a fuzzy extension of the silhouette width criterion for cluster analysis the present paper proposes a new cluster validity measure as an additional criterion to help the decision making process in fuzzy cluster analysis this measure named fuzzy silhouette is a generalization to the fuzzy case of the average silhouette width criterion originally conceived to assess crisp non fuzzy data partitions the fuzzy silhouette is more appealing than its crisp counterpart in the context of fuzzy cluster analysis since it makes explicit use of the fuzzy partition matrix provided by the clustering algorithm in addition it has been designed to improve performance of the original silhouette criterion in detecting regions with higher data density when the data set involves overlapping clusters the performance of the fuzzy silhouette is evaluated and compared to that of five well known cluster validity measures six data sets are used to illustrate different scenarios in which the proposed fuzzy silhouette performs similar to or better than these other criteria thus becoming eligible to join a pool of measures to be used all together in fuzzy cluster analysis

towards a theory of bv functions in abstract wiener spaces functions of bounded variation in an abstract wiener space i e an infinite dimensional banach space endowed with a gaussian measure and a related differentiable structure have been introduced by m fukushima and m hino using dirichlet forms and their properties have been studied with tools from stochastics in this paper we reformulate with purely analytical tools the definition and the main properties of bv functions and start investigating further properties

ℋ index for continuous time stochastic systems with markov jump and multiplicative noise this paper investigates the problem of index for stochastic linear continuous time systems involving markov jump and multiplicative noise a set of generalized differential riccati equations gdres are presented and it is shown that the solvability of gdres is necessary and sufficient for the feasibility of an index larger than 0 our results extend the corresponding deterministic cases to stochastic systems furthermore the infinite horizon index problem for square systems is considered finally the effectiveness of the obtained results is tested by two examples

a probabilistic fuzzy logic system for modeling and control in this paper a probabilistic fuzzy logic system pfls is proposed for the modeling and control problems similar to the ordinary fuzzy logic system fls the pfls consists of the fuzzification inference engine and defuzzification operation to process the fuzzy information different to the fls it uses the probabilistic modeling method to improve the stochastic modeling capability by using a three dimensional membership function mf the pfls is able to handle the effect of random noise and stochastic uncertainties existing in the process a unique defuzzification method is proposed to simplify the complex operation finally the proposed pfls is applied to a function approximation problem and a robotic system it shows a better performance than an ordinary fls in stochastic circumstance

segmentation and classification of range images the recognition of objects in three dimensional space is a desirable capability of a computer vision system range images which directly measure 3 d surface coordinates of a scene are well suited for this task in this paper we report a procedure to detect connected planar convex and concave surfaces of 3 d objects this is accomplished in three stages the first stage segments the range image into surface patches by a square error criterion clustering algorithm using surface points and associated surface normals the second stage classifies these patches as planar convex or concave based on a non parametric statistical test for trend curvature values and eigenvalue analysis in the final stage boundaries between adjacent surface patches are classified as crease or noncrease edges and this information is used to merge compatible patches to produce reasonable faces of the object s this procedure has been successfully applied to a large number of real and synthetic images four of which we present in this paper

fuzzy rule selection by multi objective genetic local search algorithms and rule evaluation measures in data mining this paper shows how a small number of simple fuzzy if then rules can be selected for pattern classification problems with many continuous attributes our approach consists of two phases candidate rule generation by rule evaluation measures in data mining and rule selection by multi objective evolutionary algorithms in our approach first candidate fuzzy if then rules are generated from numerical data and prescreened using two rule evaluation measures i e confidence and support in data mining then a small number of fuzzy if then rules are selected from the prescreened candidate rules using multi objective evolutionary algorithms in rule selection we use three objectives maximization of the classification accuracy minimization of the number of selected rules and minimization of the total rule length thus the task of multi objective evolutionary algorithms is to find a number of non dominated rule sets with respect to these three objectives the main contribution of this paper is to propose an idea of utilizing the two rule evaluation measures as prescreening criteria of candidate rules for fuzzy rule selection an arbitrarily specified number of candidate rules can be generated from numerical data for high dimensional pattern classification problems through computer simulations we demonstrate that such a prescreening procedure improves the efficiency of our approach to fuzzy rule selection we also extend a multi objective genetic algorithm moga in our former studies to a multi objective genetic local search mogls algorithm where a local search procedure adjusts the selection i e inclusion or exclusion of each candidate rule furthermore a learning algorithm of rule weights i e certainty factors is combined with our mogls algorithm such extensions to our moga for fuzzy rule selection are another contribution of this paper

image filtering edge detection and edge tracing using fuzzy reasoning we characterize the problem of detecting edges in images as a fuzzy reasoning problem the edge detection problem is divided into three stages filtering detection and tracing images are filtered by applying fuzzy reasoning based on local pixel characteristics to control the degree of gaussian smoothing filtered images are then subjected to a simple edge detection algorithm which evaluates the edge fuzzy membership value for each pixel based on local image characteristics finally pixels having high edge membership are traced and assembled into structures again using fuzzy reasoning to guide the tracing process the filtering detection and tracing algorithms are tested on several test images comparison is made with a standard edge detection technique

conditional density estimation using probabilistic fuzzy systems we consider conditional density approximation by fuzzy systems fuzzy systems are typically used to approximate deterministic functions in which the stochastic uncertainty is ignored we propose probabilistic fuzzy systems pfss in which the probabilistic nature of uncertainty is taken into account these systems take also fuzzy uncertainty into account by their fuzzy partitioning of input and output spaces we discuss an additive reasoning scheme for pfss that leads to the estimation of conditional probability densities and prove how such fuzzy systems compute the expected value of this conditional density function we show that some of the most commonly used fuzzy systems can compute the same expected output value and we derive how their parameters should be selected in order to achieve this goal the additional information and process understanding provided by the different interpretations of the pfs models are illustrated using a real world example

stabilization of networked control systems with both network induced delay and packet dropout this paper is concerned with the mean square stabilization problem for discrete time networked control systems ncss it is assumed that control signal is sent to plant over a lossy communication channel where network induced delay and packet dropout occur simultaneously a necessary and sufficient stabilizing condition is developed in terms of the unique positive definite solutions to some coupled algebraic riccati equations cares the contributions of this paper are twofold first an existence theorem of the maximum packet dropout rate is proposed second for one dimensional single input system and the decoupled multi input system it is shown that the ncs is stabilizable iff the network induced delay and the packet dropout rate satisfy some simple algebraic inequalities if the network induced delay is known a priori the maximum packet dropout rate is given explicitly in terms of network induced delay and unstable eigenvalues of the system matrix if the packet dropout rate is known a priori the maximum allowable delay bound is also given explicitly

classical dirichlet forms on topological vector spaces closability and a cameron martin formula abstract we prove a sufficient condition for the closability of classical dirichlet forms on l 2 e which is also necessary if all components of the dirichlet form are closable here e is a locally convex topological vector space and a not necessarily quasi invariant probability measure on e the same condition is shown to imply the existence of a closed extension whose domain can be described explicitly in the special case where is quasi invariant with respect to certain vectors in e our result generalises previous theorems on closability in addition we prove a cameron martin type formula for a large class of measures if e is finite dimensional our characterisation of closability is the analogue of the corresponding one dimensional result applications to quantum fields and the connection with the well studied case of abstract wiener spaces are discussed

quantized output feedback control for networked control systems this paper addresses the problem of output feedback control for networked control systems ncss with limited communication capacity firstly we propose a new model to describe the non ideal network conditions and the input output state quantization of the ncss in a unified framework secondly based on our newly proposed model and an improved separation lemma the observer based controller is developed for the asymptotical stabilization of the ncss which are shown in terms of nonlinear matrices inequalities the nonlinear problems can be computed through solving a convex optimization problems and the observed and controller gains could be derived by solving a set of linear matrix inequalities thirdly two simulation examples are given to demonstrate the effectiveness of the proposed method

bv functions in hilbert spaces we study the basic theory of bv functions in a hilbert space x endowed with a not necessarily gaussian probability measure nu we present necessary and sufficient conditions in order that a function u in l p x nu is of bounded variation we also discuss the de giorgi approach to bv functions through the behavior as t rightarrow 0 of int x vert nabla t t u vert d nu for a smoothing semigroup t t particular attention is devoted to the case where u is the indicator function of a sublevel set x g x r of a real borel function g we give several examples for different measures nu such as weighted gaussian measures infinite products of non gaussian measures and invariant measures of some stochastic pdes such as reaction diffusion equations and burgers equation

general c means clustering model partitional clustering is an important part of cluster analysis based on various theories numerous clustering algorithms have been developed and new clustering algorithms continue to appear in the literature it is known that occam s razor plays a pivotal role in data based models and partitional clustering is categorized as a data based model however no relation had previously been discovered between occam s razor and partitional clustering as we discuss in this paper the three main contributions of this paper can be summarized as follows 1 according to a novel definition of the mean a unifying generative framework for partitional clustering algorithms called a general c means clustering model gcm is presented and studied and 2 based on the local optimality test of the gcm the connection between occam s razor and partitional clustering is established for the first time as its application a comprehensive review of the existing objective function based clustering algorithms is presented based on gcm 3 under a common assumption about partitional clustering a theoretical guide for devising and implementing clustering algorithm is discovered these conclusions are verified by numerical experimental results

ray holder continuity for fractional sobolev spaces in infinite dimensions and applications we prove holder continuity on rays in the direction of vectors in the generalized cameron martin space for functions in sobolev spaces in lp of fractional order 1 over infinite dimensional linear spaces the underlying measures are required to satisfy some easy standard structural assumptions only apart from wiener measure they include gibbs measures on a lattice and euclidean interacting quantum fields in infinite volume a number of applications e g to the two dimensional polymer measure are presented in particular irreducibility of the dirichlet form associated with the latter measure is proved without restrictions on the coupling constant

mosco convergence of dirichlet forms in infinite dimensions with changing reference measures let e be an infinite dimensional locally convex space let n be a weakly convergent sequence of probability measures on e and let en be a sequence of dirichlet forms on e such that en is defined on l2 n general sufficient conditions for mosco convergence of the gradient dirichlet forms are obtained applications to gibbs states on a lattice and to the gaussian case are given weak convergence of the associated processes is discussed

an efficient configuration for probabilistic fuzzy logic system a novel inference configuration is proposed to improve the computational efficiency and information loss in the probabilistic fuzzy inference process the probabilistic inference and the fuzzy inference are unified in one operation based on the continuous form of the probabilistic fuzzy set besides the faster inference operation it is able to produce fuzzy outputs in a complete probabilistic distribution that in turn will provide information about the approximation bound the computational analyses of six different fuzzy systems demonstrate the inference efficiency of the proposed method its effectiveness can be further demonstrated on the application to modeling of an industrial curing process the robust modeling performance discloses its potential in process modeling under complex environment

on the space of bv functions and a related stochastic calculus in infinite dimensions functions of bounded variation bv functions are defined on an abstract wiener space e h in a way similar to that in finite dimensions some characterizations are given which justify describing a bv function as a function in l log l 1 2 with the first order derivative being an h valued measure it is also shown that the space of bv functions is obtained by a natural extension of the sobolev space d1 1 moreover some stochastic formulae related to bv functions are investigated

a novel approach to fuzzy clustering based on a dissimilarity relation extracted from data using a ts system clustering refers to the process of unsupervised partitioning of a data set based on a dissimilarity measure which determines the cluster shape considering that cluster shapes may change from one cluster to another it would be of the utmost importance to extract the dissimilarity measure directly from the data by means of a data model on the other hand a model construction requires some kind of supervision of the data structure which is exactly what we look for during clustering so the lower the supervision degree used to build the data model the more it makes sense to resort to a data model for clustering purposes conscious of this we propose to exploit very few pairs of patterns with known dissimilarity to build a ts system which models the dissimilarity relation among other things the rules of the ts system provide an intuitive description of the dissimilarity relation itself then we use the ts system to build a dissimilarity matrix which is fed as input to an unsupervised fuzzy relational clustering algorithm denoted any relation clustering algorithm arca which partitions the data set based on the proximity of the vectors containing the dissimilarity values between each pattern and all the other patterns in the data set we show that combining the ts system and the arca algorithm allows us to achieve high classification performance on a synthetic data set and on two real data sets further we discuss how the rules of the ts system represent a sort of linguistic description of the dissimilarity relation

left ventricle automated detection method in gated isotopic ventriculography using fuzzy clustering a method that uses the fuzzy isodata clustering algorithm and fourier analysis is proposed for automated detection of heart left ventricle contours this operation is used for quantitative analysis of cardiac function the computation begins by finding the phase image the fuzzy isodata algorithm is first applied to this image to generate a number of clusters that correspond to the organ substructures ventricles atria second the ventricles cluster is isolated and the intensities of its points are replaced by the corresponding ones from the original end diastolic frame finally a reduced image representing the ventricular region is obtained and an additional clustering is performed to find the left ventricular boundary automatically this algorithm is tested by application of 105 sets of 16 images each these results are compared with the measurements obtained with two semi automatic methods used respectively on the philips and the sopha medical gamma cameras

a validity measure for fuzzy clustering the authors present a fuzzy validity criterion based on a validity function which identifies compact and separate fuzzy c partitions without assumptions as to the number of substructures inherent in the data this function depends on the data set geometric distance measure distance between cluster centroids and more importantly on the fuzzy partition generated by any fuzzy algorithm used the function is mathematically justified via its relationship to a well defined hard clustering validity function the separation index for which the condition of uniqueness has already been established the performance of this validity function compares favorably to that of several others the application of this validity function to color image segmentation in a computer color vision system for recognition of ic wafer defects which are otherwise impossible to detect using gray scale image processing is discussed

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

kernel induced fuzzy clustering of image pixels with an improved differential evolution algorithm a modified differential evolution de algorithm is presented for clustering the pixels of an image in the gray scale intensity space the algorithm requires no prior information about the number of naturally occurring clusters in the image it uses a kernel induced similarity measure instead of the conventional sum of squares distance use of the kernel function makes it possible to partition data that is linearly non separable and non hyper spherical in the original input space into homogeneous groups in a transformed high dimensional feature space a novel search variable representation scheme is adopted for selecting the optimal number of clusters from several possible choices extensive performance comparison over a test suite of 10 gray scale images and objective comparison with manually segmented ground truth indicates that the proposed algorithm has an edge over a few state of the art algorithms for automatic multi class image segmentation

bootstrap technique in cluster analysis abstract we define a method to estimate the number of clusters in a data set e using the bootstrap technique this approach involves the generation of several fake data sets by sampling patterns with replacement in e bootstrapping for each number k of clusters a measure of stability of the k cluster partitions over the bootstrap samples is used to characterize the significance of the k cluster partition for the original data set the value of k which provides the most stable partitions is the estimate of the number of clusters in e the performance of this new technique is demonstrated on both synthetic and real data and is applied to the segmentation of range images

designing fuzzy inference systems from data an interpretability oriented review fuzzy inference systems fis are widely used for process simulation or control they can be designed either from expert knowledge or from data for complex systems fis based on expert knowledge only may suffer from a loss of accuracy this is the main incentive for using fuzzy rules inferred from data designing a fis from data can be decomposed into two main phases automatic rule generation and system optimization rule generation leads to a basic system with a given space partitioning and the corresponding set of rules system optimization can be done at various levels variable selection can be an overall selection or it can be managed rule by rule rule base optimization aims to select the most useful rules and to optimize rule conclusions space partitioning can be improved by adding or removing fuzzy sets and by tuning membership function parameters structure optimization is of a major importance selecting variables reducing the rule base and optimizing the number of fuzzy sets over the years many methods have become available for designing fis from data their efficiency is usually characterized by a numerical performance index however for human computer cooperation another criterion is needed the rule interpretability an implicit assumption states that fuzzy rules are by nature easy to be interpreted this could be wrong when dealing with complex multivariable systems or when the generated partitioning is meaningless for experts the paper analyzes the main methods for automatic rule generation and structure optimization they are grouped into several families and compared according to the rule interpretability criterion for this purpose three conditions for a set of rules to be interpretable are defined

modeling and control of ito stochastic networked control systems with random packet dropouts subject to time varying sampling in this note we discuss the modeling and control of a class of ito stochastic networked control systems ncss with packet dropouts that are subject to time varying sampling the system under consideration is first modeled as a continuous time system with input delay that is subject to double randomness via the input delay approach then by assuming the packet drop rate and recurring to the celebrated formula of total probability an equivalent model which takes full advantage of probability distribution characteristics of both packet dropouts and sampling periods is established in particular the probability distribution values of the stochastic delay taking values in two given intervals can be explicitly obtained which is of crucial importance to model and analyze the actual problem in ncss based on that robustly exponentially mean square stability of the system with an h infty performance is guaranteed an h infty controller design procedure is then proposed finally a numerical simulation example is exploited to show the effectiveness and applicability of the results derived and some less conservative results are obtained

brief paper robust sampled data h control with stochastic sampling in this paper the problem of robust h control is investigated for sampled data systems with probabilistic sampling the parameter uncertainties are time varying norm bounded and appear in both the state and input matrices for the simplicity of technical development only two different sampling periods are considered whose occurrence probabilities are given constants and satisfy bernoulli distribution which can be further extended to the case with multiple stochastic sampling periods by applying an input delay approach the probabilistic sampling system is transformed into a continuous time delay system with stochastic parameters in the system matrices by linear matrix inequality lmi approach sufficient conditions are obtained which guarantee the robust mean square exponential stability of the system with an h performance moreover an h controller design procedure is then proposed an illustrative example is included to demonstrate the effectiveness of the proposed techniques

a novel cluster validity index for fuzzy clustering based on bipartite modularity a novel cluster validity index whose implementation is based on the membership degrees and improved bipartite modularity of bipartite network is proposed for the validation of partitions produced by the fuzzy c means fcm algorithm fcm algorithm is employed to group the dataset in order to obtain the membership degree of samples then a weighted bipartite network is constructed by samples and centroids of each cluster this allows the introduction of a new measurement for optimizing the numbers of clusters for fuzzy partitions the proposed index utilizes the optimum membership as its global property and the modularity of bipartite network as its local independent property the proposed index is compared with a number of popular validation indices on fifteen datasets the experimental results show that the effectiveness and reliability of the proposal is superior to other indices

a clustering performance measure based on fuzzy set decomposition clustering is primarily used to uncover the true underlying structure of a given data set and for this purpose it is desirable to subject the same data to several different clustering algorithms this paper attempts to put an order on the various partitions of a data set obtained from different clustering algorithms the goodness of each partition is expressed by means of a performance measure based on a fuzzy set decomposition of the data set under consideration several experiments reported in here show that the proposed performance measure puts an order on different partitions of the same data which is consistent with the error rate of a classifier designed on the basis of the obtained cluster labelings

performance evaluation of some clustering algorithms and validity indices in this article we evaluate the performance of three clustering algorithms hard k means single linkage and a simulated annealing sa based technique in conjunction with four cluster validity indices namely davies bouldin index dunn s index calinski harabasz index and a recently developed index i based on a relation between the index i and the dunn s index a lower bound of the value of the former is theoretically estimated in order to get unique hard k partition when the data set has distinct substructures the effectiveness of the different validity indices and clustering methods in automatically evolving the appropriate number of clusters is demonstrated experimentally for both artificial and real life data sets with the number of clusters varying from two to ten once the appropriate number of clusters is determined the sa based clustering technique is used for proper partitioning of the data into the said number of clusters

a symmetry based multiobjective clustering technique for automatic evolution of clusters in this paper the problem of automatic clustering a data set is posed as solving a multiobjective optimization moo problem optimizing a set of cluster validity indices simultaneously the proposed multiobjective clustering technique utilizes a recently developed simulated annealing based multiobjective optimization method as the underlying optimization strategy here variable number of cluster centers is encoded in the string the number of clusters present in different strings varies over a range the points are assigned to different clusters based on the newly developed point symmetry based distance rather than the existing euclidean distance two cluster validity indices one based on the euclidean distance xb index and another recently developed point symmetry distance based cluster validity index sym index are optimized simultaneously in order to determine the appropriate number of clusters present in a data set thus the proposed clustering technique is able to detect both the proper number of clusters and the appropriate partitioning from data sets either having hyperspherical clusters or having point symmetric clusters a new semi supervised method is also proposed in the present paper to select a single solution from the final pareto optimal front of the proposed multiobjective clustering technique the efficacy of the proposed algorithm is shown for seven artificial data sets and six real life data sets of varying complexities results are also compared with those obtained by another multiobjective clustering technique mock two single objective genetic algorithm based automatic clustering techniques vgaps clustering and gcuk clustering

sampled data synchronization control of dynamical networks with stochastic sampling this technical note is concerned with the sampled data synchronization control problem for a class of dynamical networks the sampling period considered here is assumed to be time varying that switches between two different values in a random way with given probability the addressed synchronization control problem is first formulated as an exponentially mean square stabilization problem for a new class of dynamical networks that involve both the multiple probabilistic interval delays mpids and the sector bounded nonlinearities sbns then a novel lyapunov functional is constructed to obtain sufficient conditions under which the dynamical network is exponentially mean square stable both gronwall s inequality and jenson integral inequality are utilized to substantially simplify the derivation of the main results subsequently a set of sampled data synchronization controllers is designed in terms of the solution to certain matrix inequalities that can be solved effectively by using available software finally a numerical simulation example is employed to show the effectiveness of the proposed sampled data synchronization control scheme

an efficient approach for unsupervised fuzzy clustering based on grouping evolution strategies fuzzy data clustering plays an important role in practical use and has become a prerequisite step for decision making in fuzzy environment in this paper we propose a new algorithm called fuzzyges for unsupervised fuzzy clustering based on adaptation of the recently proposed grouping evolution strategy ges to adapt ges for fuzzy clustering we devise a fuzzy counterpart of the grouping mutation operator typically used in ges and employ it in a two phase procedure to generate a new clustering solution unlike conventional clustering algorithms which should get the number of clusters as an input fuzzyges tries to determine the true number of clusters as well as providing the optimal cluster centroids after several iterations the proposed approach is validated through using several data sets and results are compared with those of fuzzy c means algorithm particle swarm optimization algorithm pso differential evolution de and league championship algorithm lca we also investigate the performance of fuzzyges through using different cluster validity indices our results indicate that fuzzyges is fast and provides acceptable results in terms of both determining the correct number of clusters and the accurate cluster centroids

stabilization of sampled data control systems with control inputs missing this note is concerned with the stabilization problem for sampled data control systems with control inputs missing a sufficient condition is derived for the existence of exponentially stabilizing state feedback controllers via the switched system approach the obtained condition establishes several quantitative relations among some system parameters such as the sampling period and the exponential decay rate the actual data missing rate and the admissible data missing rate bound two illustrative examples are given to show the effectiveness of the proposed results

bv functions and distorted ornstein uhlenbeck processes over the abstract wiener space let e h be an abstract wiener space and h be the class of functions l1 e satisfying the ray hamza condition in every direction l e for h the closure e f of the symmetric form e u v e u z v z h z dz u v fc1b is a quasi regular dirichlet form on l2 f d f supp yielding an associated diffusion m xt pz on f called a distorted ornstein uhlenbeck process a function on e is called a bv function bv e in notation if p 1 lp e and v supg fc1b e g h z 1 e g z z dz is finite for h bv e there exist a positive finite measure d on f and a weakly measurable function f h such that z h 1 d a e and f g z z dz f g z z h d dz g fc1b e further the sample path of m admits an expression as a sum of e valued cafs xt x0 wt 12 t0 xs ds 12 t0 xs dl d s where wt is an e valued brownian motion and l d t is a pcaf of m with revuz measure d a measurable set e is called caccioppoli if i bv e in this case the support of the measure di is concentrated in and the above equations reduce to the gauss formula and the skorohod equation for the modified reflecting ornstein uhlenbeck process respectively a related coarea formula is also presented

tightness of general c1 p capacities on banach space abstract we prove tightness of c 1 p capacities on a banach space e these capacities are defined in terms of measures on e which are not necessarily gaussian our methods are purely analytic and completely different from earlier approaches which were implemented under more restrictive assumptions

bv functions in abstract wiener spaces abstract functions of bounded variation in an abstract wiener space i e an infinite dimensional banach space endowed with a gaussian measure and a related differential structure have been introduced by m fukushima and m hino using dirichlet forms and their properties have been studied with tools from analysis and stochastics in this paper we reformulate in an integral geometric vein and with purely analytical tools the definition and the main properties of bv functions and investigate further properties

fuzzy min max neural networks i classification a supervised learning neural network classifier that utilizes fuzzy sets as pattern classes is described each fuzzy set is an aggregate union of fuzzy set hyperboxes a fuzzy set hyperbox is an n dimensional box defined by a min point and a max point with a corresponding membership function the min max points are determined using the fuzzy min max learning algorithm an expansion contraction process that can learn nonlinear class boundaries in a single pass through the data and provides the ability to incorporate new and refine existing classes without retraining the use of a fuzzy set approach to pattern classification inherently provides a degree of membership information that is extremely useful in higher level decision making the relationship between fuzzy sets and pattern classification is described the fuzzy min max classifier neural network implementation is explained the learning and recall algorithms are outlined and several examples of operation demonstrate the strong qualities of this new neural network classifier

some new qualitative insights into quality of fuzzy rule based models rules in fuzzy rule based models convey essential knowledge about the system under discussion as such they capture the essence of relationships occurring among input and output variables while the quality of such fuzzy models is predominantly related with the accuracy and eventual interpretability of rules although to a limited extent the quality of rules being regarded as generic pieces of knowledge has not been studied so far in this study we formulate and investigate this problem by looking at the quality of rules including aspects of a stability b generalizability and c conflict we identify a concept of rule multiplicity conflict and study an emergence of rule generalization a number of pertinent performance indices are developed and their usage is presented through a series of experimental studies

iterative fuzzy clustering algorithm with supervision to construct probabilistic fuzzy rule base from numerical data to deal with data patterns with linguistic ambiguity and with probabilistic uncertainty in a single framework we construct an interpretable probabilistic fuzzy rule based system that requires less human intervention and less prior knowledge than other state of the art methods specifically we present a new iterative fuzzy clustering algorithm that incorporates a supervisory scheme into an unsupervised fuzzy clustering process the learning process starts in a fully unsupervised manner using fuzzy c means fcm clustering algorithm and a cluster validity criterion and then gradually constructs meaningful fuzzy partitions over the input space the corresponding fuzzy rules with probabilities are obtained through an iterative learning process of selecting clusters with supervisory guidance based on the notions of cluster pureness and class separability the proposed algorithm is tested first with synthetic data sets and benchmark data sets from the uci repository of machine learning database and then with real facial expression data and tv viewing data

sobolev functions on infinite dimensional domains abstract we study extensions of sobolev and bv functions on infinite dimensional domains along with some positive results we present a negative solution of the long standing problem of existence of sobolev extensions of functions in gaussian sobolev spaces from a convex domain to the whole space

fuzzy neural networks with reference neurons as pattern classifiers a heterogeneous neural network consisting of logic neurons and realizing mappings in 0 1 hypercubes is presented the two kinds of neurons studied are utilized to perform matching functions equality or reference neurons and aggregation operations aggregation neurons all computations are driven by logic operations widely used in fuzzy set theory the network is heterogeneous in its nature and includes two types of neurons organized into a structure detecting individual regions of patterns using reference neurons and combining them to yield a final classification decision

parameter dependent lyapunov functional for stability of time delay systems with polytopic type uncertainties this note concerns the problem of the robust stability of a linear system with a time varying delay and polytopic type uncertainties in order to construct a parameter dependent lyapunov functional for the system we first devised a new method of dealing with a time delay system without uncertainties in this method the derivative terms of the state which is in the derivative of the lyapunov functional are retained and some free weighting matrices are used to express the relationships among the system variables and among the terms in the leibniz newton formula as a result the lyapunov matrices are not involved in any product terms of the system matrices in the derivative of the lyapunov functional this method is then easily extended to a system with polytopic type uncertainties numerical examples demonstrate the validity of the proposed criteria

lda based clustering algorithm and its application to an unsupervised feature extraction research has shown fuzzy c means fcm clustering to be a powerful tool to partition samples into different categories however the objective function of fcm is based only on the sum of distances of samples to their cluster centers which is equal to the trace of the within cluster scatter matrix in this study we propose a clustering algorithm based on both within and between cluster scatter matrices extended from linear discriminant analysis lda and its application to an unsupervised feature extraction fe our proposed methods comprise between and within cluster scatter matrices modified from the between and within class scatter matrices of lda the scatter matrices of lda are special cases of our proposed unsupervised scatter matrices the results of experiments on both synthetic and real data show that the proposed clustering algorithm can generate similar or better clustering results than 11 popular clustering algorithms k means k medoid fcm the gustafson kessel gath geva possibilistic c means pcm fuzzy pcm possibilistic fcm fuzzy compactness and separation a fuzzy clustering algorithm based on a fuzzy treatment of finite mixtures of multivariate student s t distributions algorithms and a fuzzy mixture of the student s t factor analyzers model the results also show that the proposed fe outperforms principal component analysis and independent component analysis

network based fuzzy control for nonlinear markov jump systems subject to quantization and dropout compensation abstract this paper focuses on the issue of network based fuzzy control for nonlinear markov jump systems with unreliable communication links the nonlinear system under consideration is described by a takagi sugeno t s fuzzy model through corresponding fuzzy rules the control signals are quantized by a logarithmic quantizer before they are transmitted to the network and in case quantized control signals lose intermittently when being passed to the actuator a compensation strategy is implemented to deal with the packet dropout based on a novel lyapunov function which is both fuzzy basis dependent and mode dependent the existence criterion for the desired controller is established to ensure the stochastic stability as well as a predefined h performance index of the resulting closed loop system a bench mark example of robot arm is presented to demonstrate the validity of the proposed design technique

a multiresolution image segmentation technique based on pyramidal segmentation and fuzzy clustering in this paper an unsupervised image segmentation technique is presented which combines pyramidal image segmentation with the fuzzy c means clustering algorithm each layer of the pyramid is split into a number of regions by a root labeling technique and then fuzzy c means is used to merge the regions of the layer with the highest image resolution a cluster validity functional is used to find the optimal number of objects automatically segmentation of a number of synthetic as well as clinical images is illustrated and two fully automatic segmentation approaches are evaluated which determine the left ventricular volume lv in 140 cardiovascular magnetic resonance mr images first fuzzy c means is applied without pyramids in the second approach the regions generated by pyramidal segmentation are merged by fuzzy c means the correlation coefficients of manually and automatically defined lv lumen of all 140 and 20 end diastolic images were equal to 0 86 and 0 79 respectively when images were segmented with fuzzy c means alone these coefficients increased to 0 90 and 0 93 when the pyramidal segmentation was combined with fuzzy c means this method can be applied to any dimensional representation and at any resolution level of an image series the evaluation study shows good performance in detecting lv lumen in mr images

detecting change points for shifts in mean and variance using fuzzy classification maximum likelihood change point algorithms knowing the time of changes called change point cp in a process is crucial for engineers to recognize the root cause fast and accurately since special causes may induce simultaneous changes in mean and variance detecting changes in both at once is required many methodologies in quality control were developed for detecting changes in either mean or variance only and process parameters were assumed known often however they are rarely known exactly and a small estimation error may lead to unfavorable cp estimates fuzzy partitioning is better suited to cases of vague boundaries between two segments which appear very often in reality a new mechanism called fuzzy classification maximum likelihood change point fcml cp algorithm is proposed to detect shifts in mean and variance simultaneously a cp framework is transferred into a mixture model and then a fcml cp algorithm is created through fuzzy classification maximum likelihood procedures the proposed fcml cp can be applied to phase i and ii processes without knowledge of in control process parameters it can estimate multiple cps of process mean or and variance simultaneously the effectiveness and superiority of fcml cp are shown by extensive experiments with numerical and real data sets specifically the proposed fcml cp is superior to the commonly used statistical mixture likelihood approach using expectation maximization em algorithm it is much more time saving especially the remarkable performance of fcml cp in detecting cps for small changes is particularly important and helpful for engineers to recognize the special cause fast and correctly since an out of control signal resulted from small changes is usually delayed long we propose a new algorithm fcml cp to detect change points in a statistical process the mixture likelihood embedded fuzzy c partition is utilized to estimate the change points the method outperforms statistical likelihood approaches various experiments show the effectiveness and practicability of the proposed method excellent performance in detecting small changes is helpful for root cause analyses

lagrangian flows driven by bv fields in wiener spaces we establish the renormalization property for essentially bounded solutions of the continuity equation associated to bounded variation bv fields in wiener spaces with values in the associated cameron martin space thus obtaining by standard arguments new uniqueness and stability results for correspondent lagrangian flows

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

clustering of the self organizing map using a clustering validity index based on inter cluster and intra cluster density the self organizing map som has been widely used in many industrial applications classical clustering methods based on the som often fail to deliver satisfactory results specially when clusters have arbitrary shapes in this paper through some preprocessing techniques for filtering out noises and outliers we propose a new two level som based clustering algorithm using a clustering validity index based on inter cluster and intra cluster density experimental results on synthetic and real data sets demonstrate that the proposed clustering algorithm is able to cluster data better than the classical clustering algorithms based on the som and find an optimal number of clusters

a new method for stabilization of networked control systems with random delays we consider the stabilization problem for a class of networked control systems in the discrete time domain with random delays the sensor to controller and controller to actuator delays are modeled as two markov chains and the resulting closed loop systems are jump linear systems with two modes the necessary and sufficient conditions on the existence of stabilizing controllers are established it is shown that state feedback gains are mode dependent an iterative linear matrix inequality lmi approach is employed to calculate the state feedback gains

use of a fuzzy granulation degranulation criterion for assessing cluster validity the identification of a suitable clustering algorithm to partition data and assessment of the validity of the resultant partitioning are ongoing quests in unsupervised learning in this study a fuzzy granulation degranulation criterion is proposed to evaluate the goodness of a fuzzy partitioning of the data this in turn is used to determine the appropriate clustering algorithm suitable for a particular data set in general the quality of a partitioning is measured by computing the variance within it which is a measure of compactness of the obtained partitioning here a new error function which reflects how well the computed cluster centers represent the whole data set is used as the goodness measure of the obtained partitioning thus a clustering algorithm providing a good set of cluster centers which approximate well the whole data set is considered to be the most suited thereafter this new fuzzy granulation degranulation criterion is used to develop six new cluster validity indices these indices mimic the definitions of the existing and well known cluster validity indices such as pbm index xb index ps index fs index k index and sv index but use the new fuzzy granulation degranulation based error function instead of cluster compactness in order to evaluate the effectiveness of the proposed error function in correctly identifying the appropriate clustering algorithm for a particular data set eight well known clustering algorithms k means fuzzy c means gak means genetic algorithm based k means algorithm a newly developed genetic point symmetry based clustering technique gaps clustering average linkage clustering algorithm expectation maximization em clustering algorithm self organizing map som and spectral clustering technique are evaluated on a set of six artificially generated and six real life data sets results show that gak means is the most appropriate for most of the data sets used for the experiments thereafter the effectiveness of the proposed cluster validity indices in identifying the appropriate number of clusters automatically from different data sets are shown for above mentioned 12 data sets for the purpose of comparison results obtained with the original versions of the proposed cluster validity indices and results obtained by a density based clustering technique are also presented

cluster validity for the fuzzy c means clustering algorithrm the uniform data function is a function which assigns to the output of the fuzzy c means fc m or fuzzy isodata algorithm a number which measures the quality or validity of the clustering produced by the algorithm for the preselected number of cluster c the fc m algorithm produces c vectors in the space in which the data lie called cluster centers which represent points about which the data are concentrated it also produces for each data point c membership values numbers between zero and one which measure the similarity of the data points to each of the cluster centers it is these membership values which indicate how the point is classified they also indicate how well the point has been classified in that values close to one indicate that the point is close to a particular center but uniformly low memberships indicate that the point has not been classified clearly the uniform data functional udf combines the memberships in such a way as to indicate how well the data have been classified and is computed as follows for each data point compute the ratio of its smallest membership to its largest and then compute the probability that one could obtain a smaller ratio indicating better classification from a clustering of a standard data set in which there is no cluster structure these probabilities are then averaged over the data set to obtain the values of the udf

integration by parts formulae for wiener measures restricted to subsets in r d abstract we study an integration by parts formula for a pinned wiener measure restricted to a space of paths staying within a subset in r d the result presented here generalizes the formula in l zambotti integration by parts formulae on convex sets of paths and applications to spdes with reflection probab theory relat fields 123 2002 579 600 for the case of a half line in r

a new fuzzy clustering validity index with a median factor for centroid based clustering determining the number of clusters which is usually approved by domain experts or evaluated by clustering validity indexes is an important issue in clustering analysis this study discusses the effectiveness of clustering validity indexes for centroid based partitional clustering algorithms most general purpose clustering validity indexes take the minimum maximum distance between a pair of data objects a pair of cluster centroids or an object and a centroid as an important evaluation factor however they may present unstable results especially when two centroids are allocated closely to alleviate this problem a new clustering validity index which is termed the wu and li index wli is proposed in this paper our proposed wli partially allows to some extent the existence of closely allocated centroids in the clustering results by considering not only the minimum but the median distances between a pair of centroids as well therefore possessing better stability the performances of wli and some existing clustering validity indexes are evaluated and compared by running the fuzzy c means algorithm for clustering various types of datasets including artificial datasets uci datasets and images experimental results have shown that wli has the more accurate and satisfactory performance than other indexes

hierarchical unsupervised fuzzy clustering a recursive algorithm for hierarchical fuzzy partitioning is presented the algorithm has the advantages of hierarchical clustering while maintaining fuzzy clustering rules each pattern can have a nonzero membership in more than one subset of the data in the hierarchy optimal feature extraction and reduction is optionally reapplied for each subset combining hierarchical and fuzzy concepts is suggested as a natural feasible solution to the cluster validity problem of real data the convergence and membership conservation of the algorithm are proven the algorithm is shown to be effective for a variety of data sets with a wide dynamic range of both covariance matrices and number of members in each class

robust stability with structured real parameter perturbations this paper considers the problem of robust stabilization of a linear time invariant system subject to variations of a real parameter vector for a given controller the radius of the largest stability hypersphere in this parameter space is calculated this radius is a measure of the stability margin of the closed loop system the results developed are applicable to all systems where the closed loop characteristic polynomial coefficients are linear functions of the parameters of interest in particular this always occurs for single input multioutput or single output multiinput systems where the transfer function coefficients are linear or affine functions of the parameters many problems with transfer function coefficients which are nonlinear functions of physical parameters can be cast into this mathematical framework by suitable weighting and redefinition of functions of physical parameters as new parameters the largest stability hyperellipsoid for the case of weighted perturbations and a stability polytope in parameter space are also determined based on these calculations a design procedure is proposed to robustify a given stabilizing controller this algorithm iteratively enlarges the stability hypersphere or hyperellipsoid in parameter space and can be used to design a controller io stabilize a plant subject to given ranges of parameter excursions these results are illustrated by an example

a clustering procedure for exploratory mining of vector time series a two step procedure is developed for the exploratory mining of real valued vector multivariate time series using partition based clustering methods the proposed procedure was tested with model generated data multiple sensor based process data as well as simulation data the test results indicate that the proposed procedure is quite effective in producing better clustering results than a hidden markov model hmm based clustering method if there is a priori knowledge about the number of clusters in the data two existing validity indices were tested and found ineffective in determining the actual number of clusters determining the appropriate number of clusters in the case that there is no a priori knowledge is a known unresolved research issue not only for our proposed procedure but also for the hmm based clustering method and further development is necessary

output feedback stabilization of networked control systems with packet dropouts in this paper we discuss the modeling and control of a class of networked control systems ncss with packet dropouts for the cases that there may be packet dropouts in both the backward and the forward channels in the communication network and that the network induced delays are shorter than one sampling period the closed loop ncs is modeled as a discrete time switched system with four subsystems by using the asynchronous dynamical systems approach and the average dwell time method sufficient conditions for the exponential stability of the closed loop ncs are presented in terms of nonlinear matrix inequalities and the relation between the packet dropout rate and the stability of the closed loop ncs is explicitly established a procedure involving an iterative algorithm is proposed to design the observer based output feedback controllers lastly an illustrative example is given to demonstrate the effectiveness of the proposed results

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

fuzzy approximation relations on fuzzy n cell number space and their applications in classification in this paper the problems of fuzzy binary relations on fuzzy n cell number space and their applications are investigated firstly we have defined some fuzzy approximation relations on fuzzy n cell number space and studied their properties secondly as application we have developed an algorithmic version of classification in an imprecise or uncertain environment by using the fuzzy approximation relations practical examples are provided to show the application and rationality of the proposed techniques

the stochastic reflection problem on an infinite dimensional convex set and bv functions in a gelfand triple in this paper we introduce a definition of bv functions in a gelfand triple which is an extension of the definition of bv functions in atti accad naz lincei cl sci fis mat natur rend lincei 9 mat appl 21 2010 405 414 by using dirichlet form theory by this definition we can consider the stochastic reflection problem associated with a self adjoint operator a and a cylindrical wiener process on a convex set in a hilbert space h we prove the existence and uniqueness of a strong solution of this problem when is a regular convex set the result is also extended to the nonsymmetric case finally we extend our results to the case when k where k f l2 0 1 f 0

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

a possibilistic fuzzy c means clustering algorithm in 1997 we proposed the fuzzy possibilistic c means fpcm model and algorithm that generated both membership and typicality values when clustering unlabeled data fpcm constrains the typicality values so that the sum over all data points of typicalities to a cluster is one the row sum constraint produces unrealistic typicality values for large data sets in this paper we propose a new model called possibilistic fuzzy c means pfcm model pfcm produces memberships and possibilities simultaneously along with the usual point prototypes or cluster centers for each cluster pfcm is a hybridization of possibilistic c means pcm and fuzzy c means fcm that often avoids various problems of pcm fcm and fpcm pfcm solves the noise sensitivity defect of fcm overcomes the coincident clusters problem of pcm and eliminates the row sum constraints of fpcm we derive the first order necessary conditions for extrema of the pfcm objective function and use them as the basis for a standard alternating optimization approach to finding local minima of the pfcm objective functional several numerical examples are given that compare fcm and pcm to pfcm our examples show that pfcm compares favorably to both of the previous models since pfcm prototypes are less sensitive to outliers and can avoid coincident clusters pfcm is a strong candidate for fuzzy rule based system identification

sets of finite perimeter and the hausdorff gauss measure on the wiener space abstract in euclidean space the integration by parts formula for a set of finite perimeter is expressed by the integration with respect to a type of surface measure according to geometric measure theory this surface measure is realized by the one codimensional hausdorff measure restricted on the reduced boundary and or the measure theoretic boundary which may be strictly smaller than the topological boundary in this paper we discuss the counterpart of this measure in the abstract wiener space which is a typical infinite dimensional space we introduce the concept of the measure theoretic boundary in the wiener space and provide the integration by parts formula for sets of finite perimeter the formula is presented in terms of the integration with respect to the one codimensional hausdorff gauss measure restricted on the measure theoretic boundary