adaptive fuzzy rule based classification systems this paper proposes an adaptive method to construct a fuzzy rule based classification system with high performance for pattern classification problems the proposed method consists of two procedures an error correction based learning procedure and an additional learning procedure the error correction based learning procedure adjusts the grade of certainty of each fuzzy rule by its classification performance that is when a pattern is misclassified by a particular fuzzy rule the grade of certainty of that rule is decreased on the contrary when a pattern is correctly classified the grade of certainty is increased because the error correction based learning procedure is not meaningful after all the given patterns are correctly classified we cannot adjust a classification boundary in such a case to acquire a more intuitively acceptable boundary we propose an additional learning procedure we also propose a method for selecting significant fuzzy rules by pruning unnecessary fuzzy rules which consists of the error correction based learning procedure and the concept of forgetting we can construct a compact fuzzy rule based classification system with high performance

fast decomposition of matrices generated by the boundary element method a new method to reduce the solution time of matrices generated by the boundary element method is presented here the method involves converting the fully populated system into a banded system by lumping certain coefficients of the matrix into fictitious nodes and then constraining these nodes to accurately represent each coefficient the major advantages of lumping over the substructuring method are that lumping can be applied to arbitrarily shaped geometries and infinite domain problems and that it preserves the diagonal dominance of the matrix it is shown here that the proposed algorithm reduces the rate of increase of solution time t of an n degree of freedom problem from t n3 to t n2 although the algorithm is for thermal problems its extension to mechanical problems is straightforward the procedure can easily be incorporated into existing boundary element based packages

the use of dual reciprocity boundary element method in coupled thermoviscoelasticity a boundary element formulation is presented in a unified form for the analysis of thermoviscoelasticity problems the formulation contains the thermoelastic material as a special case the boundary only nature of boundary element method is retained through the use of particular integral method where the particular solutions are evaluated with the aid of dual reciprocity approximation the proposed formulation can be used in both coupled and uncoupled thermoviscoelasticity analyses and it permits performing the analysis in terms of fundamental solutions of viscoelastodynamics and diffusion thermal equation and eliminates the need for using the complicated fundamental solutions of coupled thermoviscoelasticity the formulation is performed in fourier space where any viscoelastic model can be simulated via the correspondence principle the determination of the response in time space requires the inversion which can be carried out conveniently by using the fast fourier transform algorithm for assessment some sample problems both uncoupled and coupled are considered and whenever possible comparisons are given with the exact data it is found that the formulation developed in the study even with the simplest base function proposed in literature may be used reliably in thermoviscoelasticity analysis at least for the problems with finite solution domains

stepwise linear regression particular integrals for uncoupled thermoelasticity with boundary elements this paper presents a simple technique for the efficient treatment of non uniform body forces in boundary elements without the need for domain discretization the distribution of the nonuniform forces in the domain is described using regression polynomials particular integrals corresponding to these polynomials are developed for the solution of the non homogeneous differential equations of elasticity the method allows the use of low order polynomials to model a general distribution of thermal effects in the domain numerical data is given to provide comparisons of boundary only data versus combined boundary and domain data based regression polynomials

the bounded variation quantity b v q and its application to feature extraction abstract the concept of bounded variation quantity b v q is proposed as a local feature of patterns especially waveform patterns and picture patterns it is closely connected with the mathematically complicated concepts of total variation and distribution but the result is shown by a simplified form i e a summation of absolute differences for concrete calculations its availability is also demonstrated through several applications such as seismic wave analysis the estimation of standard deviation in an independent gaussian process and a method of detecting the directionality of picture patterns

polynomial particular solutions based boundary element analysis of acoustic eigenfrequency problems the boundary element formulation for acoustic eigenfrequency analysis based on treating the forcing function in the governing differential equation as an initially unknown distributed source within the domain is presented the volume integral due to this distributed source is eliminated by approximating the internal source by global interpolation and polynomial function representations and finding particular solutions for the governing inhomogeneous equations the resulting non symmetric system matrix is solved by using arnoldi s algorithm modified to take advantage of the special structure of the substructured boundary element method the techniques described here are embedded in a computer program gpbest and the numerical results are obtained by using this computer code

feature analysis through information granulation and fuzzy sets feature analysis and feature selection are fundamental pursuits in pattern recognition we revisit and generalize an issue of feature selection by introducing a mechanism of soft fuzzy feature selection the underlying idea is to consider features to be granular rather than numeric by varying the level of granularity we modify the level of contribution of the specific feature to the overall feature space we admit an interval model of the features meaning that their values assume a form of numeric intervals the intervalization of the features exhibits a clear cut interpretation moreover a contribution of the features to the formation of the feature space can be easily controlled the broader the interval the less essential contribution of the feature to the entire feature space in limit when the intervals get broad enough one may view the feature to be completely eliminated dropped from the feature space the quantification of the features in terms of their importance is realized in the setting of the clustering fcm model namely a process of the binary or fuzzy feature selection is carried out and numerically quantified in the space of membership values generated by fuzzy clusters as the focal point of this study concerns an interval like form of information granules we reveal how such feature intervalization helps approximate fuzzy sets described by any type of membership function detailed computations give rise to a detailed quantification of such granular features numerical experiments provide a comprehensive numerical illustration of the problem

fuzzy tree automata and syntactic pattern recognition an approach of representing patterns by trees and processing these trees by fuzzy tree automata is described fuzzy tree automata are defined and investigated the results include that the class of fuzzy root to frontier recognizable trees is closed under intersection union and complementation thus the class of fuzzy root to frontier recognizable trees forms a boolean algebra fuzzy tree automata are applied to processing fuzzy tree representation of patterns based on syntactic pattern recognition the grade of acceptance is defined and investigated quantitative measures of approximate isosceles triangle approximate elongated isosceles triangle approximate rectangle and approximate cross are defined and used in the illustrative examples of this approach by using these quantitative measures a house a house with high roof and a church are also presented as illustrative examples in addition three fuzzy tree automata are constructed which have the capability of processing the fuzzy tree representations of fuzzy houses houses with high roofs and fuzzy churches respectively the results may have useful applications in pattern recognition image processing artificial intelligence pattern database design and processing image science and pictorial information systems

two and three dimensional soil consolidation by bem via particular integral abstract particular integral formulations are presented for two and three dimensional soil consolidation poroelasticity analysis the steady state poroelasticity equation is used as the complementary solution and a set of global shape functions is considered to approximate the transient terms of the poroelasticity equation to obtain the required particular integrals some numerical results for four example problems are given and compared with their analytical solutions or the results from the convolution method developed earlier by dargush and banerjee int j numer meth engng 28 1989 2423 j appl mech 58 1991 28

a generalized concept of a fuzzy probabilistic controller this paper deals with some theoretical aspects of generalization of the concept called fuzzy probabilistic controller some basic operations on probabilistic sets and their distribution function characterization are discussed here then the main idea of the generalized algorithm of fuzzy probabilistic controller is described the considerations are illustrated by means of several examples

a hybrid forecasting model reducing gaussian noise based on the gaussian support vector regression machine and chaotic particle swarm optimization in this paper the relationship between gaussian noise and the loss function of the support vector regression machine svrm is analyzed and then a gaussian loss function proposed to reduce the effect of such noise on the regression estimates since the e insensitive loss function cannot reduce noise a novel support vector regression machine g svrm is proposed then a chaotic particle swarm optimization cpso algorithm developed to estimate its unknown parameters finally a hybrid forecasting model combining g svrm with the cpso is proposed to forecast a multi dimensional time series the results of two experiments demonstrate the feasibility of this approach

non local boundary integral formulation for softening damage a strongly non local boundary element method bem for structures with strain softening damage treated by an integral type operator is developed a plasticity model with yield limit degradation is implemented in a boundary element program using the initial stress boundary element method with iterations in each load increment regularized integral representations and boundary integral equations are used to avoid the difficulties associated with numerical computation of singular integrals a numerical example is solved to verify the physical correctness and efficiency of the proposed formulation the example consists of a softening strip perforated by a circular hole subjected to tension the strain softening damage is described by a plasticity model with a negative hardening parameter the local formulation is shown to exhibit spurious sensitivity to cell mesh refinements localization of softening damage into a band of single cell width and excessive dependence of energy dissipation on the cell size by contrast the results for the non local theory are shown to be free of these physically incorrect features compared to the classical non local finite element approach an additional advantage is that the internal cells need to be introduced only within the small zone or band in which the strain softening damage tends to localize within the structure copyright 2003 john wiley sons ltd

isogeometric boundary element analysis of steady incompressible viscous flow part 1 plane problems abstract a novel approach is presented to the boundary element analysis of steady incompressible flow nurbs basis functions are used for describing the geometry of the problem and for approximating the unknowns in addition the arising volume integrals are treated differently to published work that is volumes are described by bounding nurbs curves instead of cells and a mapping is used the advantage of our approach is that non trivial boundary shapes can be described with very few parameters and that no generation of cells is required for the solution of the non linear equations both classical and modified newton raphson methods are used a comparison of the two methods is made on the classical example of a forced cavity flow where accurate solutions are available in the literature the results obtained agree well with published ones for moderate reynolds numbers using both methods but it is found that the latter requires a relaxation scheme and considerably more iterations to converge finally it is shown on a practical example of an airfoil how more complex boundary shapes can be approximated with few parameters and a solution obtained with a small number of unknowns

entropic one class classifiers the one class classification problem is a well known research endeavor in pattern recognition the problem is also known under different names such as outlier and novelty anomaly detection the core of the problem consists in modeling and recognizing patterns belonging only to a so called target class all other patterns are termed nontarget and therefore they should be recognized as such in this paper we propose a novel one class classification system that is based on an interplay of different techniques primarily we follow a dissimilarity representation based approach we embed the input data into the dissimilarity space ds by means of an appropriate parametric dissimilarity measure this step allows us to process virtually any type of data the dissimilarity vectors are then represented by weighted euclidean graphs which we use to determine the entropy of the data distribution in the ds and at the same time to derive effective decision regions that are modeled as clusters of vertices since the dissimilarity measure for the input data is parametric we optimize its parameters by means of a global optimization scheme which considers both mesoscopic and structural characteristics of the data represented through the graphs the proposed one class classifier is designed to provide both hard boolean and soft decisions about the recognition of test patterns allowing an accurate description of the classification process we evaluate the performance of the system on different benchmarking data sets containing either feature based or structured patterns experimental results demonstrate the effectiveness of the proposed technique

boundary element analysis of two dimensional elastoplastic contact problems in this paper a boundary element method for two dimensional elastoplastic stress analysis of frictional contact problems is presented the bodies in contact are treated as separate regions the contact conditions are used to join the different system of equations for different regions of contacted bodies and hence an overall system of equation is obtained an incremental and iterative procedure can be used to find the contact load or the contact extent and the proper contact conditions to include the plastic deformation in the analysis the initial strain algorithm is employed elastic perfectly plastic or work hardening material behaviour can be assumed for the numerical analysis an isoparametric three noded line elements are used to represent the boundary and eight noded quadrilateral or six noded triangular elements are used for the interior of the domain the displacement rates and traction rates are assumed to vary quadratically and the shape functions for the interior strain rates are also of quadratic type as an example the behaviour of an elastic and elastoplastic body with a smooth circular inclusion under the increasing load is presented

a picture of moduli space in this paper we construct an explicit fundamental domain for the action of the teichm uller modular group on the teichm uller space of closed surfaces of genus g 2 fundamental domains for the modular groups of surfaces of low signature have been obtained by keen k rosenberger r and others including this author m1 m2 fundamental domains for modular groups of hyperbolic surfaces of nite area with punctures have been obtained by penner p his technique makes essential use of the punctures while our technique seems to work only for closed surfaces there is also a related fundamental domain for closed surfaces of genus 2 obtained by semmler s his method uses dividing geodesics while we use non dividing geodesics throughout this paper the word geodesic refers to a closed geodesic which we will usually regard as being unoriented the author is indebted to the referee for pointing out that there is some related work due to thurston unpublished in which he attempts to give a natural cell decomposition of the teichm uller space of closed surfaces using sequences of disjoint shortest geodesics there is also some related work by n a at anen and penner n p attempting to use dirichlet domains for the same purpose while we do not know the topology of our fundamental domain in particular we do not know if it is a cell one can regard this work as a step in the direction of nding a cell decomposition of teichm uller space given a discrete group g of isometries on a manifold x the classical literature regards a fundamental domain d as an object one can integrate over in place of x g in particular d satis es the following three properties i no two points of the interior of d are equivalent under g ii every point of x is equivalent under g to some point of the closure of d iii the boundary of d has measure zero

additional criteria in fuzzy two level pattern recognition abstract pattern recognition with fuzzy sets is considered with regard to medical diagnostic problems an alternative interpretation of membership grade is suggested which expresses the degree of illness of a patient with respect to a certain disease a formal statement of a two level fuzzy classifier is presented the main emphasis is put on additional criteria designed to evaluate a fuzzy diagnostic decision for an unknown object two groups of criteria are formed decision making connected and domain dependent the decision making group of criteria can be viewed as related to the soft consensus measure in group decisions theory interconnections between criteria are discussed the notions proposed are illustrated with real medical data from the fields of aviation medicine and neonatology

fuzzy sets in pattern recognition methodology and methods abstract an objective of the paper is to discuss a state of the art of methodology and algorithms of fuzzy sets in the field of pattern recognition in real world recognition and classification problems we are faced with fuzziness that is connected with diverse facets of cognitive activity of the human being an origin of sources of fuzziness is related to labels expressed in feature space as well as to labels of classes taken into account in classification procedures an evident difference between a way of information processing by means of probability and fuzzy set theory and a way of interpretation of results is explained in detail in sequel methods of pattern recognition are studied in two main streams namely supervised and unsupervised learning different approaches to designing of classification schemes as e g relation calculus decision making approach etc are put into account a method of feature selection with the aid of fuzzy measure and fuzzy integral is introduced in clustering techniques methods relying on minimization of objective function are analyzed in detail also a problem of cluster validity expressed in terms of clustering indices is addressed numerical examples are also provided

a new boundary element technique without domain integrals for elastoplastic solids summary a simple idea is proposed to solve boundary value problems for elastoplastic solids via boundary elements namely to use the green s functions corresponding to both the loading and unloading branches of the tangent constitutive operator to solve for plastic and elastic regions respectively in this way domain integrals are completely avoided in the boundary integral equations though a discretization of the region where plastic flow occurs still remains necessary to account for the inhomogeneity of plastic deformation the elastoplastic analysis reduces in essence to a straightforward adaptation of techniques valid for anisotropic linear elastic constitutive equations the loading branch of the elastoplastic constitutive operator may be viewed formally as a type of anisotropic elastic law numerical examples using j2 flow theory with linear hardening demonstrate that the proposed method retains all the advantages related to boundary element formulations is stable and performs well the method presented is for simplicity developed for the associative flow rule however a full derivation of green s function and boundary integral equations is also given for the general case of non associative flow rule it is shown that in the non associative case a domain integral unavoidably arises in the formulation copyright 2005 john wiley sons ltd

solving nonlinear differential equations of mechanics with the boundary element method and radial basis functions the boundary element method is a very effective method for solving linear differential equations to use it also in the consideration of non linear problems some different procedures were developed among them the dual reciprocity method and the particular integral method both procedures use interpolation conditions for the approximation with radial basis functions in this paper a method is presented which avoids problems connected with interpolation by means of quasi interpolation it is possible to solve differential equations of the kind mu p u approximately the application to two non linear problems of plate theory yield good results hints to a theoretical examination of the method including sufficient conditions for feasibility and convergence are given 1997 by john wiley sons ltd

fuzzy relation equations theory as a basis of fuzzy modelling an overview abstract we give a wide overview on the applications of fuzzy relation equations theory to decision making processes to the construction of preference relations and to knowledge engineering mainly fuzzy control and fuzzy pattern recognition general theoretical results and methodological aspects are pointed out

knowledge based networks in classification problems abstract the paper proposes a distributed computational structure called knowledge based network as a classification scheme in pattern recognition unlike the existing architectures and algorithms of pattern recognition the network allows for an explicit representation of domain classification knowledge while maintaining its learning capabilities the knowledge based network blends useful properties of knowledge based systems namely explicit knowledge representation with those advantageous for neural networks viz learning the network is composed of basic and and or neurons fuzzy clustering constitutes a preprocessing phase leading towards developing geometric constructs they contribute to a conceptual level around which numerical processing of the classifier is centred

strategy based decision making of a soccer robot system using a real time self organizing fuzzy decision tree in a soccer robot game the environment is highly competitive and dynamic in order to work in the dynamically changing environment the decision making system of a soccer robot system should have the features of flexibility and on line adaptation this paper proposed a strategy based decision making system for a soccer robot system the decision system is based on the proposed self organizing fuzzy decision tree sofdt due to event driven strategies the proposed decision making system has the advantage of flexibility the proposed sofdt possesses simple apparent and fast generation reasoning processes the resultant system is a self organizing strategy based decision making system according to decision results sofdt can on line modify its parameters and structure for achieving better adaptability and improvement the performance of the proposed systems was verified by applying them to the simulation and experiment of 3 to 3 robot soccer games the results are satisfactory

on the meaning of dunn s partition coefficient for fuzzy clusters abstract a constantly recurring problem in cluster analysis is that of evaluating the number of clusters that are present in a data set the development of fuzzy clustering has brought no definite answer to this question although some new means have been provided offering new ways to tackle this problem one of the promising approaches was dunn s partition coefficient f k u that has been shown to vary between 1 for hard clusters and 1 k for completely fuzzy sets of objects hence the idea that f k u expresses a measure of how far a given fuzzy partition is from a hard one assuming moreover that an optimal partition in an optimal number of clusters will have a harder look than any other partition f k u could be considered as a cluster validity index that this procedure is unjustified is shown by the study of the d f diagram in which by analogy to the partition coefficient f a fuzziness coefficient d is defined an important result of this study is that a higher f k u value does not always correspond to a better allocation than a partition with a lower value this observation contradicts the role of the partition coefficient as cluster validity measurement these results are emply confirmed by various artificial and classical numerical examples

isogeometric boundary element analysis with elasto plastic inclusions part 1 plane problems abstract in this work a novel approach is presented for the isogeometric boundary element analysis of domains that contain inclusions with different elastic properties than the ones used for computing the fundamental solutions in addition the inclusion may exhibit inelastic material behavior in this paper only plane stress strain problems are considered in our approach the geometry of the inclusion is described using nurbs basis functions the advantage over currently used methods is that no discretization into cells is required in order to evaluate the arising volume integrals the other difference to current approaches is that kernels of lower singularity are used in the domain term the implementation is verified on simple finite and infinite domain examples with various boundary conditions finally a practical application in geomechanics is presented

incorporating fuzzy membership functions into the perceptron algorithm the perceptron algorithm one of the class of gradient descent techniques has been widely used in pattern recognition to determine linear decision boundaries while this algorithm is guaranteed to converge to a separating hyperplane if the data are linearly separable it exhibits erratic behavior if the data are not linearly separable fuzzy set theory is introduced into the perceptron algorithm to produce a fuzzy algorithm which ameliorates the convergence problem in the nonseparable case it is shown that the fuzzy perceptron like its crisp counterpart converges in the separable case a method of generating membership functions is developed and experimental results comparing the crisp to the fuzzy perceptron are presented

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

generalized k nearest neighbor rules abstract this paper discusses a suitable framework for generalizing the k nearest neighbor k nnr algorithms to cases where the design labels are not necessarily crisp i e not binary valued the proposed framework imbeds all crisp k nnr s into a larger structure of fuzzy k nnr s the resultant model enables neighborhood voting to be a continuous function of local labels at a point to be classified we emphasize that the decision itself may be crisp even when a fuzzy k nnr is utilized the usefulness of this extension of the conventional technique is illustrated by comparing the observed error rates of four classifiers the hard k nnr two fuzzy k nnr s and a fuzzy 1 nearest prototype rule 1 npr on three data sets anderson s iris data and samples from synthetic univariate and bivariate normal mixtures our conclusions all four designs yield comparable usually within 4 error rates the fuzzy c means fcm based k nnr is usually the best design the fcm 1 npr is the most efficient and perhaps most useful of the four designs and finally that generalized nnr s are an important and useful extension of the conventional ones

color image segmentation advances and prospects abstract image segmentation is very essential and critical to image processing and pattern recognition this survey provides a summary of color image segmentation techniques available now basically color segmentation approaches are based on monochrome segmentation approaches operating in different color spaces therefore we first discuss the major segmentation approaches for segmenting monochrome images histogram thresholding characteristic feature clustering edge detection region based methods fuzzy techniques neural networks etc then review some major color representation methods and their advantages disadvantages finally summarize the color image segmentation techniques using different color representations the usage of color models for image segmentation is also discussed some novel approaches such as fuzzy method and physics based method are investigated as well

fuzzy characterization of coronary disease abstract the paper presents a methodology based on fuzzy set theory to study the influence of social and psychological factors on the coronary disease a life history questionnaire has been used to collect data from control subjects and coronary patients the two groups made homogeneous in respect to objective features like sex age job etc have been used as training sets to learn the most relevant combinations of social and psychological features in the characterization of the coronary disease each of these features like stress social mobility hysteria etc is represented by means of a fuzzy linguistic variable whose membership value is evaluated on the basis of the answers to the questions relative to the particular feature

representation of uncertainty in computer vision using fuzzy sets uncertainty in computer vision can arise at various levels it can occur in the low level in the raw sensor input and extends all the way through intermediate and higher levels ideally at any level where decisions are being made on the basis of previous processing steps a computer vision system must have sufficient flexibility for representation of uncertainty in any of these levels

a novel fuzzy classifier based on product aggregation operator the present article proposes a fuzzy set based classifier with a better learning and generalization capability the proposed classifier exploits the feature wise degree of belonging of a pattern to all classes generalization in the fuzzification process and the combined class wise contribution of features effectively the classifier uses a p type membership function and product aggregation reasoning rule operator its effectiveness is verified with two conventional completely labeled data sets and two remote sensing images partially labeled data sets the proposed classifier is compared with similar fuzzy methods different performance measures are used for quantitative evaluation of the proposed classifier

a three dimensional bem solution for plasticity using regression interpolation within the plastic field this paper presents an improved solution of three dimensional plasticity problems using the boundary element method bem the bem formulation for plasticity requires volume as well as boundary discretizations an initial stress formulation is used to satisfy the material non linearity conventionally the plastic field in the volume element or cell is interpolated based on the value of plastic stress at the nodes of the cell in this paper the distribution of the plastic field in the cell is based on a number of points interior to the cell the plastic field is described using regression interpolation polynomials through these interior points the constitutive relation is satisfied at each interior point the number of points can be varied in each cell thus allowing for adaptive volume cells the plastic stresses are computed at the interior points only therefore the need for surface stress computation which uses numerical derivatives at the surface is completely eliminated three dimensional applications are used to compare the present regression interpolation procedure with the conventional method for elasto plasticity problems in all variations of the applications studied regression interpolation based on interior points provided superior results to those determined via the conventional nodal interpolation method

finding the overlap integral between two classes of object abstract probability densities which are described by hyperellipsoids are transformed into hyperspheres the hypersphere is topologically equivalent to the hyperellipsoid hence there is a transformation the consequences for the design of neural networks is discussed

interval valued hesitant fuzzy linguistic sets and their applications in multi criteria decision making problems an interval valued hesitant fuzzy linguistic set ivhfls can serve as an extension of both a linguistic term set and an interval valued hesitant fuzzy set this new set combines quantitative evaluation with qualitative evaluation these can describe the real preferences of decision makers and reflect their uncertainty hesitancy and inconsistency this work focuses on multi criteria decision making mcdm problems in which the criteria are in different priority levels and the criteria values take the form of interval valued hesitant fuzzy linguistic numbers ivhflns the new approach to solving these problems is based on the prioritized aggregation operators of ivhflns having reviewed the relevant literature we provide interval valued hesitant fuzzy linguistic operations and apply some linguistic scale functions which have been improved on the basis of psychological theory and prospect theory ultimately two kinds of prioritized aggregation operators of ivhflns are developed which extend to a grouping prioritized situation and are applied to mcdm problems finally an example is provided to illustrate and verify the proposed approach in two separate situations which are then compared to other representative methods

partitioning of feature space for pattern classification the article proposes a simple approach for finding a fuzzy partitioning of a feature space for pattern classification problems a feature space is initially decomposed into some overlapping hyperboxes depending on the relative positions of the pattern classes found in the training samples a few fuzzy if then rules reflecting the pattern classes by the generated hyperboxes are then obtained in terms of a relational matrix the relational matrix is utilized in the modified compositional rule of inference in order to recognize an unknown pattern the proposed system is capable of handling imprecise information both in the learning and the processing phases the imprecise information is considered to be either incomplete or mixed or interval or linguistic in form ways of handling such imprecise information are also discussed the effectiveness of the system is demonstrated on some synthetic data sets in two dimensional feature space the practical applicability of the system is verified on four real data such as the iris data set an appendicitis data set a speech data set and a hepatic disease data set

advanced boundary element analysis of two and three dimensional problems of elasto plasticity an advanced formulation of the boundary element method has been developed for inelastic analysis based on an initial stress approach the iterative solution algorithm makes use of an accelerated initial stress approach in which the past history of initial stresses are used to obtain an initial estimate for the current increment in the present analysis the geometry and functions are represented by higher order quadratic shape functions to model complex geometries and rapid functional variations accurately the methods of numerical integration of the kernels particularly the singular type are substantially improved by devising suitable automatic sub segmentation routines that incorporate the recent developments in mapping procedures the formulations have been implemented for two dimensional plane stress plane strain and three dimensional elasto plasticity problems

2d and 3d transient heat conduction analysis by bem via particular integrals abstract particular integral formulations are presented for 2d and 3d transient potential flow heat conduction analysis the results of the analysis are compared with an alternative formulation developed using the volume integral conversion approach although the mathematical foundation of the two methods are different both formulations are shown to produce almost identical results for the particular integral formulation the steady state heat conduction equation is used as the complementary solution and two global shape functions gsfs are considered to approximate the transient term of the heat conduction equation the numerical results for three example problems are given and compared with their analytical solutions

estimation of fuzzy gaussian mixture and unsupervised statistical image segmentation this paper addresses the estimation of fuzzy gaussian distribution mixture with applications to unsupervised statistical fuzzy image segmentation in a general way the fuzzy approach enriches the current statistical models by adding a fuzzy class which has several interpretations in signal processing one such interpretation in image segmentation is the simultaneous appearance of several thematic classes on the same site we introduce a new procedure for estimating of fuzzy mixtures which is an adaptation of the iterative conditional estimation ice algorithm to the fuzzy framework we first describe the blind estimation i e without taking into account any spatial information valid in any context of independent noisy observations then we introduce in a manner analogous to classical hard segmentation the spatial information by two different approaches contextual segmentation and adaptive blind segmentation in the first case the spatial information is taken into account at the segmentation step level and in the second case it is taken into account at the parameter estimation step level the results obtained with the iterative conditional estimation algorithm are compared to those obtained with expectation maximization em and the stochastic em algorithms on both parameter estimation and unsupervised segmentation levels via simulations the methods proposed appear as complementary to the fuzzy c means algorithms

efficient fuzzy partition of pattern space for classification problems abstract this paper proposes an efficient fuzzy partition method of a pattern space for classification problems the proposed method is based on the sequential subdivision of fuzzy subspaces and the generated fuzzy subspaces have different sizes in the proposed method first an n dimensional pattern space is divided into 2 n fuzzy subspaces with the same size next one of the fuzzy subspaces is selected and subdivided into 2 n fuzzy subspaces this procedure is iterated until a stopping condition is satisfied some criteria for selecting a fuzzy subspace to be subdivided are proposed and compared with each other by computer simulations the proposed method is also compared with other fuzzy classification methods

a new bem formulation for tow and three dimensional elastoplasticity using particular integras new two and three dimensional bem formulations are developed for elastoplastic stress analysis these new procedures differ from previous work in that volume integration is not required to incorporate the nonlinear effects in the analysis instead initial stress rates are introduced in the bem system via particular integrals the present formulation is implemented in a general purpose multi region system and examples are presented to demonstrate the accuracy and versatility of the method

a comparison of domain integral evaluation techniques for boundary element methods in many cases boundary integral equations contain a domain integral this can be evaluated by discretization of the domain into domain elements historically this was seen as going against the spirit of boundary element methods and several methods were developed to avoid this discretization notably dual and multiple reciprocity methods and particular solution methods these involved the representation of the interior function with a set of basis functions generally of the radial type in this study meshless methods dual reciprocity and particular solution are compared to the direct domain integration methods the domain integrals are evaluated using traditional methods and also with multipole acceleration it is found that the direct integration always results in better accuracy as well as smaller computation times in addition the multipole method further improves on the computation times in particular where multiple evaluations of the integral are required as when iterative solvers are used the additional error produced by the multipole acceleration is negligible copyright 2001 john wiley sons ltd

concepts of probabilistic sets abstract in the field of pattern recognition or decision making theory the important subjects are as follows 1 ambiguity of property of objects 2 variety of character of objects 3 subjectivity of observers 4 evolution of knowledge of observers i e learning considering these points the concept of probabilistic set is proposed it is based on both probability theory and fuzzy concepts a probabilistic set on a total space is defined by a point wise measurable function from a parameter space which is a probability space to a characteristic space which is a measurable space it is shown that the family of all probabilistic sets constitutes a complete pseudo boolean algebra moment analysis is possible by using a probability measure of the parameter space other useful concepts are also mentioned such as probabilistic mappings and expected cardinal numbers

approximate solutions of fuzzy relational equations in the previous chs we have discussed various problems concerning solutions of fuzzy relation equations obviously an underlying assumption is that there exists a nonempty set of solutions a situation may occurr and indeed it is quite common in which no solution exists nevertheless even in this case one might be interested to obtain an approximate solution and know to which extent it can be viewed as a solution this stream of investigations is particularly interesting for applicational purposes contrary to the topics already discussed in the previous chs this is a field of research which has not been developed enough so far it concerns studies on solvability properties of fuzzy relation equations in this ch we shall try to answer by using several techniques the following basic question how difficult is it to attain a situation in which the system of equations has solutions and then how to measure this property

elastoplastic bie analysis of cracked plates and related problems part 2 numerical results part 1 of this paper reports on the formulation of an advanced boundary integral equation model for fracture mechanics analysis of cracked plates subject to elastoplastic behaviour or other related body force problems the basis of this formulation contrasts with other bie elastoplastic formulations in the use of the green s function for an infinite plane containing a stress free crack this green s function formulation assures that the total elastic strain field for the crack problem is accurately imbedded in the numerical model the second part of this paper reports on the numerical implementation of this algorithm as currently developed the anelastic strain field residual strains thermal strains plastic strains etc is approximated as piecewise constant while the boundary data is modelled with linear interpolations an iteration solution scheme is adopted which eliminates the need for recalculation of the bie matrices the stability and accuracy of the algorithm are demonstrated for an uncracked notch geometry and comparison to finite element results is made for the centre cracked panel the data shows that even the crude plastic strain model applied is capable of excellent resolution of crack tip plastic behaviour

processing in relational structures fuzzy relational equations abstract the paper provides an overview of methodology for processing fuzzy information in relational structures completed in terms of fuzzy relational equations the origin and the central role of relational calculus in general and fuzzy sets in particular is explained with special emphasis paid to its role and representation capabilities it is pointed out that fuzzy relational equations play a significant role as a platform for a uniform development of techniques in fuzzy sets many of the problems and frameworks developed in fuzzy sets so far can be easily translated into the language of fuzzy relational equations which immediately takes a significant advantage of their solid well developed formalisms techniques and clarity of exposition we will study the role of approximate solutions to fuzzy relational equations as a convenient tool to handle probabilistic type of uncertainty moreover those solutions can easily explain the origin and generate a way in which fuzzy sets of higher generality such as for instance type 2 sets interval valued sets can be algorithmically determined finally we study the role of equations in diverse fields of applications making use of an ample framework of general systems theory

a new boundary element formulation for two and three dimensional thermoelasticity using particular integrals new two and three dimensional boundary element formulations are developed for steady state and transient uncoupled thermoelasticity these new procedures differ from previous work in that additional surface or volume integration is not required to incorporate thermal loads in the analysis instead thermal body forces are introduced in the boundary element system via particular integrals the present formulation is implemented in a general purpose multi region system and examples are presented to demonstrate the accuracy and versatility of the method

a new approach to the similarity relations in the fuzzy set theory abstract the subtle theory of fuzzy sets has long been proposed by zadeh as an extension of the classical theory of hard sets in this paper we show how the properties of reflexivity and transitivity of a fuzzy relation may be reconsidered if they are used in view of another intuitive support and new mathematical developments as a consequence we propose a new modified system of leading definitions for the fuzzy equivalence relationship that could be used profitably to support the concept of fuzzy partition the role of an internal basis is also emphasized corollary properties are derived from this new approach

cluster validity for fuzzy clustering algorithms abstract the proportion exponent is introduced as a measure of the validity of the clustering obtained for a data set using a fuzzy clustering algorithm it is assumed that the output of an algorithm includes a fuzzy nembership function for each data point we show how to compute the proportion of possible memberships whose maximum entry exceeds the maximum entry of a given membership function and use these proportions to define the proportion exponent its use as a validity functional is illustrated with four numerical examples and its effectiveness compared to other validity functionals namely classification entropy and partition coefficient

microcalcification detection using fuzzy logic and scale space approaches abstract breast cancer is one of the leading causes of women mortality in the world since the causes are unknown breast cancer cannot be prevented it is difficult for radiologists to provide both accurate and uniform evaluation over the enormous number of mammograms generated in widespread screening computer aided mammography diagnosis is an important and challenging task microcalcifications and masses are the early signs of breast carcinomas and their detection is one of the key issues for breast cancer control in this study a novel approach to microcalcification detection based on fuzzy logic and scale space techniques is presented first we employ fuzzy entropy principal and fuzzy set theory to fuzzify the images then we enhance the fuzzified image finally scale space and laplacian of gaussian filter techniques are used to detect the sizes and locations of microcalcifications a free response operating characteristic curve is used to evaluate the performance the major advantage of the proposed method is its ability to detect microcalcifications even in the mammograms of very dense breasts a data set of 40 mammograms nijmegen database containing 105 clusters of microcalcifications is studied experimental results demonstrate that the microcalcifications can be accurately and efficiently detected using the proposed approach it can produce lower false positives and false negatives than the existing methods

problems of classification in a fuzzy environment this paper presents a classification model in a fuzzy environment by using possibility distributions and fuzzy measures optimal in bayes sense membership functions are induced these functions are similar to decision rules used in classical discriminant analysis the relations between fuzzy measures and possibility measures are also discussed to formulate a classification model where sugeno s fuzzy measures and integrals are used

efficient evaluation of volume integrals in the boundary element method abstract nonlinear formulations of the boundary element method as for example elastoplastic analysis require integration over internal cells due to the singularity of the integrand this volume integration is cumbersome the paper presents a closed concept of direct evaluation of these domain integrals by means of simple transformations and standard gaussian quadrature rules for regular but nearly singular integrals an adaptive integration scheme is presented for the strongly singular case a regularized formulation based on gauss theorem is proposed numerical examples concerning elastoplastic analysis are included

dealing with a priori knowledge by fuzzy labels abstract the performances of two different estimators of a discriminant function of a statistical pattern recognizer are compared one estimator is based on binary label values of the objects of the learning set hard labels and the other on continuous or multi discrete label values in the interval 0 1 fuzzy labels by the latter estimator more detailed a priori knowledge of the contributing learning objects is used in a discrete feature space in which a multi nomial distribution function has been assumed to exist the expected classification error based on fuzzy labels can be more accurate than the one based on hard

a bem formulation for transient dynamic elastoplastic analysis via particular integrals abstract this paper presents the particular integral formulation for two 2d and three 3d dimensional transient dynamic elastoplastic analyses the elastostatic equation is used for the complementary solution the particular integrals for displacement traction and stress rates are obtained by introducing the concept of a global shape function to approximate acceleration and initial stress rate terms of the inhomogeneous equation the houbolt time integration scheme is used for the time marching process the newton raphson algorithm for plastic multiplier is used to solve the system equation the developed program is integrated with the pre and post processor numerical results for four example problems are given to demonstrate the validity and accuracy of the present formulation

competitive interaction reasoning in designing fuzzy rule based classification systems frbcss complex fuzzy rule extraction techniques and tuning membership functions are frequently used to enhance classification accuracy however these approaches not only decrease system s transparency which is the hallmark of fizzy design but also are oftentimes computationally expensive and require multiple parameters to be optimized using a large amount of training data in this paper inspired by the so called competitive behavior of mini columns in the brain neuronal circuitry we proposed a new reasoning method for fuzzy classifiers referred to as competitive interaction reasoning cir that employs the cumulative information provided by all fuzzy rules and adjusts the decision boundaries as if the membership functions are directly modified this mechanism is mathematically implemented by a linear transformation and resembles the competitive interaction observed in brain neuronal columns cross rule competition weights are optimized using hebbian reinforcement learning using a large number of simulations on benchmark data sets we show that the proposed cir significantly improves classification accuracy without compromising interpretability of the fuzzy classifier in addition cir can further facilitate formation of the fuzzy rules and incorporation of the expert knowledge by confining the destructive effects of noisy rules or expert inconsistencies experiments on 23 well known benchmark data sets confirm high performance of cir in comparison with a number of popular classifiers

on some properties of a linguistic classifier abstract a general structure of a linguistic classifier wherein sub subclassifiers are the building blocks is suggested some properties of these sub subclassifiers are proposed and proved the physical significances of these properties are explored and it is shown that a condensed measure of belongingness of patterns to any class can be obtained which can conveniently be used for forming classification rules

designing of classification procedures with the use of equality and difference operations abstract the paper addresses a problem of classification formulated in a framework of fuzzy relation calculus an aspect of partial matching is addressed this enables us to represent an information supporting class membership as well as information of disconfirmatory character both of these sources of information are quantitatively characterized by relevant measures known as degrees of equality and inequality difference respectively two basic forms of fuzzy relational equations are proposed in sequel a way of aggregating confirmatory and disconfirmatory information characterizing class membership is introduced numerical illustration highlights the properties of the method developed

bem analysis of free vibration problems using polynomial particular integrals abstract the development of a boundary element method for free vibration analysis using particular solutions is discussed the formulation presented is based on treating the forcing function in the governing differential equation as an initially unknown distributed body force within the domain the volume integral due to this body force is then eliminated by approximating the inertia force by global interpolation and polynomial function representations and finding particular solutions for the governing inhomogeneous equations the resulting non symmetric system matrix is solved by using a modified arnoldi s algorithm that takes advantage of the special structure of the substructured boundary element method the techniques described here are embedded in a computer program gpbest and the numerical examples arc solved by using this computer code

on edge detection of x ray images using fuzzy sets the effectiveness of the theory of fuzzy sets in detecting different regional boundaries of x ray images is demonstrated the algorithm includes a prior enhancement of the contrast among the regions having small change in gray levels using the contrast intensification int operation along with smoothing in the fuzzy property plane before detecting its edges the property plane is extracted from the spatial domain using s and 1 functions and the fuzzifiers final edge detection is achieved using max or min operator the system performance for different parameter conditions is illustrated by application to an image of a radiograph of the wrist

general fuzzy min max neural network for clustering and classification this paper describes a general fuzzy min max gfmm neural network which is a generalization and extension of the fuzzy min max clustering and classification algorithms of simpson 1992 1993 the gfmm method combines supervised and unsupervised learning in a single training algorithm the fusion of clustering and classification resulted in an algorithm that can be used as pure clustering pure classification or hybrid clustering classification it exhibits a property of finding decision boundaries between classes while clustering patterns that cannot be said to belong to any of existing classes similarly to the original algorithms the hyperbox fuzzy sets are used as a representation of clusters and classes learning is usually completed in a few passes and consists of placing and adjusting the hyperboxes in the pattern space this is an expansion contraction process the classification results can be crisp or fuzzy new data can be included without the need for retraining while retaining all the interesting features of the original algorithms a number of modifications to their definition have been made in order to accommodate fuzzy input patterns in the form of lower and upper bounds combine the supervised and unsupervised learning and improve the effectiveness of operations a detailed account of the gfmm neural network its comparison with the simpson s fuzzy min max neural networks a set of examples and an application to the leakage detection and identification in water distribution systems are given

the homology of the mapping class group 1 2 h btg a h mg q in this paper we will show that m g btg and b i l sg get more and more complicated as the genus g tends to infinity more precisely we will prove theorem 1 1 let q z2 z4 z6 denote the polynomial algebra of generators z2n in dimension in n 1 2 3 there are classes y2 y4 y2n with y2n in the 2nth cohomology group h 2n b i sg z such that the homomorphism of algebras sending z2n toy2n

fuzzy markov random fields versus chains for multispectral image segmentation this paper deals with a comparison of recent statistical models based on fuzzy markov random fields and chains for multispectral image segmentation the fuzzy scheme takes into account discrete and continuous classes which model the imprecision of the hidden data in this framework we assume the dependence between bands and we express the general model for the covariance matrix a fuzzy markov chain model is developed in an unsupervised way this method is compared with the fuzzy markovian field model previously proposed by one of the authors the segmentation task is processed with bayesian tools such as the well known mpm mode of posterior marginals criterion our goal is to compare the robustness and rapidity for both methods fuzzy markov fields versus fuzzy markov chains indeed such fuzzy based procedures seem to be a good answer e g for astronomical observations when the patterns present diffuse structures moreover these approaches allow us to process missing data in one or several spectral bands which correspond to specific situations in astronomy to validate both models we perform and compare the segmentation on synthetic images and raw multispectral astronomical data