paper we give a common characterization of all these classical groups with isotropic transvections as linear groups generated by a class of abstract transvection groups such that the elements of a are transvections

invading clusters in fractal media two dimensional invasion percolation simulations into regular fractals are performed to study the dependence of the invading cluster fractal dimension on the geometry of the medium the fractal dimension of the invading cluster di neither depends on the average coordination number of the network nor on the links of the backbone the authors find that di only depends on the fractal dimension of the backbone of the medium dbb and varies linearly with it

interval fuzzy model identification using l_infty norm in this paper we present a new method of interval fuzzy model identification the method combines a fuzzy identification methodology with some ideas from linear programming theory we consider a finite set of measured data and we use an optimality criterion that minimizes the maximum estimation error between the data and the proposed fuzzy model output the idea is then extended to modeling the optimal lower and upper bound functions that define the band which contains all the measurement values this results in lower and upper fuzzy models or a fuzzy model with a set of lower and upper parameters the model is called the interval fuzzy model infumo we also showed that the proposed structure uniformly approximates the band of any nonlinear function the interval fuzzy model identification is a methodology to approximate functions by taking into account a finite set of input and output measurements this approach can also be used to compress information in the case of large amount of data and in the case of robust system identification the method can be efficiently used in the case of the approximation of the nonlinear functions family if the family is defined by a band containing the whole measurement set the interval of parameters is obtained as the result this is of great importance in the case of nonlinear circuits modeling especially when the parameters of the circuits vary within certain tolerance bands

detection and separation of ring shaped clusters using fuzzy clustering a new fuzzy clustering algorithm designed to detect and characterize ring shaped clusters and combinations of ring shaped and compact spherical clusters has been developed this fkr algorithm includes automatic search for proper initial conditions in the two cases of concentric and excentric intersected combinations of clusters validity criteria based on total fuzzy area and fuzzy density are used to estimate the optimal number of substructures in the data set the fkr algorithm has been tested on a variety of simulated combinations of ring shaped and compact spherical clusters and its performance proved to be very good both in identifying the input shapes and in recovering the input parameters application of the fkr algorithm to an mri image of the heart s left ventricle was used to investigate the possibility of using this algorithm as an aid in image processing

geometrical fuzzy clustering algorithms fuzzy clustering algorithms are a basic tool for cluster analysis among these the geometrical fuzzy clustering algorithms are used when the clustering problem can be viewed as trying to find linear or ellipsoidal concentrations in data this paper provides a theoretical framework in which currently used geometrical fuzzy clustering algorithms become special cases also a family of functions called feasible are defined which can be used to construct such algorithms and convergence results are obtained

invasion percolation a new form of percolation theory a new kind of percolation problem is described which differs from ordinary percolation theory in that it automatically finds the critical points of the system the model is motivated by the problem of one fluid displacing another from a porous medium under the action of capillary forces but in principle it may be applied to any kind of invasion process which proceeds along a path at least resistance the name invasion percolation is proposed for this new process similarities to and differences from ordinary percolation theory are discussed

linear fuzzy clustering techniques with missing values and their application to local principal component analysis in this paper we propose two methods for partitioning an incomplete data set with missing values into several linear fuzzy clusters by extracting local principal components one is an extension of fuzzy c varieties clustering that can be regarded as the algorithm for the local principal component analysis of fuzzy covariance matrices the other is a simultaneous application of fuzzy clustering and principal component analysis of fuzzy correlation matrices both methods estimate prototypes ignoring only missing values and they need no preprocessing of data such as the elimination of samples with missing values or the imputation of missing elements numerical examples show that the methods provide useful tools for interpretation of the local structures of a database

a clustering algorithm for fuzzy model identification the fuzzy model proposed by takagi and sugeno can represent highly nonlinear systems and is widely used for the representation of fuzzy rules in this paper the model is firstly modified to make its identification easier based on the fuzzy c partition space four criteria are proposed for optimization of the model parameters following that a clustering algorithm composed of fuzzy c linear functions clustering and like fuzzy c means clustering is developed for minimizing the four criteria an identification scheme for rule s premise and consequence parameters is deduced from the clustering algorithm in succession finally four examples are demonstrated to verify the effectiveness of the proposed algorithm

relational generalizations of cluster validity indices numerous computational schemes have arisen over the years that attempt to learn information about objects based upon the similarity or dissimilarity of one object to another one such scheme clustering looks for self similar groups of objects to use clustering algorithms an investigator must often have a priori knowledge of the number of clusters i e c to search for in the data moreover it is often convenient to have ways to rank the returned results either for a single value of c a range of c s different clustering methods or any combination thereof however the task of assessing the quality of the results so that c may be determined objectively is currently ill defined for object object relationships to bridge this gap we generalize three well known validity indices the modified hubert s gamma xie beni and the generalized dunn s indices to relational data in doing so we develop a framework to convert many other validity indices to a relational form numerical examples on 12 datasets samples from four normal mixtures four real world object datasets and four real world pure relational datasets using the relational duals of the hard fuzzy and possibilistic c means cluster algorithms are offered to illustrate and evaluate the new indices

relational duals of cluster validity functions for the c means family clustering aims to identify groups of similar objects to evaluate the results of cluster algorithms an investigator uses cluster validity indices while the theory of cluster validity is well established for vector object data little effort has been made to extend it to relationship based data as such this paper proposes a theory of reformulation for object data validity indices so that they can be used to rank the results produced by the relational means clustering algorithms more specifically we create a class of relational validity indices which is called dual relational indices that are guaranteed under certain but easily met constraints to produce the same results and hence the same cluster counts as their object data counterparts

local convergence of the fuzzy c means algorithms abstract much understanding has recently been gained concerning global convergence properties of the fuzzy c means fcm family of clustering algorithms these global convergence properties which hold for all iteration sequences guarantee that every fcm iteration sequence converges at least along a subsequence to a stationary point of an fcm objective function in this paper we prove a local convergence property that is a property pertaining to iteration sequences started near a solution specifically a simple result is proved which shows that whenever an fcm algorithm is started sufficiently near a minimizer of the corresponding objective function then the iteration sequence must converge to that particular minimizer the result guarantees that once captured by the local neighborhood of a minimizer the succeeding iterate sequence will not escape thus infinite oscillation of such a sequence cannot occur the rate of convergence of the sequence to such a point is also discussed

estimation of multiple accelerated motions using chirp fourier transform and clustering motion estimation in the spatiotemporal domain has been extensively studied and many methodologies have been proposed which however cannot handle both time varying and multiple motions extending previously published ideas we present an efficient method for estimating multiple linearly time varying motions it is shown that the estimation of accelerated motions is equivalent to the parameter estimation of superpositioned chirp signals from this viewpoint one can exploit established signal processing tools such as the chirp fourier transform it is shown that accelerated motion results in energy concentration along planes in the 4 d space spatial frequencies temporal frequency chirp rate using fuzzy c planes clustering we estimate the plane motion parameters the effectiveness of our method is verified on both synthetic as well as real sequences and its advantages are highlighted

a fuzzy based customer classification method for demand responsive logistical distribution operations in some cases customer classification is important for the development of advanced logistical distribution strategies in response to the growing complexity in business logistical markets this paper presents a new approach that can be employed to cluster customers before executing fleet routing in logistical operations the proposed approach is developed on the basis of fuzzy clustering techniques and involves three sequential mechanisms including 1 binary transformation 2 generation of a fuzzy correlation matrix and 3 customer clustering such a customer clustering method should be performed prior to vehicle dispatching and routing in the process of goods distribution the proposed methodology clusters customers on the basis of their demand attributes rather than the static geographic property which is considered extensively in most published vehicle routing algorithms in addition to methodology development a case study was conducted to demonstrate the potential advantages of the proposed fuzzy clustering based method it is expected that this study can stimulate more research on time based logistics control and management

maximal unipotent subgroups of finitary linear groups finitary linear groups have been in recent years the subject of intensiveinvestigations the structure of these groups has been studied and nowmuch is known about the locally solvable or locally nilpotent finitary lineargroups or about the locally finite ones a remarkable achievement is forinstance the classification of the simple locally finite finitary linear groups recently completed by j hall

multisurface proximal support vector machine classification via generalized eigenvalues a new approach to support vector machine svm classification is proposed wherein each of two data sets are proximal to one of two distinct planes that are not parallel to each other each plane is generated such that it is closest to one of the two data sets and as far as possible from the other data set each of the two nonparallel proximal planes is obtained by a single matlab command as the eigenvector corresponding to a smallest eigenvalue of a generalized eigenvalue problem classification by proximity to two distinct nonlinear surfaces generated by a nonlinear kernel also leads to two simple generalized eigenvalue problems the effectiveness of the proposed method is demonstrated by tests on simple examples as well as on a number of public data sets these examples show the advantages of the proposed approach in both computation time and test set correctness

periodic simple groups of finitary linear transformations a group is locally finite if every finite subset generates a finite subgroup a group of linear transformations is finitary if each element minus the identity is an endomorphism of finite rank the classification and structure theory for locally finite simple groups splits naturally into two cases those groups that can be faithfully represented as groups of finitary linear transformations and those groups that are not finitary linear this paper completes the finitary case we classify up to isomorphism those infinite locally finite simple groups that are finitary linear but not linear

order propagation near the percolation threshold a new monte carlo method for studying bond percolation clusters is developed and used to identify new critical quantities associated with the percolation threshold the bonds in each cluster are partitioned into three distinct connectivity classes red singly connected backbone bonds blue multiply connected backbone bonds and yellow non backbone bonds often called dangling ends among the new cluster properties studied are the mean number of red bonds a critical quantity diverging at p c with exponent y r approximately 1 and the length of the shortest connected path through the cluster which is critical with exponent y min 1 35 0 02 for all cluster properties studies the authors also compute averages over only the largest clusters the corresponding critical exponents are found to be significantly different from those obtained by averaging over clusters of all sizes

a spatially constrained fuzzy hyper prototype clustering algorithm we present in this paper a fuzzy clustering algorithm which can handle spatially constraint problems often encountered in pattern recognition the proposed method is based on the notions of hyperplanes the fuzzy c means and spatial constraints by adding a spatial regularizer into the fuzzy hyperplane based objective function the proposed method can take into account additionally important information of inherently spatial data experimental results have demonstrated that the proposed algorithm achieves superior results to some other popular fuzzy clustering models and has potential for cluster analysis in spatial domain

detection and characterization of cluster substructure ii fuzzy c varieties and convex combinations thereof in part i siam j appl math 40 1981 pp 339 357 fuzzy c lines was introduced as an algorithm for detection and characterization of linearly clustered data in part ii we address two extensions of the theory in part i specifically we will first generalize the straight line prototype of a cluster developed in part i to any r dimensional linear variety of r s 0 leqq r s secondly we will consider a distance functional which utilizes convex combinations of the distance functionals developed here and in part i all of the notation and symbols used here are unchanged from part i

single point iterative weighted fuzzy c means clustering algorithm for remote sensing image segmentation in this paper a remote sensing image segmentation procedure that utilizes a single point iterative weighted fuzzy c means clustering algorithm is proposed based upon the prior information this method can solve the fuzzy c means algorithm s problem that the clustering quality is greatly affected by the data distributing and the stochastic initializing the centrals of clustering after the probability statistics of original data the weights of data attribute are designed to adjust original samples to the uniform distribution and added in the process of cyclic iteration which could be suitable for the character of fuzzy c means algorithm so as to improve the precision furthermore appropriate initial clustering centers adjacent to the actual final clustering centers can be found by the proposed single point adjustment method which could promote the convergence speed of the overall iterative process and drastically reduce the calculation time otherwise the modified algorithm is updated from multidimensional data analysis to color images clustering moreover with the comparison experiments of the uci data sets public berkeley segmentation dataset and the actual remote sensing data the real validity of proposed algorithm is proved

extremal presentations for classical lie algebras abstract the long root elements in lie algebras of chevalley type have been well studied and can be characterized as extremal elements that is elements x such that the image of ad x 2 lies in the subspace spanned by x in this paper assuming an algebraically closed base field of characteristic not 2 we find presentations of the lie algebras of classical chevalley type by means of minimal sets of extremal generators the relations are described by simple graphs on the sets for example for c n the graph is a path of length 2n and for a n the graph is the triangle connected to a path of length n 3

a fast diffeomorphic image registration algorithm abstract this paper describes dartel which is an algorithm for diffeomorphic image registration it is implemented for both 2d and 3d image registration and has been formulated to include an option for estimating inverse consistent deformations nonlinear registration is considered as a local optimisation problem which is solved using a levenberg marquardt strategy the necessary matrix solutions are obtained in reasonable time using a multigrid method a constant eulerian velocity framework is used which allows a rapid scaling and squaring method to be used in the computations dartel has been applied to intersubject registration of 471 whole brain images and the resulting deformations were evaluated in terms of how well they encode the shape information necessary to separate male and female subjects and to predict the ages of the subjects

detection and characterization of cluster substructure i linear structure fuzzy c lines in part i a generalization of the fuzzy c means or fuzzy isodata clustering algorithms is developed necessary conditions for minimization of a generalized total weighted squared orthogonal error objective function lead to a picard iteration scheme which generates simultaneously i c fuzzy clusters in the data ii a set of c prototypical straight lines in feature space which best fit the data in a well defined sense iii a set of c prototpyical centers of mass on the c lines which characterize the core of each linear fuzzy cluster theoretical optimization is achieved using principal components of generalized within cluster fuzzy scatter matrices a convergence theorem for each algorithm in the infinite family is given the algorithms are exemplified by five numerical examples using both real and artificial data sets having essentially linear substructure in part ii the fuzzy c means and fuzzy c lines algorithms are shown to be special cases of a more general class of fuzzy algorithms the