design of fuzzy control systems with guaranteed stability abstract this paper addresses the analysis and design of fuzzy control systems the fuzzy systems are represented by a family of local state space models with aggregation the controller is designed by considering each local state feedback controller and a compensating controller the compensating controller is based on the well known variable structure control theory it is shown that this controller guarantees global stability of the closed loop fuzzy system the issues of a state observer for the fuzzy system is also addressed a numerical example and an example of nonlinear system control are given for demonstration of the performance of the method

design and analysis of optimal controller for fuzzy systems with input constraint in this paper we present a design method of the optimal and robust controller subject to the constraint on control inputs for continuous time takagi sugeno ts fuzzy systems in order to establish this design method we consider an optimal and robust control problem for nonlinear dynamic systems for this problem we present an analytic way which can provide the optimal controller for nonlinear dynamic systems by the dynamic programming approach and the inverse optimal approach moreover we analyze the robustness property of the proposed optimal controller with respect to a class of input uncertainties by the passivity approach then based on the theoretical results presented in this paper we formulate the design problem of the optimal and robust controller with input constraint for continuous time ts fuzzy systems as the semidefinite programming problem and find the controller by solving it the usefulness of the proposed approach is illustrated by considering the three axis attitude stabilization problem of rigid spacecraft

robust fuzzy clustering of relational data popular relational data clustering algorithms relational dual of fuzzy c means rfcm non euclidean rfcm nerfcm both by hathaway et al and fanny by kaufman and rousseeuw are examined a new algorithm which is a generalization of fanny called the fuzzy relational data clustering frc algorithm is introduced having an identical objective functional as rfcm however the frc does not have the restriction of rfcm which is that the relational data is derived from euclidean distance as the measure of dissimilarity between the objects and it also does not have limitations of fanny including the use of a fixed membership exponent or a fuzzifier exponent m the frc algorithm is further improved by incorporating the concept of dave s object data noise clustering nc algorithm done by proposing a concept of noise dissimilarity next based on the constrained minimization which includes an inequality constraint for the memberships and corresponding kuhn tucker conditions a noise resistant frc algorithm is derived which works well for all types of non euclidean dissimilarity data thus it is shown that the extra computations for data expansion spl beta spread transformation required by the nerfcm algorithm are not necessary this new algorithm is called robust non euclidean fuzzy relational data clustering robust ne frc and its robustness is demonstrated through several numerical examples advantages of this new algorithm are faster convergence robustness against outliers and ability to handle all kinds of relational data including non euclidean the paper also presents a new and better interpretation of the noise class

implicit solutions of incompressible navier stokes equations using the pressure gradient method a modified pressure gradient method is developed for solving the incompressible twoand three dimensional navier stokes equations in primitive variables velocity and pressure gradient vectors rather than the velocity and pressure are considered as dependent variables this choice of the dependent variables is consistent with the flow physics as the velocity field of incompressible flows is not dependent on the pressure but rather the pressure gradient this introduces one and two additional dependent variables for two and three dimensions respectively to close the system of equations additional equations are obtained from the identity that the curl of the pressure gradient is zero this choice of dependent variables also leads to dirichlet boundary conditions for the pressure gradient which improves numerical stability and convergence rates the modified pressure gradient method includes a pressure gradient averaging term in the momentum equations to stabilize the solution this term is extended here to general curvilinear coordinates the system of equations is discritized using a conservative finite volume formulation time integration is achieved with a fully implicit scheme including implicit boundary conditions the implicit scheme guarantees that continuity is satisfied to machine zero numerical results compare well with solutions available in the literature for the cavity flow problem and flow about a circular cylinder at reynolds number 40

application of time iterative schemes to incompressible flow the computation of steady incompressible flows by an euler implicit algorithm is studied using both the incompressible equations and the low mach number compressible equations the incompressible equations are handled by adding an artificial time derivative to the continuity equation this allows both the pressure and velocity to be obtained implicitly in one dimensional problems both systems converge rapidly even at low mach numbers where the eigenvalues are very stiff in two dimensions where approximate factorization is required the presence of stiff eigenvalues is highly detrimental stiffness can be avoided in the incompressible equations by selecting an appropriate pseudo mach number this insures reliable convergence and results in an efficient incompressible flow algorithm in the case of compressible equations the mach number cannot be chosen arbitrarily and the contamination introduced by approximate factorization must be removed a matrix preconditioning factor that accomplishes this is developed and demonstrated with this modification the convergence rate is the same as in the incompressible case and is independent of mach number rapid convergence is observed at mach numbers as low as 6 05

robust self learning fuzzy controller design for a class of nonlinear mimo systems a new learning paradigm that can be applied for the design of a fuzzy logic based learning controller that is robust to external signals such as disturbances and set point changes is proposed in the paper it is well known that the self organizing fuzzy controller proposed by procyk and mamdani is sensitive to external signals such a phenomenon may be observed in other types of direct fuzzy logic based learning controllers that utilize an adaptation scheme in which the locational information of the current error state vector determines the degree of adaptation that should be made in the learning controller to resolve the problem of sensitivity to external signals it is proposed that learning and modification of the controller be made in consideration of the motional trend of the error state vector as well as its locational information this paradigm is adopted in the design of a new robust self learning fuzzy controller for a class of nonlinear mimo systems the well known techniques of sliding mode control and the fuzzy decision making method are utilized to implement the proposed learning scheme in the fuzzy learning controller via simulation study and experimental results the proposed learning controller is verified to be robust in the presence of external disturbances

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

a methodology for dynamic data mining based on fuzzy clustering dynamic data mining is increasingly attracting attention from the respective research community on the other hand users of installed data mining systems are also interested in the related techniques and will be even more since most of these installations will need to be updated in the future for each data mining technique used we need different methodologies for dynamic data mining in this paper we present a methodology for dynamic data mining based on fuzzy clustering using the implementation of the proposed system we show its benefits in two application areas customer segmentation and traffic management

cumulative voting consensus method for partitions with variable number of clusters over the past few years there has been a renewed interest in the consensus clustering problem several new methods have been proposed for finding a consensus partition for a set of n data objects that optimally summarizes an ensemble in this paper we propose new consensus clustering algorithms with linear computational complexity in n we consider clusterings generated with a random number of clusters which we describe by categorical random variables we introduce the idea of cumulative voting as a solution for the problem of cluster label alignment where unlike the common one to one voting scheme a probabilistic mapping is computed we seek a first summary of the ensemble that minimizes the average squared distance between the mapped partitions and the optimal representation of the ensemble where the selection criterion of the reference clustering is defined based on maximizing the information content as measured by the entropy we describe cumulative vote weighting schemes and corresponding algorithms to compute an empirical probability distribution summarizing the ensemble given the arbitrary number of clusters of the input partitions we formulate the problem of extracting the optimal consensus as that of finding a compressed summary of the estimated distribution that preserves the maximum relevant information an efficient solution is obtained using an agglomerative algorithm that minimizes the average generalized jensen shannon divergence within the cluster the empirical study demonstrates significant gains in accuracy and superior performance compared to several recent consensus clustering algorithms

implicit solution of the incompressible navier stokes equations on a non staggered grid abstract this paper presents an implicit procedure for the solution of the incompressible navier stokes equations in primitive variables the time dependent momentum equations are solved implicitly for the velocity field using the approximate factorization technique the continuity equation is satisfied at each time step through the solution of a poisson type equation for the static pressure a consistent finite difference scheme which satisfies the compatibility condition using a non staggered grid is used in the finite difference approximation of the static pressure poisson equation the results of the numerical computations in a driven cavity which are presented for the history of the residues at several reynolds numbers using different computational parameters demonstrate the excellent convergence characteristics of the solution procedure a stability analysis is conducted for the non iterative phase and numerical results are presented for a given set of compational parameters numerical results obtained for the steady state static pressure in the driven cavity are presented for the first time at re 1000 using a non staggered grid and the steady state velocity vorticity and pressure contours at re 100 400 and 1000 are compared with the computational results of other investigators additional results using a curvilinear grid are also presented for the flow in a cascade of circular airfoils at re 1000

parallel processing for implicit solutions of the navier stokes equations an implicit scheme employing superposition of two three one dimensional solutions in two three dimensions is proposed for the solution of navier stokes equations is proposed boundary conditions are implemented in the discrete governing equations before the super position takes place hence no boundary conditions are needed for the one dimensional solutions details of the method as well as numerical confirmation of the analytical developments are discussed 9 refs

robustness of fuzzy logic control for an uncertain dynamic system based on the similarity between prevalent fuzzy logic controllers flc and the conventional robust controller i e the variable structure controller control theoretic analysis of a fuzzy control system is presented in the sense of lyapunov as well as the robustness of the fuzzy control system against uncertainties of a controlled process this analysis gives an account of the relationship between control performance and the design parameters of the flc which has been obscure in the theory of fuzzy control

a hybrid ψ v hoc approach for surface tension driven flows in level set framework abstract in this study a higher order compact hoc finite difference scheme is proposed for the simulation of multiphase flows with surface tension effects by coupling the pure streamfunction formulation of navier stokes n s equations with the level set method unlike most of the existing methods for multiphase flows that solve the incompressible navier stokes equations in the velocity pressure form or the stream function vorticity form we recast the governing equations into the biharmonic form of the n s equations which carries stream function as the only variable to be computed the coupling of this formulation with level set ls enables the simulation of two phase flows by the core computation of only the single variable free from discontinuities in the whole physical domain in the process we also propose a novel hybrid hoc algorithm for post processing the pressure on either side of the interface including the jump across it the robustness of this method is established through a series of benchmark problems such as dispersion of capillary waves static bubble and oscillating bubble at equilibrium in a fluid at rest and deforming circular drops in shear flows we compare our numerical results with available benchmark results and excellent match is obtained in all the cases along with accurate representation of overall trends our approach is proved to be very efficient in terms of its easy implementation relatively low computational time and high order of accuracy

cluster ensembles a knowledge reuse framework for combining multiple partitions this paper introduces the problem of combining multiple partitionings of a set of objects into a single consolidated clustering without accessing the features or algorithms that determined these partitionings we first identify several application scenarios for the resultant knowledge reuse framework that we call cluster ensembles the cluster ensemble problem is then formalized as a combinatorial optimization problem in terms of shared mutual information in addition to a direct maximization approach we propose three effective and efficient techniques for obtaining high quality combiners consensus functions the first combiner induces a similarity measure from the partitionings and then reclusters the objects the second combiner is based on hypergraph partitioning the third one collapses groups of clusters into meta clusters which then compete for each object to determine the combined clustering due to the low computational costs of our techniques it is quite feasible to use a supra consensus function that evaluates all three approaches against the objective function and picks the best solution for a given situation we evaluate the effectiveness of cluster ensembles in three qualitatively different application scenarios i where the original clusters were formed based on non identical sets of features ii where the original clustering algorithms worked on non identical sets of objects and iii where a common data set is used and the main purpose of combining multiple clusterings is to improve the quality and robustness of the solution promising results are obtained in all three situations for synthetic as well as real data sets

convergence of the single pass and online fuzzy c means algorithms scalable versions of the widely used fuzzy c means clustering algorithm called single pass fuzzy c means and online fuzzy c means have been recently introduced both algorithms facilitate scaling to very large numbers of examples while providing partitions that very closely approximate those one would obtain using fuzzy c means both algorithms have been successfully applied to a number of datasets most notably magnetic resonance image volumes of the human brain in this letter we show that weighting examples in the fuzzy c means algorithm does not cause a violation in its convergence proof and we provide a separate proof of convergence that holds for any dataset

combining image compression and classification using vector quantization we describe a method of combining classification and compression into a single vector quantizer by incorporating a bayes risk term into the distortion measure used in the quantizer design algorithm once trained the quantizer can operate to minimize the bayes risk weighted distortion measure if there is a model providing the required posterior probabilities or it can operate in a suboptimal fashion by minimizing the squared error only comparisons are made with other vector quantizer based classifiers including the independent design of quantization and minimum bayes risk classification and kohonen s lvq a variety of examples demonstrate that the proposed method can provide classification ability close to or superior to learning vq while simultaneously providing superior compression performance

an approach to fuzzy control of nonlinear systems stability and design issues presents a design methodology for stabilization of a class of nonlinear systems first the authors represent a nonlinear plant with a takagi sugeno fuzzy model then a model based fuzzy controller design utilizing the concept of the so called parallel distributed compensation is employed the main idea of the controller design is to derive each control rule so as to compensate each rule of a fuzzy system the design procedure is conceptually simple and natural moreover the stability analysis and control design problems can be reduced to linear matrix inequality lmi problems therefore they can be solved efficiently in practice by convex programming techniques for lmis the design methodology is illustrated by application to the problem of balancing and swing up of an inverted pendulum on a cart

the discrete continuity equation in primitive variable solutions of incompressible flow abstract the use of a non staggered computational grid for the numerical solutions of the incompressible flow equations has many advantages over the use of a staggered grid a penalty however is inherent in the finite difference approximations of the governing equations on non staggered grids in the primitive variable solutions the penalty is that the discrete continuity equation does not converge to machine accuracy rather it converges to a source term which is proportional to the fourth order derivative of the pressure the time increment and the square of the grid spacing an approach which minimizes the error in the discrete continuity equation is developed numerical results obtained for the driven cavity problem confirm the analytical developments

multiple kernel fuzzy clustering while fuzzy c means is a popular soft clustering method its effectiveness is largely limited to spherical clusters by applying kernel tricks the kernel fuzzy c means algorithm attempts to address this problem by mapping data with nonlinear relationships to appropriate feature spaces kernel combination or selection is crucial for effective kernel clustering unfortunately for most applications it is uneasy to find the right combination we propose a multiple kernel fuzzy c means mkfc algorithm that extends the fuzzy c means algorithm with a multiple kernel learning setting by incorporating multiple kernels and automatically adjusting the kernel weights mkfc is more immune to ineffective kernels and irrelevant features this makes the choice of kernels less crucial in addition we show multiple kernel k means to be a special case of mkfc experiments on both synthetic and real world data demonstrate the effectiveness of the proposed mkfc algorithm

the generalized c index for internal fuzzy cluster validity the c index is an internal cluster validity index that was introduced in 1970 as a way to define and identify a best crisp partition on n objects represented by either unlabeled feature vectors or dissimilarity matrix data this index is often one of the better performers among the plethora of internal indices available for this task this paper develops a soft generalization of the c index that can be used to evaluate sets of candidate partitions found by either fuzzy or probabilistic clustering algorithms we define four generalizations based on relational transformations of the soft partition and then compare their performance to eight other popular internal fuzzy cluster indices using two methods of comparison internal best c and internal external i e best match six synthetic datasets and six real world labeled datasets our main conclusion is that the sum min generalization is the second best performer in the best c tests and the best performer in the i e tests on small data

toward a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic there are three basic concepts that underlie human cognition granulation organization and causation informally granulation involves decomposition of whole into parts organization involves integration of parts into whole and causation involves association of causes with effects granulation of an object a leads to a collection of granules of a with a granule being a clump of points objects drawn together by indistinguishability similarity proximity or functionality for example the granules of a human head are the forehead nose cheeks ears eyes etc in general granulation is hierarchical in nature a familiar example is the granulation of time into years months days hours minutes etc modes of information granulation ig in which the granules are crisp c granular play important roles in a wide variety of methods approaches and techniques crisp ig however does not reflect the fact that in almost all of human reasoning and concept formation the granules are fuzzy f granular the granules of a human head for example are fuzzy in the sense that the boundaries between cheeks nose forehead ears etc are not sharply defined furthermore the attributes of fuzzy granules e g length of nose are fuzzy as are their values long short very long etc the fuzziness of granules their attributes and their values is characteristic of ways in which humans granulate and manipulate information

combining multiple clusterings using evidence accumulation we explore the idea of evidence accumulation eac for combining the results of multiple clusterings first a clustering ensemble a set of object partitions is produced given a data set n objects or patterns in d dimensions different ways of producing data partitions are 1 applying different clustering algorithms and 2 applying the same clustering algorithm with different values of parameters or initializations further combinations of different data representations feature spaces and clustering algorithms can also provide a multitude of significantly different data partitionings we propose a simple framework for extracting a consistent clustering given the various partitions in a clustering ensemble according to the eac concept each partition is viewed as an independent evidence of data organization individual data partitions being combined based on a voting mechanism to generate a new n times n similarity matrix between the n patterns the final data partition of the n patterns is obtained by applying a hierarchical agglomerative clustering algorithm on this matrix we have developed a theoretical framework for the analysis of the proposed clustering combination strategy and its evaluation based on the concept of mutual information between data partitions stability of the results is evaluated using bootstrapping techniques a detailed discussion of an evidence accumulation based clustering algorithm using a split and merge strategy based on the k means clustering algorithm is presented experimental results of the proposed method on several synthetic and real data sets are compared with other combination strategies and with individual clustering results produced by well known clustering algorithms

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

comments on robust stabilization of a class of uncertain nonlinear systems via fuzzy control quadratic stabilizability h sup spl infin control theory and linear matrix inequalities this paper presents stability analysis for a class of uncertain nonlinear systems and a method for designing robust fuzzy controllers to stabilize the uncertain nonlinear systems first a stability condition for takagi and sugeno s fuzzy model is given in terms of lyapunov stability theory next new stability conditions for a generalized class of uncertain systems are derived from robust control techniques such as quadratic stabilization h sup spl infin control theory and linear matrix inequalities the derived stability conditions are used to analyze the stability of takagi and sugeno s fuzzy control systems with uncertainty which can be regarded as a generalized class of uncertain nonlinear systems the design method employs the so called parallel distributed compensation important issues for the stability analysis and design are remarked finally three design examples of fuzzy controllers for stabilizing nonlinear systems and uncertain nonlinear systems are presented

robust stability analysis and fuzzy scheduling control for nonlinear systems subject to actuator saturation takagi sugeno ts fuzzy models can provide an effective representation of complex nonlinear systems in terms of fuzzy sets and fuzzy reasoning applied to a set of linear input output submodels in this paper the ts fuzzy modeling approach is utilized to carry out the stability analysis and control design for nonlinear systems with actuator saturation the ts fuzzy representation of a nonlinear system subject to actuator saturation is presented in our ts fuzzy representation the modeling error is also captured by norm bounded uncertainties a set invariance condition for the system in the ts fuzzy representation is first established based on this set invariance condition the problem of estimating the domain of attraction of a ts fuzzy system under a constant state feedback law is formulated and solved as a linear matrix inequality lmi optimization problem by viewing the state feedback gain as an extra free parameter in the lmi optimization problem we arrive at a method for designing state feedback gain that maximizes the domain of attraction a fuzzy scheduling control design method is also introduced to further enlarge the domain of attraction an inverted pendulum is used to show the effectiveness of the proposed fuzzy controller

mixed h sub 2 h sub spl infin fuzzy output feedback control design for nonlinear dynamic systems an lmi approach this study introduces a mixed h sub 2 h sub spl infin fuzzy output feedback control design method for nonlinear systems with guaranteed control performance first the takagi sugeno fuzzy model is employed to approximate a nonlinear system next based on the fuzzy model a fuzzy observer based mixed h sub 2 h sub spl infin controller is developed to achieve the suboptimal h sub 2 control performance with a desired h sub spl infin disturbance rejection constraint a robust stabilization technique is also proposed to override the effect of approximation error in the fuzzy approximation procedure by the proposed decoupling technique and two stage procedure the outcome of the fuzzy observer based mixed h sub 2 h sub spl infin control problem is parametrized in terms of the two eigenvalue problems evps one for observer and the other for controller the evps can be solved very efficiently using the linear matrix inequality lmi optimization techniques a simulation example is given to illustrate the design procedures and performances of the proposed method

fuzzy regulators and fuzzy observers relaxed stability conditions and lmi based designs this paper presents new relaxed stability conditions and lmi linear matrix inequality based designs for both continuous and discrete fuzzy control systems they are applied to design problems of fuzzy regulators and fuzzy observers first takagi and sugeno s fuzzy models and some stability results are recalled to design fuzzy regulators and fuzzy observers nonlinear systems are represented by takagi sugeno s ts fuzzy models the concept of parallel distributed compensation is employed to design fuzzy regulators and fuzzy observers from the ts fuzzy models new stability conditions are obtained by relaxing the stability conditions derived in previous papers lmi based design procedures for fuzzy regulators and fuzzy observers are constructed using the parallel distributed compensation and the relaxed stability conditions other lmi s with respect to decay rate and constraints on control input and output are also derived and utilized in the design procedures design examples for nonlinear systems demonstrate the utility of the relaxed stability conditions and the lmi based design procedures

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

quaternion based adaptive output feedback attitude control of spacecraft using chebyshev neural networks this paper investigates the problem of output feedback attitude control of an uncertain spacecraft two robust adaptive output feedback controllers based on chebyshev neural networks cnn termed adaptive neural networks nn controller i and adaptive nn controller ii are proposed for the attitude tracking control of spacecraft the four parameter representations quaternion are employed to describe the spacecraft attitude for global representation without singularities the nonlinear reduced order observer is used to estimate the derivative of the spacecraft output and the cnn is introduced to further improve the control performance through approximating the spacecraft attitude motion the implementation of the basis functions of the cnn used in the proposed controllers depends only on the desired signals and the smooth robust compensator using the hyperbolic tangent function is employed to counteract the cnn approximation errors and external disturbances the adaptive nn controller ii can efficiently avoid the over estimation problem i e the bound of the cnns output is much larger than that of the approximated unknown function and hence the control input may be very large existing in the adaptive nn controller i both adaptive output feedback controllers using cnn can guarantee that all signals in the resulting closed loop system are uniformly ultimately bounded for performance comparisons the standard adaptive controller using the linear parameterization of spacecraft attitude motion is also developed simulation studies are presented to show the advantages of the proposed cnn based output feedback approach over the standard adaptive output feedback approach

proximity based clustering a search for structural consistency in data with semantic blocks of features a class of clustering problems that is studied here is concerned with the development of a structure of a global nature given a collection of structures clusters constructed locally for data that are represented by several collections blocks of features these blocks of features come with a well defined semantics for instance in spatiotemporal data a certain block of features concerns a spatial component of the data say x y or x y z coordinates while another one deals with the features that describe time series associated with the corresponding locations the results of clustering that are being produced locally are reconciled by minimizing a distance between the proximity matrices that are formed at the higher conceptual level and induced by the individual partition matrices the optimization problem is formulated and presented along with its iterative scheme

positional and confidence voting based consensus functions for fuzzy cluster ensembles consensus clustering i e the task of combining the outcomes of several clustering systems into a single partition has lately attracted the attention of researchers in the unsupervised classification field as it allows the creation of clustering committees that can be applied with multiple interesting purposes such as knowledge reuse or distributed clustering however little attention has been paid to the development of algorithms known as consensus functions especially designed for consolidating the outcomes of multiple fuzzy or soft clustering systems into a single fuzzy partition despite the fact that fuzzy clustering is far more informative than its crisp counterpart as it provides information regarding the degree of association between objects and clusters that can be helpful for deriving richer descriptive data models for this reason this paper presents a set of fuzzy consensus functions capable of creating soft consensus partitions by fusing a collection of fuzzy clusterings our proposals base clustering combination on a cluster disambiguation process followed by the application of positional and confidence voting techniques the modular design of these algorithms makes it possible to sequence their constituting steps in different manners which allows to derive versions of the proposed consensus functions optimized from a computational standpoint the proposed consensus functions have been evaluated in terms of the quality of the consensus partitions they deliver and in terms of their running time on multiple benchmark data sets a comparison against several representative state of the art consensus functions reveals that our proposals constitute an appealing alternative for conducting fuzzy consensus clustering as they are capable of yielding high quality consensus partitions at a low computational cost

stability analysis and design of fuzzy control systems abstract the stability analysis and the design technique of fuzzy control systems using fuzzy block diagrams are discussed first we show the concept of fuzzy blocks and consider the connection problems of fuzzy blocks diagrams we derive some theorems and corollaries with respect to two basic types of connections of fuzzy blocks in order to preserve some properties in a connection of fuzzy blocks continuous piecewise polynomial membership functions are defined secondly a sufficient condition which guarantees the stability of fuzzy systems is obtained in terms of lyapunov s direct method we give an important fact based on this condition thirdly we propose a new design technique of a fuzzy controller the fuzzy block diagrams and the stability analysis are applied to the design problems of a model based fuzzy controller

optimal fuzzy controller design local concept approach in this paper we present a global optimal and stable fuzzy controller design method for both continuous and discrete time fuzzy systems under both finite and infinite horizons first a sufficient condition is proposed which indicates that the global optimal effect can be achieved by the fuzzily combined local optimal controllers based on this sufficient condition we derive a local concept approach to designing the optimal fuzzy controller by applying traditional linear optimal control theory the stability of the entire closed loop continuous fuzzy system can be ensured by the designed optimal fuzzy controller the optimal feedback continuous fuzzy system can not only be guaranteed to be exponentially stable but also be stabilized to any desired degree also the total energy of system output is absolutely finite moreover the resultant feedback continuous fuzzy system possesses an infinite gain margin that is its stability is guaranteed no matter how large the feedback gain becomes two examples are given to illustrate the proposed optimal fuzzy controller design approach and to demonstrate the proved stability properties

coupled fully implicit solution procedure for the steady incompressible navier stokes equations abstract this paper presents a new fully implicit procedure for the solution of the steady incompressible navier stokes equations in primitive variables the momentum equations are coupled with a poisson type equation for the pressure and solved using the beam and warming approximate factorization method the present formulation does not require the iterative solution of the pressure equation at each time step thus the major drawback of the pressure poisson approach which made it prohibitively expensive for complex three dimensional applications is eliminated numerical solutions for the problem of the two dimensional driven cavity are obtained using a non staggered grid at re 100 400 and 1000 all the computed results are obtained without any artificial dissipation this feature of the present procedure demonstrates its excellent convergence and stability characteristics those characteristics result from the coupling of the pressure equation which is elliptic in space with the momentum equations

lmi based design of stabilizing fuzzy controllers for nonlinear systems described by takagi sugeno fuzzy model abstract there have been several recent studies concerning the stability of fuzzy control systems and the synthesis of stabilizing fuzzy controllers this paper reports on a related study of the takagi sugeno ts fuzzy systems and it is shown that the controller synthesis problems for the nonlinear systems described by the ts fuzzy model can be reduced to convex problems involving linear matrix inequalities lmis after classifying the ts fuzzy systems into three families based on how diverse their input matrices are a unique controller synthesis procedure is given for each of the families a numerical example is presented to illustrate the synthesis procedures developed in this paper

evolutionary fuzzy modeling this study is concerned with a general methodology of identification of fuzzy models unlike numeric models fuzzy models operate at a level of information granules fuzzy sets and this aspect brings up an important design requirement of transparency of the model we propose a three phase development framework by distinguishing between structural and parametric optimization processes the underlying topology of the model dwells on fuzzy neural networks architectures governed by fuzzy logic and equipped with parametric flexibility two general optimization mechanisms are explored the structural optimization is realized via genetic programming whereas for the ensuing detailed parametric optimization we proceed with gradient based learning the main advantages of this approach are discussed in detail the study is illustrated with the aid of a numeric example that provides a detailed insight into the performance of the fuzzy models and quantifies crucial design issues

tetrahedral mesh optimisation and adaptivity for steady state and transient finite element calculations abstract a method for optimising a pre existing mesh of tetrahedral finite elements is described it is based on a series of mesh connectivity and node position searches of the landscape defining mesh quality a riemannian metric reflecting the a posteriori error measure is used to calculate element size and shape a functional is defined which embodies both shape and size quality of an element with respect to the metric and is used to gauge mesh quality a heuristic based local search strategy is adopted local in the sense that it has no hill climbing abilities the paper presents applications of the method to complex steady state and time dependent problems which highlight its anisotropic feature capturing abilities numerical evidence is provided which suggests that the computational complexity time of the proposed algorithm varies linearly with the number of elements or nodes of the finite element mesh

a nonmodal approach for time integration of a barotropic limited area model abstract in this work we integrate a semidiscrete nonlinear matrix differential system arising from a barotropic limited area model with periodic boundary conditions on the plane we use a new formulation for the state transition matrix the nonmodal matrix in order to carry out the time integration the helmholtz wind field reconstruction is performed by singular value decomposition svd

general siso takagi sugeno fuzzy systems with linear rule consequent are universal approximators takagi sugeno ts fuzzy systems have been employed as fuzzy controllers and fuzzy models in successfully solving difficult control and modeling problems in practice virtually all the ts fuzzy systems use linear rule consequent at present there exist no results qualitative or quantitative to answer the fundamentally important question that is especially critical to ts fuzzy systems as fuzzy controllers and models are ts fuzzy systems with linear rule consequent universal approximators if the answer is yes then how can they be constructed to achieve prespecified approximation accuracy and what are the sufficient renditions on systems configuration in this paper we provide answers to these questions for a general class of single input single output siso fuzzy systems that use any type of continuous input fuzzy sets ts fuzzy rules with linear consequent and a generalized defuzzifier containing the widely used centroid defuzzifier as a special case we first constructively prove that this general class of siso ts fuzzy systems can uniformly approximate any polynomial arbitrarily well and then prove by utilizing the weierstrass approximation theorem that the general ts fuzzy systems can uniformly approximate any continuous function with arbitrarily high precision furthermore we have derived a formula as part of sufficient conditions for the fuzzy approximation that can compute the minimal upper bound on the number of input fuzzy sets and rules needed for any given continuous function and prespecified approximation error bound an illustrative numerical example is provided

a primitive variable method for the solution of three dimensional incompressible viscous flows abstract in this paper we present a new primitive variable method for the solution of the three dimensional incompressible reynolds averaged navier stokes equations in generalized curvilinear coordinates the governing equations are discretized on a non staggered grid and the discrete continuity equation is replaced by a discrete pressure poisson equation the discrete pressure equation is designed in such a way that i the compatibility condition for the poisson neumann problem is automatically satisfied and ii the discrete incompresibility constraint is satisfied to at least truncation error accuracy while the computed pressure is smooth the momentum equations are integrated in time using the four stage runge kutta algorithm while the pressure equation is solved using the point successive relaxation technique the method is applied to calculate the turbulent flow field over a ship model the computed results are in very good agreement with the experimental data

weighted partition consensus via kernels the combination of multiple clustering results clustering ensemble has emerged as an important procedure to improve the quality of clustering solutions in this paper we propose a new cluster ensemble method based on kernel functions which introduces the partition relevance analysis step this step has the goal of analyzing the set of partition in the cluster ensemble and extract valuable information that can improve the quality of the combination process besides we propose a new similarity measure between partitions proving that it is a kernel function a new consensus function is introduced using this similarity measure and based on the idea of finding the median partition related to this consensus function some theoretical results that endorse the suitability of our methods are proven finally we conduct a numerical experimentation to show the behavior of our method on several databases by making a comparison with simple clustering algorithms as well as to other cluster ensemble methods

dilation free solutions for the incompressible flow equations on nonstaggered grids the present method employs a pressure poisson formulation that has the unique capability of satisfying the discrete continuity equation exactly while producing smooth pressure on nonstaggered grids a fourth order accurate discretization is employed for the pressure gradient operator in both the momentum equation and the pressure poisson equation the use of higher order accurate approximations for the pressure derivatives results in the enlargement of laplace operator which incorporates both odd and even grid points and thus spatially couples the pressure field the numerical solutions are compared to solutions obtained from the classic pressure poisson approach which uses artificial dissipation to couple the pressure field as well as benchmark results of a stream function vorticity formulation which automatically produces dilatation free solutions

nerf c means non euclidean relational fuzzy clustering abstract the relational fuzzy c means rfcm algorithm can be used to cluster a set of n objects described by pair wise dissimilarity values if and only if there exist n points in r n 1 whose squared euclidean distances precisely match the given dissimilarity data this strong restriction on the dissimilarity data renders rfcm inapplicable to most relational clustering problems this paper substantially improves rfcm by generalizing it to the case of arbitrary symmetric dissimilarity data the generalization is obtained using a computationally efficient modification of the existing algorithm that is equivalent to applying a spreading transformation to the dissimilarity data while the method given applies specifically to dissimilarity data a simple transformation can be used to convert similarity relations into dissimilarity data so the method is applicable to any numerical relational data that are positive reflexive or anti reflexive and symmetric numerical examples illustrate and compare the present approach to problems that can be studied with alternatives such as the linkage algorithms

development of a continuity preserving segregated method for incompressible navier stokes equations the present study aims to develop a new method for obtaining the non oscillatory incompressible navier stokes solutions on the non staggered grids within the segregated grid framework the divergence free equation is chosen to replace one of the momentum equations so as to preserve the fluid incompressibility for the sake of numerical accuracy the five point stencil convection diffusion reaction scheme is developed to obtain the nodally exact solution for this chosen momentum equation the validity of the proposed mass preserving navier stokes method is justified by solving the three problems which are amenable to analytical solutions the simulated solution quality is shown to outperform that of the conventional segregated approach besides gaining a very high spatial rate of convergence

numerical solutions for the incompressible navier stokes equations in primitive variables using a non staggered grid 11 abstract in part i of this study a method was developed for the solution of the pressure poisson equation with neumann boundary conditions on a non staggered grid this method was used to determine the pressure when given the velocity field from a stream function vorticity solution in part ii the pressure equation is solved iteratively with the momentum navier stokes equations on a non staggered grid in this case the solution of the pressure equation not only provides the pressure but also serves to indirectly satisfy the continuity equation this primitive variables formulation has a major advantage over the stream function vorticity method in its applicability for three dimensional flow numerical results are obtained and compared with the stream function vorticity results for the driven cavity of part i

axiomatic generalization of the membership degree weighting function for fuzzy c means clustering for decades practitioners have been using the center based partitional clustering algorithms like fuzzy c means fcm which rely on minimizing an objective function comprising of an appropriately weighted sum of distances of each data point from the cluster representatives numerous generalizations in terms of choice of the distance function have been introduced for fcm since its inception in a stark contrast to this fact to the best of our knowledge there has not been any significant effort to address the issue of convergence of the algorithm under the structured generalization of the weighting function here by generalization we mean replacing the conventional weighting function uijm where uij indicates the membership of data xi to cluster cj and m is the real valued fuzzifier with 1 m with a more general function g uij which can assume a wide variety of forms under some mild assumptions in this article for the first time we present a novel axiomatic development of the general weighting function based on the membership degrees we formulate the fuzzy clustering problem along with the intuitive justification of the technicalities behind the axiomatic approach we develop an alternative optimization ao procedure to solve the main clustering problem by solving the partial optimization problems in an iterative way the novelty of the article lies in the development of an axiomatic generalization of the weighting function of fcm formulation of an ao algorithm for the fuzzy clustering problem with the extension to this general class of weighting functions and a detailed convergence analysis of the proposed algorithm

inverse optimal stabilization of a rigid spacecraft the authors present an approach for constructing optimal feedback control laws for regulation of a rotating rigid spacecraft they employ the inverse optimal control approach which circumvents the task of solving a hamilton jacobi equation and results in a controller optimal with respect to a meaningful cost functional the inverse optimality approach requires the knowledge of a control lyapunov function and a stabilizing control law of a particular form for the spacecraft problem they are both constructed using the method of integrator backstepping the authors give a characterization of nonlinear stability margins achieved with the inverse optimal control law

clustering ensembles models of consensus and weak partitions clustering ensembles have emerged as a powerful method for improving both the robustness as well as the stability of unsupervised classification solutions however finding a consensus clustering from multiple partitions is a difficult problem that can be approached from graph based combinatorial or statistical perspectives this study extends previous research on clustering ensembles in several respects first we introduce a unified representation for multiple clusterings and formulate the corresponding categorical clustering problem second we propose a probabilistic model of consensus using a finite mixture of multinomial distributions in a space of clusterings a combined partition is found as a solution to the corresponding maximum likelihood problem using the em algorithm third we define a new consensus function that is related to the classical intraclass variance criterion using the generalized mutual information definition finally we demonstrate the efficacy of combining partitions generated by weak clustering algorithms that use data projections and random data splits a simple explanatory model is offered for the behavior of combinations of such weak clustering components combination accuracy is analyzed as a function of several parameters that control the power and resolution of component partitions as well as the number of partitions we also analyze clustering ensembles with incomplete information and the effect of missing cluster labels on the quality of overall consensus experimental results demonstrate the effectiveness of the proposed methods on several real world data sets

assessing a fuzzy extension of rand index and related measures this empirical study extends the results of hullermeier rifqi henzgen and senge 2012 it examines the ability of a generalization of the rand index and four related measures of similarity to recover the cluster structure of the data in the framework of fuzzy c means clustering the index range is also used as a criterion statistic a monte carlo simulation is conducted for both the null case and where the data have a well defined cluster structure the fuzzy extension of the related measures is not so effective for imbalanced data on the contrary whether the index is dice fowlkes and mallows hurbert and arabie or jaccard it provides reliable results for noise data or for data containing fairly balanced clusters the criticisms of the rand index in the context of crisp clustering can also be extended to its fuzzy version

collaborative clustering with the use of fuzzy c means and its quantification in this study we introduce the concept of collaborative fuzzy clustering a conceptual and algorithmic machinery for the collective discovery of a common structure relationships within a finite family of data residing at individual data sites there are two fundamental features of the proposed optimization environment first given existing constraints which prevent individual sites from exchanging detailed numeric data any communication has to be realized at the level of information granules the specificity of these granules impacts the effectiveness of ensuing collaborative activities second the fuzzy clustering realized at the level of the individual data site has to constructively consider the findings communicated by other sites and act upon them while running the optimization confined to the particular data site adhering to these two general guidelines we develop a comprehensive optimization scheme and discuss its two phase character in which the communication phase of the granular findings intertwines with the local optimization being realized at the level of the individual site and exploits the evidence collected from other sites the proposed augmented form of the objective function is essential in the navigation of the overall optimization that has to be completed on a basis of the data and available information granules the intensity of collaboration is optimized by choosing a suitable tradeoff between the two components of the objective function the objective function based clustering used here concerns the well known fuzzy c means fcm algorithm experimental studies presented include some synthetic data selected data sets coming from the machine learning repository and the weather data coming from environment canada

fuzzy consensus clustering with applications on big data consensus clustering aims to find a single partition of data that agrees as much as possible with existing basic partitions given its robustness and generalizability consensus clustering has emerged as a promising solution to find cluster structures inside heterogeneous big data rising from various application domains in the area of fuzzy systems however research along this line is still in its initial stage with some unsystematic algorithmic studies finding a fuzzy consensus partition from multiple fuzzy basic partitions in an efficient flexible and robust way is still an exciting open problem calling for further investigation in light of this this paper provides a systematic study of fuzzy consensus clustering fcc from a utility perspective specifically we first define the objective function of fcc clearly using the novel fuzzified contingency matrix we then derive a family of fcc utility functions termed as fccu that can transform fcc to a weighted piecewise fuzzy c means clustering pifcm problem this helps us to establish an algorithmic framework for fcc with flexible choice of utility functions and speeds fcc significantly with a fcm like iterative process of pifcm to meet the big data challenge we further parallelize fcc on the spark platform with both vertical and horizontal segmentation schemes extensive experiments on various real world datasets demonstrate the excellent performance of fcc even with a majority of poor basic partitions in particular our method exhibits interesting potential for big data clustering in two real life applications concerned with online event detection and overlapping community detection respectively

stable and optimal fuzzy control of linear systems a number of stable and optimal fuzzy controllers are developed for linear systems based on some classical results in control theory we design the structure and parameters of fuzzy controllers such that the closed loop fuzzy control systems are stable provided that the process under control is linear and satisfies certain conditions it turns out that if stability is the only requirement there is much freedom in choosing the fuzzy controller parameters therefore a performance criterion is set to optimalize the parameters using the pontryagin minimum principle we design an optimal fuzzy controller for linear systems with quadratic cost function finally the optimal fuzzy controller is applied to a ball and beam system