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

high breakdown point and high efficiency robust estimates for regression a class of robust estimates for the linear model is introduced these estimates called mm estimates have simultaneously the following properties i they are highly efficient when the errors have a normal distribution and ii their breakdown point is 0 5 the mm estimates are defined by a three stage procedure in the first stage an initial regression estimate is computed which is consistent robust and with high breakdown point but not necessarily efficient in the second stage an m estimate of the errors scale is computed using residuals based on the initial estimate finally in the third stage an m estimate of the regression parameters based on a proper redescending psi function is computed consistency and asymptotical normality of the mm estimates assuming random carriers are proved a convergent iterative numerical algorithm is given finally the asymptotic biases under contamination of optimal bounded influence estimates and mm estimates are compared

the stochastic location model with risk pooling abstract in this paper we present a stochastic version of the location model with risk pooling lmrp that optimizes location inventory and allocation decisions under random parameters described by discrete scenarios the goal of our model called the stochastic lmrp or slmrp is to find solutions that minimize the expected total cost including location transportation and inventory costs of the system across all scenarios the location model explicitly handles the economies of scale and risk pooling effects that result from consolidating inventory sites the slmrp framework can also be used to solve multi commodity and multi period problems we present a lagrangian relaxation based exact algorithm for the slmrp the lagrangian subproblem is a non linear integer program but it can be solved by a low order polynomial algorithm we discuss simple variable fixing routines that can drastically reduce the size of the problem we present quantitative and qualitative computational results on problems with up to 150 nodes and 9 scenarios describing both algorithm performance and solution behavior as key parameters change

neuro fuzzy system with learning tolerant to imprecision in this paper a new learning method tolerant to imprecision is introduced and used in neuro fuzzy modeling this method can be called e insensitive learning where in order to fit the fuzzy model to real data a weighted e insensitive loss function is used the proposed method makes it possible to exclude an intrinsic inconsistency of neuro fuzzy modeling where zero tolerance learning is used to obtain a fuzzy model tolerant to imprecision the e insensitive learning leads to a model with the minimal vapnik chervonenkis dimension complexity which results in improving generalization ability of this system and its robustness to outliers finally numerical examples are given to demonstrate the validity of the introduced method

switching regression models and fuzzy clustering a family of objective functions called fuzzy c regression models which can be used too fit switching regression models to certain types of mixed data is presented minimization of particular objective functions in the family yields simultaneous estimates for the parameters of c regression models together with a fuzzy c partitioning of the data a general optimization approach for the family of objective functions is given and corresponding theoretical convergence results are discussed the approach is illustrated by two numerical examples that show how it can be used to fit mixed data to coupled linear and nonlinear models

gaussian clustering method based on maximum fuzzy entropy interpretation abstract a new method of fuzzy clustering is proposed this is a complete gaussian membership function derived by means of the maximum entropy interpretation compared to the traditional fuzzy c means fcm method our approach exhibits the following two advantages 1 having clearer physical meaning and well defined mathematical features 2 having an optimal choice for feature parameter in theory moreover we also review some existing measures of uncertainty of fuzzy sets and redefine fuzzy entropy as analogous to probabilistic entropy

an axiomatic approach to soft learning vector quantization and clustering this paper presents an axiomatic approach to soft learning vector quantization lvq and clustering based on reformulation the reformulation of the fuzzy c means fcm algorithm provides the basis for reformulating entropy constrained fuzzy clustering ecfc algorithms according to the proposed approach the development of specific algorithms reduces to the selection of a generator function linear generator functions lead to the fcm and fuzzy learning vector quantization algorithms while exponential generator functions lead to ecfc and entropy constrained learning vector quantization algorithms the reformulation of lvq and clustering algorithms also provides the basis for developing uncertainty measures that can identify feature vectors equidistant from all prototypes these measures are employed by a procedure developed to make soft lvq and clustering algorithms capable of identifying outliers in the data set this procedure is evaluated by testing the algorithms generated by linear and exponential generator functions on speech data

generalized fuzzy c means clustering strategies using l sub p norm distances fuzzy c means fcm is a useful clustering technique modifications of fcm using l sub 1 norm distances increase robustness to outliers object and relational data versions of fcm clustering are defined for the more general case where the l sub p norm p spl ges 1 or semi norm 0 0 in order to facilitate the empirical examination of the object data models both object and relational approaches are included in a numerical study

on robust fuzzy c regression models one of the most popular clustering methods based on minimization of a criterion function is the fuzzy c means one its generalization by application of hyperplane shaped prototypes of the clusters is known as the fuzzy c regression models fcrm method although with this generalization many new applications of clustering emerged it appeared to be rather sensitive to poor initialization and to the presence of noise and outliers in data in this paper we introduce a new objective function using the huber s m estimators and the yager s owa operators to overcome the disadvantages of the approach considered we derive and describe an algorithm for minimization of the objective function defined we have called it the fuzzy c ordered regression models fcorm clustering algorithm the algorithm is compared to a few other important reference ones to this end experiments on synthetic data with various types of noise and different numbers of outliers are carried out we investigate the methods performance in the conditions that can be encountered in signal analysis large scale simulations demonstrate the competitiveness and usefulness of the method proposed

a generalization of distance functions for fuzzy c means clustering with centroids of arithmetic means fuzzy c means fcm is a widely used fuzzy clustering method which allows an object to belong to two or more clusters with a membership grade between zero and one despite the considerable efforts made by the clustering community the common characteristics of distance functions suitable for fcm remain unclear to fill this crucial void in this paper we first provide a generalized definition of distance functions that fit fcm directly the goal is to provide more flexibility to fcm in the choice of distance functions while preserving the simplicity of fcm by using the centroids of arithmetic means indeed we show that any distance function that fits fcm directly can be derived by a continuously differentiable convex function and thus is an instance of the generalized point to centroid distance p2c d by definition in addition we prove that if the membership grade matrix is nondegenerate any instance of the p2c d fits fcm directly finally extensive experiments have been conducted to demonstrate that the p2c d leads to the global convergence of fcm and that the clustering performances are significantly affected by the choices of distance functions

fuzzy clustering with structural constraints abstract in this paper we propose a generalization of the standard clustering problem which we call structural constrained clustering scc problem in scc problem the cluster interconnections are given by a binary relation r if this relation is empty then scc problem reduces to the standard classification problem the cluster structure imposed by r may be described by the covering graph of r for example if this graph is a rooted tree then a hierarchical structure is imposed to the clusters we formulate scc as a fuzzy clustering problem with prototype inter relation a general algorithm to solve this problem is proposed for three particular distance measures squared euclidean and l1 metric we compute the prototypes by solving a particular multifacility location problem

application of entropy and energy measures of fuzziness to processing of ecg signal the paper deals with the application of entropy and energy measure of fuzziness to processing of ecg signal after formulation of the problem the notion of entropy measure of fuzziness is recalled next the idea of a fuzzy signal created from the original signal is proposed and the entropy measure of fuzziness determined for each sample is calculated the application of this measure to building a detection function of ecg signal is presented the theoretical considerations have been illustrated with digital processing of the real ecg signal

a time domain constrained fuzzy clustering method and its application to signal analysis this paper introduces a new fuzzy clustering method with time domain constraints which is used to signal analysis proposed method makes it possible to include natural constraints for signal analysis using fuzzy clustering that is the neighboring samples of signal belong to the same cluster this method can be called time domain constrained fuzzy clustering this paper introduces two approaches to include the above kind of constraints the first approach leads to the time domain constrained fuzzy c regression models method the second approach leads to the insensitive version of the above method which results in additional robustness for outliers and non gaussian noise finally simulations on synthetic as well as real life signals are realized to evaluate the performance of the time domain constrained fuzzy clustering methods a comparison with the traditional fuzzy c regression models is also made large scale simulations demonstrate the competitiveness of the proposed methods for signal analysis with respect to the traditional fuzzy clustering methods

mercer kernel based clustering in feature space the article presents a method for both the unsupervised partitioning of a sample of data and the estimation of the possible number of inherent clusters which generate the data this work exploits the notion that performing a nonlinear data transformation into some high dimensional feature space increases the probability of the linear separability of the patterns within the transformed space and therefore simplifies the associated data structure it is shown that the eigenvectors of a kernel matrix which defines the implicit mapping provides a means to estimate the number of clusters inherent within the data and a computationally simple iterative procedure is presented for the subsequent feature space partitioning of the data

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

parameter estimation of k distributed sea clutter based on fuzzy inference and gustafson kessel clustering the detection performance of maritime radars is restricted by the unwanted sea echo or clutter although the number of these target like data is small they may cause false alarm and perturb the target detection k distribution is known as the best fit probability density function for the radar sea clutter this paper proposes a novel approach to estimate the parameters of k distribution based on fuzzy gustafson kessel clustering and fuzzy takagi sugeno kang modelling the main contribution of the proposed method is the ability to estimate the parameters given a small number of data which will usually be the case in practical applications this is achieved by a pre estimation using fuzzy clustering that provides a prior knowledge and forms a rough model to be fine tuned using the least square method the algorithm also improves the calculations of shape and width of membership functions by means of clustering in order to improve the accuracy the resultant estimator then acts to overcome the bottleneck of the existing methods in which it achieves a higher performance and accuracy in spite of small number of data

clustering algorithms based on volume criteria clustering algorithms such as the k means algorithm and the fuzzy c means algorithm are based on the minimization of the trace of the fuzzy within fluster scatter matrix in this paper we explore the use of determinant volume criteria for clustering we derive an algorithm called the minimum scatter volume msv algorithm that minimizes the scatter volume and another algorithm called the minimum cluster volume mcv that minimizes the sum of the volumes of the individual clusters the behavior of msv is shown to be similar to that of k means whereas mcv is more versatile

a new possibilistic clustering algorithm for line detection in real world imagery though promising in nature line detection algorithms based on fuzzy clustering suffer from excessive sensitivity to noise and non linear structures a new detection scheme is proposed here which is suitable for the processing of real world images possibilistic clustering is used instead of fuzzy clustering to achieve a higher immunity to noise whereas a set of criteria to eliminate non linear clusters is provided to take into account the presence of curved lines merging of segments is possible due to a fuzzy reasoning module exploiting human perception considerations the number of parameters to be set is kept to a minimum thus ensuring generality and robustness tests confirm the ability of the proposed system in interpreting the linear structures present in the image

an integrated approach to fuzzy learning vector quantization and fuzzy c means clustering derives an interpretation for a family of competitive learning algorithms and investigates their relationship to fuzzy c means and fuzzy learning vector quantization these algorithms map a set of feature vectors into a set of prototypes associated with a competitive network that performs unsupervised learning derivation of the new algorithms is accomplished by minimizing an average generalized distance between the feature vectors and prototypes using gradient descent a close relationship between the resulting algorithms and fuzzy c means is revealed by investigating the functionals involved it is also shown that the fuzzy c means and fuzzy learning vector quantization algorithms are related to the proposed algorithms if the learning rate at each iteration is selected to satisfy a certain condition

a solvable lie algebra condition for stability of linear multidimensional systems this note analyzes exponential stability of a class of linear discrete multidimensional systems using a multidimensional comparison principle for estimating the system componentwise exponential convergence and a solvable lie algebra condition a sufficient condition for exponential stability of linear multidimensional systems is presented the stability condition can be easily examined by computing the system matrices in finite steps this is demonstrated by an example

detection of influential observation in linear regression a new measure based on confidence ellipsoids is developed for judging the contribution of each data point to the determination of the least squares estimate of the parameter vector in full rank linear regression models it is shown that the measure combines information from the studentized residuals and the variances of the residuals and predicted values two examples are presented

fuzzy clustering and switching regression models using ambiguity and distance rejects abstract this paper examines how reject options can be used in performing fuzzy clustering and switching regression models we define an objective function in which reject options are introduced to optimization of certain clustering models this approach can be directly applied to any clustering model which can be represented as a functional dependent upon a set of cluster centers the approach can be further generalized for models that require parameters other than the cluster centers two types of reject have been included 1 the ambiguity reject which concerns patterns lying near the cluster boundaries or in the case of switching regression problems the data points which fit several models equally well 2 the distance or error reject dealing with patterns that are far away from all the clusters clustering and fuzzy c regression algorithms such as fcm fuzzy c means and fcrm fuzzy c regression models which use calculus based optimization methods suffer from several drawbacks they are very sensitive to the presence of noise moreover the memberships are relative numbers the membership of a point in a cluster depends on the membership of the point in all other clusters so the cluster centers or estimates for the parameters are poor this can be a serious problem in situations where one wishes to generate membership functions from training data this paper provides answers to these problems to avoid the memberships to be spread across the clusters and to allow the distinction between equally likely and unknown we define partial ambiguity rejects which introduce a discounting process between the classical fcm or fcrm membership functions to improve the performance of our algorithm in the presence of noise we use an amorphous noise cluster defined in demko et al actes des sixiemes rencontres del la societe francophone de classification montpellier france september 1998 to compute these rejects we propose an extension of fcrm algorithm hathaway and bezdek ieee trans fuzzy systems 1 3 1993 195 203 this algorithm is called the fuzzy c 2 regression model fc 2rm preliminary computational experiences on the developed algorithm are encouraging and compare favorably with results from other methods as fcrm and afc algorithms on the same data sets

fuzzy c ordered means clustering fuzzy clustering helps to find natural vague boundaries in data the fuzzy c means method is one of the most popular clustering methods based on minimization of a criterion function however one of the greatest disadvantages of this method is its sensitivity to the presence of noise and outliers in data this paper introduces a new robust fuzzy clustering method named fuzzy c ordered means fcom clustering this method uses both the huber s m estimators and the yager s owa operators to obtain its robustness the proposed method is compared to many other ones e g the fuzzy c means fcm the possibilistic clustering pc the fuzzy noise clustering method ncm the l p norm clustering l p fcm 0 p 1 the l 1 norm clustering l 1 fcm the fuzzy clustering with polynomial fuzzifier pfcm and the e insensitive fuzzy c means fcm to this end experiments on synthetic data with outliers have been performed as well as on data with heavy tailed and overlapping groups of points in background noise

fuzzy and possibilistic shell clustering algorithms and their application to boundary detection and surface approximation ii shell clustering algorithms are ideally suited for computer vision tasks such as boundary detection and surface approximation particularly when the boundaries have jagged or scattered edges and when the range data is sparse this is because shell clustering is insensitive to local aberrations it can be performed directly in image space and unlike traditional approaches it does assume dense data and does not use additional features such as curvatures and surface normals the shell clustering algorithms introduced in part i of this paper assume that the number of clusters is known however which is not the case in many boundary detection and surface approximation applications this problem can be overcome by considering cluster validity we introduce a validity measure called surface density which is explicitly meant for the type of applications considered in this paper we show through theoretical derivations that surface density is relatively invariant to size and partiality incompleteness of the clusters we describe unsupervised clustering algorithms that use the surface density measure and other measures to determine the optimum number of shell clusters automatically and illustrate the application of the proposed algorithms to boundary detection in the case of intensity images and to surface approximation in the case of range images

exponential stability of 2 d systems exponential stability of 2 d systems is defined and characterized the definition of exponential stability works also with unbounded data as for the case of 1 d systems we show in particular that exponential stability and asymptotic stability are equivalent properties

specially structured uncapacitated facility location problems this paper considers a specially structured uncapacitated facility location problem we show that several problems including certain tool selection problems substitutable inventory problems supplier sourcing problems discrete lot sizing problems and capacity expansion problems can be formulated as instances of the problem we also show that the problem with m facilities and n customers can be solved in o mn as a shortest path problem on a directed graph

a kernel fuzzy c means clustering based fuzzy support vector machine algorithm for classification problems with outliers or noises the support vector machine svm has provided higher performance than traditional learning machines and has been widely applied in real world classification problems and nonlinear function estimation problems unfortunately the training process of the svm is sensitive to the outliers or noises in the training set in this paper a common misunderstanding of gaussian function based kernel fuzzy clustering is corrected and a kernel fuzzy c means clustering based fuzzy svm algorithm kfcm fsvm is developed to deal with the classification problems with outliers or noises in the kfcm fsvm algorithm we first use the fcm clustering to cluster each of two classes from the training set in the high dimensional feature space the farthest pair of clusters where one cluster comes from the positive class and the other from the negative class is then searched and forms one new training set with membership degrees finally we adopt fsvm to induce the final classification results on this new training set the computational complexity of the kfcm fsvm algorithm is analyzed a set of experiments is conducted on six benchmarking datasets and four artificial datasets for testing the generalization performance of the kfcm fsvm algorithm the results indicate that the kfcm fsvm algorithm is robust for classification problems with outliers or noises

robust clustering methods a unified view clustering methods need to be robust if they are to be useful in practice in this paper we analyze several popular robust clustering methods and show that they have much in common we also establish a connection between fuzzy set theory and robust statistics and point out the similarities between robust clustering methods and statistical methods such as the weighted least squares technique the m estimator the minimum volume ellipsoid algorithm cooperative robust estimation minimization of probability of randomness and the epsilon contamination model by gleaning the common principles upon which the methods proposed in the literature are based we arrive at a unified view of robust clustering methods we define several general concepts that are useful in robust clustering state the robust clustering problem in terms of the defined concepts and propose generic algorithms and guidelines for clustering noisy data we also discuss why the generalized hough transform is a suboptimal solution to the robust clustering problem

soft learning vector quantization and clustering algorithms based on ordered weighted aggregation operators this paper presents the development and investigates the properties of ordered weighted learning vector quantization lvq and clustering algorithms these algorithms are developed by using gradient descent to minimize reformulation functions based on aggregation operators an axiomatic approach provides conditions for selecting aggregation operators that lead to admissible reformulation functions minimization of admissible reformulation functions based on ordered weighted aggregation operators produces a family of soft lvq and clustering algorithms which includes fuzzy lvq and clustering algorithms as special cases the proposed lvq and clustering algorithms are used to perform segmentation of magnetic resonance mr images of the brain the diagnostic value of the segmented mr images provides the basis for evaluating a variety of ordered weighted lvq and clustering algorithms

fuzzy weighted c ordered means clustering algorithm abstract in real life data sets some attributes may have lower importance or even may be completely noninformative the subspace clustering algorithms have been proposed to handle this the soft subspace algorithms are vulnerable to noise and outliers the paper presents a novel algorithm that handles both various importance of attributes and outliers the proposed fuzzy weighted c ordered mean fwcom clustering algorithm elaborates clusters in soft subspaces in each cluster each attribute is assigned a weight from interval 0 1 each attribute has its individual weight importance in each cluster the proposed algorithm applies the ordering technique to effectively reduce the influence of outliers and noise the paper is accompanied by numerical experiments

a method of identifying influential data in fuzzy clustering in multivariate statistical methods it is important to identify influential observations for a reasonable interpretation of the data structure in this paper we propose a method for identifying influential data in the fuzzy c means fcm algorithm to investigate such data we consider a perturbation of the data points and evaluate the effect of a perturbation as a perturbation we consider two cases one is the case in which the direction of a perturbation is specified and the other is the case in which the direction of a perturbation is not specified by computing the change in the clustering result of fcm when given data points are slightly perturbed we can look for data points that greatly affect the result also we confirm an efficacy of the proposed method by numerical examples

generalized weighted conditional fuzzy clustering fuzzy clustering helps to find natural vague boundaries in data the fuzzy c means method is one of the most popular clustering methods based on minimization of a criterion function among many existing modifications of this method conditional or context dependent c means is the most interesting one in this method data vectors are clustered under conditions based on linguistic terms represented by fuzzy sets this paper introduces a family of generalized weighted conditional fuzzy c means clustering algorithms this family include both the well known fuzzy c means method and the conditional fuzzy c means method performance of the new clustering algorithm is experimentally compared with fuzzy c means using synthetic data with outliers and the box jenkins database

stability of switched systems a lie algebraic condition we present a sucient condition for asymptotic stability of a switched linear system in terms of the lie algebra generated by the individual matrices namely if this lie algebra is solvable then the switched system is exponentially stable for arbitrary switching in fact we show that any family of linear systems satisfying this condition possesses a quadratic common lyapunov function we also discuss the implications of this result for switched nonlinear systems c 1999 elsevier science b v all rights reserved

fuzzy order statistics and their application to fuzzy clustering the median and the median absolute deviation mad are robust statistics based on order statistics order statistics are extended to fuzzy sets to define a fuzzy median and a fuzzy mad the fuzzy c means fcm clustering algorithm is defined for any p norm pfcm including the l sub 1 norm 1fcm the 1fcm clustering algorithm is implemented via the alternating optimization ao method and the clustering centers are shown to be the fuzzy median the resulting ao 1fcm clustering algorithm is called the fuzzy c medians fcmed clustering algorithm an example illustrates the robustness of the fcmed

fuzzy c ordered medoids clustering for interval valued data fuzzy clustering for interval valued data helps us to find natural vague boundaries in such data the fuzzy c medoids clustering fcmdc method is one of the most popular clustering methods based on a partitioning around medoids approach however one of the greatest disadvantages of this method is its sensitivity to the presence of outliers in data this paper introduces a new robust fuzzy clustering method named fuzzy c ordered medoids clustering for interval valued data fcomdc id the huber s m estimators and the yager s ordered weighted averaging owa operators are used in the method proposed to make it robust to outliers the described algorithm is compared with the fuzzy c medoids method in the experiments performed on synthetic data with different types of outliers a real application of the fcomdc id is also provided highlightsfuzzy clustering for interval valued data helps us to find natural vague boundaries in such data a new robust fuzzy clustering method named fuzzy c ordered medoids clustering for interval valued data fcomdc id is proposedthe method uses both the huber s m estimators and the yager s owa operators to obtain its robustness experiments performed on synthetic data with different types of outliers and a real application are provided

a dual based procedure for stochastic facility location in this paper we study how the uncapacitated facility location problem is transformed into a two stage stochastic program with recourse when uncertainty on demand selling prices production and transportation costs are introduced we then present a dual based procedure and indicate how the dual descent and primal dual adjustment procedures proposed by d erlenkotter 1978 in the static case can be made monotonically improving in the stochastic case results of computer experiments are reported

partitional fuzzy clustering methods based on adaptive quadratic distances this paper presents partitional fuzzy clustering methods based on adaptive quadratic distances the methods presented furnish a fuzzy partition and a prototype for each cluster by optimizing an adequacy criterion based on adaptive quadratic distances these distances change at each algorithm iteration and can either be the same for all clusters or different from one cluster to another moreover various fuzzy partition and cluster interpretation tools are introduced experiments with real and synthetic data sets show the usefulness of these adaptive fuzzy clustering methods and the merit of the fuzzy partition and cluster interpretation tools

scenarios and policy aggregation in optimization under uncertainty a common approach in coping with multiperiod optimization problems under uncertainty where statistical information is not really enough to support a stochastic programming model has been to set up and analyze a number of scenarios the aim then is to identify trends and essential features on which a robust decision policy can be based this paper develops for the first time a rigorous algorithmic procedure for determining such a policy in response to any weighting of the scenarios the scenarios are bundled at various levels to reflect the availability of information and iterative adjustments are made to the decision policy to adapt to this structure and remove the dependence on hindsight

towards a robust fuzzy clustering fuzzy clustering helps to find natural vague boundaries in data the fuzzy c means method fcm is one of the most popular clustering methods based on minimization of a criterion function however one of the greatest disadvantages of this method is its sensitivity to presence of noise and outliers in data this paper introduces a new e insensitive fuzzy c means efcm clustering algorithm as a special case this algorithm includes the well known fuzzy c medians method fcmed also methods with insensitivity control named fcm and fcm are introduced performance of the new clustering algorithm is experimentally compared with the fcm method using synthetic data with outliers and heavy tailed and overlapped groups of data in background noise

stability analysis of multidimensional m d direct realization digital filters under the influence of nonlinearities a stability test of m d direct realization digital filters with nonlinearities such as quantization overflow saturation etc is presented the method presented reduces a given nonlinear m d system to a nonlinear 1 d system such that the stability of the latter is sufficient for the stability of the former to check stability of the nonlinear 1 d system some new results on 1 d recursive systems with positive coefficients are applied the case of multiple nonlinearities in multidimensions is also addressed examples are given illustrating the application of the method

fuzzy clustering in cell formation with multiple attributes an approach based on fuzzy clustering and aggregation operators is proposed to design cell formation involving multiple criteria or multiple attributes the three most basic attributes in cell formation namely number of machines required processing time and common tools required on machines are considered the results are compared with the single attribute results of chu and hayya 1991 27

a hybrid modified pso approach to var based facility location problems with variable capacity in fuzzy random uncertainty this paper studies a facility location model with fuzzy random parameters and its swarm intelligence approach a value at risk var based fuzzy random facility location model var frflm is built in which both the costs and demands are assumed to be fuzzy random variables and the capacity of each facility is unfixed but a decision variable assuming continuous values under this setting the var frflm is inherently a two stage mixed 0 1 integer fuzzy random programming problem to which analytical nonlinear programming methods are not applicable a hybrid modified particle swarm optimization mpso approach is proposed to solve the var frflm in this hybrid mechanism an approximation algorithm is utilized to compute the fuzzy random var objective a continuous nbest gbest based pso and a genotype phenotype based binary pso vehicles are designed to deal with the continuous capacity decisions and the binary location decisions respectively and two mutation operators are incorporated into the pso to further decrease the possibility of becoming trapped in the local optima a numerical experiment illustrates the application of the proposed hybrid mpso algorithm and lays out its robustness to the system parameter settings the comparison shows that the hybrid mpso exhibits better performance than that when hybrid regular continuous binary pso and genetic algorithm ga are used to solve the var frflm

solving a class of stochastic mixed integer programs with branch and price we begin this paper by identifying a class of stochastic mixed integer programs that have column oriented formulations suitable for solution by a branch and price algorithm b p we then survey a number of examples and use a stochastic facility location problem sflp for a detailed demonstration of the relevant modeling and solution techniques computational results with a scenario representation of uncertain costs demands and capacities show that b p can be orders of magnitude faster than solving the standard formulation by branch and bound we also demonstrate how b p can solve sflp exactly as exactly as a deterministic mixed integer program when demands and other parameters can be represented as certain types of independent random variables e g independent normal random variables with integer means and variances

the simple plant location problem survey and synthesis abstract with emphasis on the simple plant location problem splp we consider an important family of discrete deterministic single criterion np hard and widely applicable optimization problems the introductory discussion on problem formulation aspects is followed by the establishment of relationships between splp and set packing set covering and set partitioning problems which all are among those structures in integer programming having the most wide spread applications an extensive discourse on solution properties and computational techniques spanning from early heuristics to the presumably most novel exact methods is then provided other subjects of concern include a subfamily of splp s solvable in polynomial time analyses of approximate algorithms transformability of p center and p median to splp and structural properties of the splp polytope along the way we attempt to synthesize these findings and relate them to other areas of integer programming

the fuzzy c spherical shells algorithm a new approach the fuzzy c spherical shells fcss algorithm is specially designed to search for clusters that can be described by circular arcs or generally by shells of hyperspheres a new approach to the fcss algorithm is presented this algorithm is computationally and implementationally simpler than other clustering algorithms that have been suggested for this purpose an unsupervised algorithm which automatically finds the optimum number of clusters is not known it uses a cluster validity measure to identify good clusters merges all compatible clusters and eliminates spurious clusters to achieve the final results experimental results on several data sets are presented

fuzzy c varieties elliptotypes clustering in reproducing kernel hilbert space abstract fuzzy clustering algorithms are successfully applied to a wide variety of problems such as pattern recognition image analysis modeling and so on the fuzzy c means fcm method is one of the most popular clustering methods based on the minimization of a criterion function however the performance of the fcm method is good only when a data set contains clusters that are approximately the same size and shape in this paper a simple idea will be used to overcome this problem the original input data space will be mapped into the high possibly infinite dimensional feature space f through some nonlinear mapping in this space the data structures will be modeled by the linear varieties or elliptotypes this method is called kernel fuzzy c varieties elliptotypes clustering algorithm performance of the new clustering algorithm is experimentally compared with fcm and fuzzy c varieties elliptotypes methods using synthetic datasets and real life datasets

hedging uncertainty approximation algorithms for stochastic optimization problems we study two stage finite scenario stochastic versions of several combinatorial optimization problems and provide nearly tight approximation algorithms for them our problems range from the graph theoretic shortest path vertex cover facility location to set theoretic set cover bin packing and contain representatives with different approximation ratios the approximation ratio of the stochastic variant of a typical problem is found to be of the same order of magnitude as its deterministic counterpart furthermore we show that common techniques for designing approximation algorithms such as lp rounding the primal dual method and the greedy algorithm can be adapted to obtain these results

l 1 norm based fuzzy clustering abstract the paper presents the l1 version of the well known fuzzy clustering method namely fuzzy isodata proposed by bezdek and dunn due to their robustness l1 norm based methods gained much attention in statistics the presented fuzzy clustering problem uses the distance between observations and location parameter vectors which is based on the l1 norm instead of the inner product induced norm used in classical fuzzy isodata two alternative methods to solve the l1 fuzzy clustering problem are derived in practice both membership grades and location parameter vectors are unknown the paper presents two iterative algorithms each the implementation of the derived method finally numerical examples are presented one of them refers to famous iris data

stochastic uncapacitated hub location we study stochastic uncapacitated hub location problems in which uncertainty is associated to demands and transportation costs we show that the stochastic problems with uncertain demands or dependent transportation costs are equivalent to their associated deterministic expected value problem evp in which random variables are replaced by their expectations in the case of uncertain independent transportation costs the corresponding stochastic problem is not equivalent to its evp and specific solution methods need to be developed we describe a monte carlo simulation based algorithm that integrates a sample average approximation scheme with a benders decomposition algorithm to solve problems having stochastic independent transportation costs numerical results on a set of instances with up to 50 nodes are reported

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