the em algorithm for kernel matrix completion with auxiliary data in biological data it is often the case that observed data are available only for a subset of samples when a kernel matrix is derived from such data we have to leave the entries for unavailable samples as missing in this paper the missing entries are completed by exploiting an auxiliary kernel matrix derived from another information source the parametric model of kernel matrices is created as a set of spectral variants of the auxiliary kernel matrix and the missing entries are estimated by fitting this model to the existing entries for model fitting we adopt the em algorithm distinguished from the em algorithm of dempster et al 1977 based on the information geometry of positive definite matrices we will report promising results on bacteria clustering experiments using two marker sequences 16s and gyrb

bayesian analysis of mixture models with an unknown number of components an alternative to reversible jump methods richardson and green present a method of performing a bayesian analysis of data from a finite mixture distribution with an unknown number of components their method is a markov chain monte carlo mcmc approach which makes use of the reversible jump methodology described by green we describe an alternative mcmc method which views the parameters of the model as a marked point process extending methods suggested by ripley to create a markov birth death process with an appropriate stationary distribution our method is easy to implement even in the case of data in more than one dimension and we illustrate it on both univariate and bivariate data there appears to be considerable potential for applying these ideas to other contexts as an alternative to more general reversible jump methods and we conclude with a brief discussion of how this might be achieved

normal forms in bl algebra and their contribution to universal approximation of functions this paper continues the investigation of approximating properties of generalized normal forms in fuzzy logic the problem is formalized and solved algebraically normal forms are considered in two variants infinite and finite it is proved that infinite normal forms are universal representation formulas whereas finite normal forms are universal approximation formulas for any l valued function where l is a support set of any complete bl algebra the estimation of the quality of approximation is suggested moreover functions which can be precisely represented by the discrete normal forms are considered

multiscale modeling and estimation of poisson processes with application to photon limited imaging many important problems in engineering and science are well modeled by poisson processes in many applications it is of great interest to accurately estimate the intensities underlying observed poisson data in particular this work is motivated by photon limited imaging problems this paper studies a new bayesian approach to poisson intensity estimation based on the haar wavelet transform it is shown that the haar transform provides a very natural and powerful framework for this problem using this framework a novel multiscale bayesian prior to model intensity functions is devised the new prior leads to a simple bayesian intensity estimation procedure furthermore we characterize the correlation behavior of the new prior and show that it has 1 f spectral characteristics the new framework is applied to photon limited image estimation and its potential to improve nuclear medicine imaging is examined

wavelet based image estimation an empirical bayes approach using jeffrey s noninformative prior the sparseness and decorrelation properties of the discrete wavelet transform have been exploited to develop powerful denoising methods however most of these methods have free parameters which have to be adjusted or estimated in this paper we propose a wavelet based denoising technique without any free parameters it is in this sense a universal method our approach uses empirical bayes estimation based on a jeffreys noninformative prior it is a step toward objective bayesian wavelet based denoising the result is a remarkably simple fixed nonlinear shrinkage thresholding rule which performs better than other more computationally demanding methods

generalization error bounds for bayesian mixture algorithms bayesian approaches to learning and estimation have played a significant role in the statistics literature over many years while they are often provably optimal in a frequentist setting and lead to excellent performance in practical applications there have not been many precise characterizations of their performance for finite sample sizes under general conditions in this paper we consider the class of bayesian mixture algorithms where an estimator is formed by constructing a data dependent mixture over some hypothesis space similarly to what is observed in practice our results demonstrate that mixture approaches are particularly robust and allow for the construction of highly complex estimators while avoiding undesirable overfitting effects our results while being data dependent in nature are insensitive to the underlying model assumptions and apply whether or not these hold at a technical level the approach applies to unbounded functions constrained only by certain moment conditions finally the bounds derived can be directly applied to non bayesian mixture approaches such as boosting and bagging

greedy algorithms for classification consistency convergence rates and adaptivity many regression and classification algorithms proposed over the years can be described as greedy procedures for the stagewise minimization of an appropriate cost function some examples include additive models matching pursuit and boosting in this work we focus on the classification problem for which many recent algorithms have been proposed and applied successfully for a specific regularized form of greedy stagewise optimization we prove consistency of the approach under rather general conditions focusing on specific classes of problems we provide conditions under which our greedy procedure achieves the nearly minimax rate of convergence implying that the procedure cannot be improved in a worst case setting we also construct a fully adaptive procedure which without knowing the smoothness parameter of the decision boundary converges at the same rate as if the smoothness parameter were known

comparing bayes model averaging and stacking when model approximation error cannot be ignored we compare bayes model averaging bma to a non bayes form of model averaging called stacking in stacking the weights are no longer posterior probabilities of models they are obtained by a technique based on cross validation when the correct data generating model dgm is on the list of models under consideration bma is never worse than stacking and often is demonstrably better provided that the noise level is of order commensurate with the coefficients and explanatory variables here however we focus on the case that the correct dgm is not on the model list and may not be well approximated by the elements on the model list we give a sequence of computed examples by choosing model lists and dgm s to contrast the risk performance of stacking and bma in the first examples the model lists are chosen to reflect geometric principles that should give good performance in these cases stacking typically outperforms bma sometimes by a wide margin in the second set of examples we examine how stacking and bma perform when the model list includes all subsets of a set of potential predictors when we standardize the size of terms and coefficients in this setting we find that bma outperforms stacking when the deviant terms in the dgm point in directions accommodated by the model list but that when the deviant term points outside the model list stacking seems to do better overall our results suggest the stacking has better robustness properties than bma in the most important settings

decomposition property of fuzzy systems and its applications this paper presents the decomposition property of fuzzy systems using a simple constructive decomposition procedure that is by properly dividing the input space into sub input spaces a general fuzzy system is decomposed into several sub fuzzy systems which are the simplest fuzzy systems in the sub input spaces based on the decomposition property of fuzzy systems the analysis of fuzzy systems can be divided into two steps first analyze the properties of the simplest fuzzy systems and then use the decomposition property to extend the results to general fuzzy systems using this idea two applications of the decomposition property are given the first is the application to the representation capability analysis of fuzzy systems the second is the application to the analysis of a class of nonlinear control systems then based on the piecewise affine fuzzy system model the existence condition and the design of a stable control for a class of single input single output siso nonlinear systems are presented

the caldeira leggett quantum master equation in wigner phase space continued fraction solution and application to brownian motion in periodic potentials the continued fraction method of solving classical fokker planck equations has been adapted to tackle quantum master equations of the caldeira leggett type this was done taking advantage of the phase space wigner representation of the quantum density matrix the approach differs from those in which some continued fraction expression is found for a certain quantity in that the full solution of the master equation is obtained by continued fraction methods this allows us to study in detail the effects of the environment fluctuations and dissipation on several classes of nonlinear quantum systems we apply the method to the canonical problem of quantum brownian motion in periodic potentials both for cosine and ratchet potentials lacking inversion symmetry

on fuzzy type theory this paper is a generalization of classical simple type theory we have developed a formal system of fuzzy type theory which differs from the classical one essentially in extension of truth values from two to infinitely many the structure of truth values is assumed to be an imtl algebra residuated lattice with prelinearity and double negation extended by the baaz delta operation various properties of fuzzy type theory are proved including its completeness

hierarchical ts fuzzy system and its universal approximation an efficient tool to deal with the rule explosion problem is the hierarchical system by which a fuzzy system can be decomposed into a number of hierarchically connected low dimensional systems in this paper a generalized hierarehical tagaki sugeno ts system is built it is shown that the input output i o relationship of this generalized hierarehical system can be represented as one of a standard ts fuzzy system and the system approximation capability is analyzed by taking piecewise linear functions as a bridge by constructive method it is proven that the hierarchical fuzzy systems hfs s can be universal approximators for the given approximation accuracy an estimation formula about the number of the rules needed in the hfs is established finally some simulation examples confirm that the hfs s with smaller size rule base can approximate the given functions with high accuracy the results obtained here provide us with the theoretical basis for various applications of hfs s

analyses for l p μ norm approximation capability of generalized mamdani fuzzy systems abstract the connected piecewise linear functions are introduced to study the l p norm approximation capability of the generalized mamdani fuzzy system it is shown that such general fuzzy systems are the universal approximators to the p integrable functions with l p norm for the given degree of accuracy an upper bound of the fuzzy rule numbers needed in the fuzzy rule base of the system is estimated finally a simulation example is analyzed to demonstrate our conclusions

information divergence and risk for binary experiments we unify f divergences bregman divergences surrogate regret bounds proper scoring rules cost curves roc curves and statistical information we do this by systematically studying integral and variational representations of these objects and in so doing identify their representation primitives which all are related to cost sensitive binary classification as well as developing relationships between generative and discriminative views of learning the new machinery leads to tight and more general surrogate regret bounds and generalised pinsker inequalities relating f divergences to variational divergence the new viewpoint also illuminates existing algorithms it provides a new derivation of support vector machines in terms of divergences and relates maximum mean discrepancy to fisher linear discriminants

approximation accuracy analysis of fuzzy systems as function approximators this paper establishes the approximation error bounds for various classes of fuzzy systems i e fuzzy systems generated by different inferential and defuzzification methods based on these bounds the approximation accuracy of various classes of fuzzy systems is analyzed and compared it is seen that the class of fuzzy systems generated by the product inference and the center average defuzzifier has better approximation accuracy and properties than the class of fuzzy systems generated by the min inference and the center average defuzzifier and the class of fuzzy systems defuzzified by the mom defuzzifier in addition it is proved that fuzzy systems can represent any linear and multilinear function and explicit expressions of fuzzy systems generated by the mom defuzzified method are given

joint segmentation of piecewise constant autoregressive processes by using a hierarchical model and a bayesian sampling approach we propose a joint segmentation algorithm for piecewise constant autoregressive ar processes recorded by several independent sensors the algorithm is based on a hierarchical bayesian model appropriate priors allow us to introduce correlations between the change locations of the observed signals numerical problems inherent to bayesian inference are solved by a gibbs sampling strategy the proposed joint segmentation methodology yields improved segmentation results when compared with parallel and independent individual signal segmentations the initial algorithm is derived for piecewise constant ar processes whose orders are fixed on each segment however an extension to models with unknown model orders is also discussed theoretical results are illustrated by many simulations conducted with synthetic signals and real arc tracking and speech signals

time scales and diffusion mechanisms in the kramers equation with periodic potentials i abstract noise assisted diffusion on a periodic substrate is studied solving the klein kramers equation kke by the matrix continued fraction method assuming a periodic cosine potential and a homogeneous friction the one particle dynamics is completely characterized both at short and long times calculating up to large momentum transfer the dynamic structure factor its full width at half maximum the velocity self correlation spectrum and the mean square displacement four different dynamical regimes are found as the potential strength or the friction vary at high potential barriers diffusion proceeds by single or multiple jumps at high and low friction respectively while two different kinds of continuous unactivated diffusion are found at lower barriers these dynamical features are discussed in terms of three characteristic time scales whose relations determine the diffusion mechanisms

eigenvalues and eigenfunctions of the kramers equation application to the brownian motion of a pendulum the brownian motion of s particle in a potential is described by a fokker planck equation with two variables position and velocity i e by the kramers equation eigenvalues and eigenfunctions can be obtained by a matrix continued fraction method this method is applied to the brownian motion of a pendulum where the force is proportional to sin x the real and complex eigenvalues with small real parts are plotted as a function of the damping constant in the low friction limit the real parts of the complex eigenvalues are proportional to the square of the friction constant whereas the real eigenvalues are proportional to the friction constant itself in the high friction limit the eigenvalues are real and the lowest ones are proportional to the inverse friction constant in the intermediate friction regime a complicated mixture of real and complex eigenvalues is found the same method is also applied to the boltzmann equation with the bgk collision operator

fuzzy control of model car this paper discusses fuzzy control of a model car fuzzy control rules are derived by modelling an expert s driving actions experiments are performed using a model car with a sensing unit and a micro computer

fuzzy control of unknown multiple input multiple output plants abstract a self learning fuzzy logic system is given for control of unknown multiple input multiple output mimo plants some nomenclature and several data types are introduced to develop a general formulation for controller activity a random optimization algorithm is given to train the controller a plant model is not required for training instead training is guided by observations of plant responses to inputs

levy statistics in a hamiltonian system enhanced diffusion in a hamiltonian system is studied in terms of the continuous time random walk formulation for l evy walks the previous l evy walk scheme is extended i to include interruptions by periods of temporal localization and ii to describe motion in two dimensions we analyze a case of conservative motion in a two dimensional periodic potential numerical calculations of the mean squared displacements and the propagators for intermediate energies are consistent with the l evy walk description

approximation of stochastic processes by t s fuzzy systems fuzzy systems can provide us with universal approximation models of deterministic input output relationships but in the stochastic environment few achievements related to the subject have so far achieved in the paper a novel stochastic takagi sugeno t s fuzzy system is introduced to represent approximately existing randomness in many real world systems by recapitulating the general architecture of the stochastic t s fuzzy rule based system we analyze systematically approximating capability of the stochastic system to a class of stochastic processes by the canonical representation of the stochastic processes the stochastic fuzzy system is capable of with arbitrary accuracy providing the approximation to the stochastic processes in mean square sense finally an efficient algorithm for the stochastic t s fuzzy system is developed a simulation example demonstrates how a stochastic t s fuzzy system can be constructed to realize the given stochastic process approximately

estimation of sparse nonnegative sources from noisy overcomplete mixtures using map in this letter we propose a new algorithm for estimating sparse nonnegative sources from a set of noisy linear mixtures in particular we consider difficult situations with high noise levels and more sources than sensors underdetermined case we show that when sources are very sparse in time and overlapped at some locations they can be recovered even with very low signal to noise ratio and by using many fewer sensors than sources a theoretical analysis based on bayesian estimation tools is included showing strong connections with algorithms in related areas of research such as ica nmf focuss and sparse representation of data with overcomplete dictionaries our algorithm uses a bayesian approach by modeling sparse signals through mixed state random variables this new model for priors imposes l0 norm based sparsity we start our analysis for the case of nonoverlapped sources 1 sparse which allows us to simplify the search of the posterior maximum avoiding a combinatorial search general algorithms for overlapped cases such as 2 sparse and k sparse sources are derived by using the algorithm for 1 sparse signals recursively additionally a combination of our map algorithm with the nn ksvd algorithm is proposed for estimating the mixing matrix and the sources simultaneously in a real blind fashion a complete set of simulation results is included showing the performance of our algorithm

sugeno type controllers are universal controllers abstract we show that given any continuous real valued function on a compact set there is a sugeno type controller that will approximate this function to any degree of accuracy an application of this result to fuzzy control is presented which shows that this type of sugeno controller is a universal controller

structure identification of fuzzy model abstract the problems of structure identification of a fuzzy model are formulated a criterion for the verification of a structure is discussed using the criterion an algorithm for identifying a structure is suggested further a successive identification algorithm of the parameters is suggested the proposed methods are applied to an example

universal fuzzy controllers based on generalized t s fuzzy models this paper investigates the universal fuzzy control problem based on generalized t s fuzzy models the universal approximation capability of the generalized t s fuzzy models is shown and an approach to robust controller design for general nonlinear systems based on this kind of generalized t s fuzzy models is developed the results of universal fuzzy controllers for two classes of nonlinear systems are then given and constructive procedures to obtain the universal fuzzy controllers are also provided an example is finally presented to show the effectiveness of our approach

on approximations of zadeh s extension principle in this paper we provide several results concerning the approximation of zadeh s extension of a given function we provide several simple observations due to which we provide a general procedure allowing to approximate zadeh s extension of any continuous map among other things we demonstrated that the technique of f transform can also be used to approximate this extension further we studied how the choice of the metric on the space of fuzzy sets resp fuzzy numbers can affect the quality of the approximation and we clarified that in comparison to recent habits the choice of the levelwise metric need not be the most appropriate one and that the approximation process could be simplified our results are general in the sense that we mostly require nothing but the continuity of the original map

the bayesian choice a decision theoretic motivation contents introduction decision theoretic foundations of statistical inference from prior information to prior distributions bayesian point estimation tests and confidence regions admissibility and complete classes invariance haar measures and equivariant estimators hierarchical and empirical bayes extensions bayesian calculations a defense of the bayesian choice

formal theories and linguistic descriptions abstract in this contribution we discuss properties which a formal logical theory we call it the theory of evaluating expressions should have to serve us as a tool for modeling of the meaning of a certain class of natural language expressions called evaluating linguistic expressions we further construct a formal theory for modeling of the meaning of sets of fuzzy if then rules called linguistic descriptions and finally present a basic schema of fuzzy logic deduction the basis for our study is first order fuzzy logic with evaluated syntax

a statistical multiscale framework for poisson inverse problems this paper describes a statistical multiscale modeling and analysis framework for linear inverse problems involving poisson data the framework itself is founded upon a multiscale analysis associated with recursive partitioning of the underlying intensity a corresponding multiscale factorization of the likelihood induced by this analysis and a choice of prior probability distribution made to match this factorization by modeling the splits in the underlying partition the class of priors used here has the interesting feature that the noninformative member yields the traditional maximum likelihood solution other choices are made to reflect prior belief as to the smoothness of the unknown intensity adopting the expectation maximization em algorithm for use in computing the maximum a posteriori map estimate corresponding to our model we find that our model permits remarkably simple closed form expressions for the em update equations the behavior of our em algorithm is examined and it is shown that convergence to the global map estimate can be guaranteed applications in emission computed tomography and astronomical energy spectral analysis demonstrate the potential of the new approach

a neuro fuzzy system modeling with self constructing rule generationand hybrid svd based learning we propose an approach for neuro fuzzy system modeling a neuro fuzzy system for a given set of input output data is obtained in two steps first the data set is partitioned automatically into a set of clusters based on input similarity and output similarity tests membership functions associated with each cluster are defined according to statistical means and variances of the data points included in the cluster then a fuzzy if then rule is extracted from each cluster to form a fuzzy rule base second a fuzzy neural network is constructed accordingly and parameters are refined to increase the precision of the fuzzy rule base to decrease the size of the search space and to speed up the convergence we develop a hybrid learning algorithm which combines a recursive singular value decomposition based least squares estimator and the gradient descent method the proposed approach has advantages of determining the number of rules automatically and matching membership functions closely with the real distribution of the training data points besides it learns faster consumes less memory and produces lower approximation errors than other methods

second order sliding fuzzy interval type 2 control for an uncertain system with real application a new second order sliding mode type 2 fuzzy controller for nonlinear uncertain perturbed systems is developed in this paper to overcome the constraint on the knowledge of the system model we have used local models that are related to some operating points to synthesize a type 2 nominal fuzzy global model the control is based on the super twisting algorithm which is among second order sliding mode controls smcs moreover two adaptive fuzzy type 2 systems have been introduced to generate the two super twisting signals to avoid both the chattering and the constraint on the knowledge of disturbances and uncertainties upper bounds these adaptive fuzzy type 2 systems are adjusted online by two adaptation laws that are deduced from the stability analysis in the lyapunov sense it has only one input i e the sliding surface and one output i e the optimal values of the gains control which are hard to compute with the original algorithm many results of the one link manipulator are obtained first by the simulation in order to compare the performances of the proposed method with that given by levant and then in a real time application in order to confirm the efficiency of the proposed approach the experimentation and simulation are done for the tracking control problem

kernel shapes of fuzzy sets in fuzzy systems for function approximation the shapes of if part fuzzy sets affect the approximating capability of fuzzy systems in this paper the fuzzy systems with the kernel shaped if part fuzzy sets are built directly from the training data it is proved that these fuzzy systems are universal approximators and their uniform approximation rates can be estimated in the single input single output siso case on the basis of these rates the relationships between the approximating capability and the shapes of if part fuzzy sets are developed for the fuzzy systems furthermore the sinc functions that serve as input membership functions are proved to have the almost best approximation property in a particular class of membership functions the theoretical results are confirmed from the simulation data in addition the estimations of the uniform approximation rates are extended to the multi input single output miso case

information gains expected from separate and joint measurements of n identical spin 1 2 systems noninformative bayesian analyses an investigator is assumed to have n replicas of a spin 1 2 system but lacks any specific knowledge pertinent to constructing a 2 2 density matrix for it we compute within a noninformative bayesian framework the expected information gains for various measurement schemes first separate and then joint in nature in particular we obtain a result which fully accords with a certain plausibility argument of peres while the parallel result in a recent analysis of massar and popescu does not

diffusion in classical periodic systems the smoluchowski equation approach abstract the classical diffusion of a particle in a periodic system is studied employing the smoluchowski equation with an external periodic field of force assuming a two dimensional rectangular symmetry and an external potential of a simple cosine shape the resulting eigenvalue problem leads to a hill equation which is solved numerically the dynamic structure factor and its full width at half maximum fwhm are calculated up to large values of the momentum transfer extending in several brillouin zones it is shown that decreasing the amplitude of the potential the smoluchowski equation describes a diffusive process which changes continuously from a jump to a liquid like regime with an intermediate behaviour which has some characteristics of both in this context recent scattering experiments on systems premelting surfaces and absorbed monolayers which seem to show such a behaviour are briefly discussed

sugeno controllers with a bounded number of rules are nowhere dense abstract in literature various results can be found claiming that fuzzy controllers are universal approximators in terms of topology this means that fuzzy controllers as subsets of adequate function spaces are dense in this paper the topological structure of fuzzy controllers composed of a bounded number of rules is investigated it turns out that these sets are nowhere dense a topological notion indicating that the sets are almost discrete this means that it is just the number of rules and e g not the great variety of parameters of fuzzy controllers why fuzzy controllers are universal approximators

nonsingleton fuzzy logic systems theory and application in this paper we present a formal derivation of general nonsingleton fuzzy logic systems nsflss and show how they can be efficiently computed we give examples for special cases of membership functions and inference and we show how an nsfls can be expressed as a nonsingleton fuzzy basis function expansion and present an analytical comparison of the nonsingleton and singleton fuzzy logic systems formulations we prove that an nsfls can uniformly approximate any given continuous function on a compact set and show that our nsfls does a much better job of predicting a noisy chaotic time series than does a singleton fuzzy logic system fls

analyses of regular fuzzy neural networks for approximation capabilities abstract by introducing a trapezoidal fuzzy function and using the properties of the function we set up a continuously increasing fuzzy function that cannot be arbitrarily closely approximated on a compact set of f 0 r by the regular fuzzy neural network rfnn thus the conclusions in buckley and hayashi fuzzy sets and systems 61 1994 43 51 are improved and the problem if the rfnn is the universal approximator to the class of continuously increasing fuzzy functions is solved finally we obtain the universal approximation to the extended fuzzy functions by rfnn

an analytical approximation to the diffusion coefficient in overdamped multidimensional systems abstract an analytical approximation for the mobility of an overdamped particle in a periodic multi dimensional system is presented attention is focused on two dimensions quasi 2d approximation in the most generic case of a 2d coupled periodic potential in a rectangular lattice and of a position dependent friction the approximation is derived in the framework of the linear response theory by fixing the value of one coordinate and solving the problem of diffusion along the other coordinate as strictly 1d this is expected to be essentially correct if all the most relevant diffusion paths are straight lines two different specific applications have been considered diffusion in a square egg carton potential and diffusion in absence of potential in a 2d channel with unsurmountable periodic walls exact results are available in literature in the latter case and are obtained in the first case by solving the smoluchowski equation matrix continued fraction method comparisons with the quasi 2d approximation show that the agreement is excellent for the egg carton potential but far less satisfying for migration in the 2d periodically shaped channel characterized by important diffusion paths not being straight lines

universal fuzzy models and universal fuzzy controllers for stochastic nonaffine nonlinear systems this paper investigates the universal fuzzy model and universal fuzzy controller problems for stochastic nonaffine nonlinear systems the underlying mechanism of stochastic fuzzy logic is first discussed and a stochastic generalized fuzzy model with new stochastic fuzzy rule base is then given based on their function approximation capability these kinds of stochastic generalized fuzzy models are shown to be universal fuzzy models for stochastic nonaffine nonlinear systems under some sufficient conditions an approach to stabilization controller design for stochastic nonaffine nonlinear systems is then developed through their stochastic generalized takagi sugeno t s fuzzy approximation models then the results of universal fuzzy controllers for two classes of stochastic nonlinear systems along with constructive procedures to obtain the universal fuzzy controllers are also provided respectively finally a numerical example is presented to illustrate the effectiveness of the proposed approach

normal forms for fuzzy logic functions and their approximation ability abstract aiming at developing theoretical backgrounds of fuzzy logic we consider an mv algebra of fuzzy logic functions two kinds of formulas regarded as disjunctive and conjunctive normal forms are introduced as a formal translation of if then rules their ability for an approximate representation of uniformly continuous functions are investigated the problem of transformation of any formula of propositional fuzzy logic into either of the normal forms is discussed

asafes2 a novel neuro fuzzy architecture for fuzzy computing based on functional reasoning abstract the functional reasoning or takagi sugeno fuzzy reasoning method is a very promising approach to the task of multi variable non linear function approximation and the design of a fuzzy model and fuzzy controller the proposed architecture asafes2 is a neuro fuzzy function approximator and is the first attempt to combine this reasoning method with stochastic reinforcement learning it can learn a function to a high degree of accuracy at a very great speed and furthermore expresses it in a set of linear relations the main ideas are the fuzzy partitioning of the input space into fuzzy subspaces each corresponding to a possible fuzzy rule and the use of a separate neural unit for every fuzzy subspace in order to calculate the optimum consequence parameters simulation results prove its superiority over back propagation in simple non linear function approximation tasks and over all previous approaches to the box and jenkins gas furnace modelling comparisons are also made with generalized radial basis function networks finally asafes2 as a building block in a learning fuzzy logic controller is applied to the well known cart pole stabilization problem with satisfactory results a new flexible membership function is also presented

fuzzy modeling and control of multilayer incinerator abstract a method to design a fuzzy controller based on a fuzzy model is suggested the identification method of a fuzzy model is also discussed the suggested method is applied for the modelling and control of a multilayer incinerator the performance of the designed fuzzy controller is tested by computer simulation using the identified process model the results are satisfactory

mamdani fuzzy system universal approximator to a class of random processes the issue of fuzzy systems as universal approximators has drawn significant attention but all results obtained are restricted to deterministic input output i o relationships it should be noted that in practice many i o systems including fuzzy systems operate in the environment which is essentially stochastic in this paper the mamdani fuzzy systems are generalized as stochastic systems by proving the mamdani systems as universal approximators with l sup 2 norm the approximation capability of the stochastic mamdani systems to a class of random processes is systematically analyzed in the mean square sense such stochastic fuzzy systems are capable of approximating the prescribed random processes with arbitrary accuracy further an efficient learning algorithm for the stochastic mamdani systems is developed finally a simulation example is employed to demonstrate our results

compressed sensing with wavelet domain dependencies for coronary mri a retrospective study coronary magnetic resonance imaging mri is a noninvasive imaging modality for diagnosis of coronary artery disease one of the limitations of coronary mri is its long acquisition time due to the need of imaging with high spatial resolution and constraints on respiratory and cardiac motions compressed sensing cs has been recently utilized to accelerate image acquisition in mri in this paper we develop an improved cs reconstruction method bayesian least squares gaussian scale mixture bls gsm that uses dependencies of wavelet domain coefficients to reduce the observed blurring and reconstruction artifacts in coronary mri using traditional l1 regularization images of left and right coronary mri was acquired in 7 healthy subjects with fully sampled k space data the data was retrospectively undersampled using acceleration rates of 2 4 6 and 8 and reconstructed using l1 thresholding l1 minimization and bls gsm thresholding reconstructed right and left coronary images were compared with fully sampled reconstructions in vessel sharpness and subjective image quality 1 4 for poor excellent mean square error mse was also calculated for each reconstruction there were no significant differences between the fully sampled image score versus rate 2 4 or 6 for bls gsm for both right and left coronaries n s however for l1 thresholding significant differences p 0 05 were observed for rates higher than 2 and 4 for right and left coronaries respectively l1 minimization also yields images with lower scores compared to the reference for rates higher than 4 for both coronaries these results were consistent with the quantitative vessel sharpness readings bls gsm allows acceleration of coronary mri with acceleration rates beyond what can be achieved with l1 regularization

controllable processes and the fuzzy controller abstract we show that any controllable process can be controlled by the scaled and averaged output of multiple elementary fuzzy controllers operating simultaneously

fuzzy control as a universal control tool abstract it is known that fuzzy control is a universal control tool because an arbitrary control strategy in particular a control strategy that is in some sense optimal can be obtained in principle by applying a fuzzy control methodology to some set of rules this result has already been proved e g 2 7 20 21 for the case when a plant is described by finitely many parameters and a special type of fuzzy control methodology is used in this paper we prove it for arbitrary plants including plants that are distributed systems i e plants whose state requires infinitely many parameters to describe and arbitrary fuzzy control methodologies we also prove that there exists a universal fuzzy controller that generates an appropriate control from an input description of a plant and the desired objective mathematically we prove that fuzzy systems can approximate arbitrary continuous functionals thus generalizing a known result about continuous functions

facts and figures on fuzzified normal forms the idea behind normal forms is to provide a standard representation or approximation of various kinds of functions in boolean logic for instance this amounts to expressing a given well formed formula wff in terms of the disjunction respectively conjunction of some conjunctions respectively disjunctions of several elementary ones interpreting these well known identical disjunctive and conjunctive normal forms in a poorer structure such as a kleene or de morgan algebra leads to a lower and upper approximation only of the corresponding identical normal forms and hence of the given wff in that poorer structure in this paper we address the question whether a similar interpretation of these normal forms in a bl algebra still provides lower and upper approximations of a given wff this question falls apart in two subquestions first are these interpretations comparable and second if so is the wff located in between the first question can be answered positively for certain bl algebras while the second one is answered negatively

method for higher order polynomial sugeno fuzzy inference systems a method for higher order polynomial sugeno fuzzy inference systems formation is presented compared to other existing higher order sugeno implementations it uses fewer parameters and compared to zero and 1st order sugeno fuzzy systems it has overall improved model performance while best models are not always obtained via a higher order representation in our proposed method it is possible to choose the polynomial order which best fits the desired data its input is a previously established model found by a clustering algorithm subtractive algorithm in this case afterward parameters of all higher order polynomials are adjusted using recursive least square algorithm for experimental validation multiple benchmark datasets are tested using hold out and k fold validation as well as data forecasting various performance measures are used although akaike information criterion is used as a primary measure to demonstrate that our proposed higher order polynomials have overall better model performance over zero and 1st order polynomials

adaptive bayesian multiuser detection for synchronous cdma with gaussian and impulsive noise we consider the problem of simultaneous parameter estimation and data restoration in a synchronous cdma system in the presence of either additive gaussian or additive impulsive white noise with unknown parameters the impulsive noise is modeled by a two term gaussian mixture distribution bayesian inference of all unknown quantities is made from the superimposed and noisy received signals the gibbs sampler a markov chain monte carlo procedure is employed to calculate the bayesian estimates the basic idea is to generate ergodic random samples from the joint posterior distribution of all unknown and then to average the appropriate samples to obtain the estimates of the unknown quantities adaptive bayesian multiuser detectors based on the gibbs sampler are derived for both the gaussian noise synchronous cdma channel and the impulsive noise synchronous cdma channel a salient feature of the proposed adaptive bayesian multiuser detectors is that they can incorporate the a priori symbol probabilities and they produce as output the a posteriori symbol probabilities that is they are soft input soft output algorithms hence these methods are well suited for iterative processing in a coded system which allows the adaptive bayesian multiuser detector to refine its processing based on the information from the decoding stage and vice versa a receiver structure termed the adaptive turbo multiuser detector

unsupervised contour representation and estimation using b splines and a minimum description length criterion this paper describes a new approach to adaptive estimation of parametric deformable contours based on b spline representations the problem is formulated in a statistical framework with the likelihood function being derived from a region based image model the parameters of the image model the contour parameters and the b spline parameterization order i e the number of control points are all considered unknown the parameterization order is estimated via a minimum description length mdl type criterion a deterministic iterative algorithm is developed to implement the derived contour estimation criterion the result is an unsupervised parametric deformable contour it adapts its degree of smoothness complexity number of control points and it also estimates the observation image model parameters the experiments reported in the paper performed on synthetic and real medical images confirm the adequate and good performance of the approach

the unique role of the łukasiewicz triplet in the theory of fuzzified normal forms in fuzzy set theory the fuzzification of a crisp concept is not seldom rooted in a straightforward adjustment of the disjunctive or conjunctive boolean normal form of the underlying mathematical expression however the fuzzified normal forms obtained can rarely be considered as true normal forms in an extended logic or algebra they are to be considered as functions defined on 0 1 n for some n n 0 and taking values in the support 0 1 of a bl algebra 0 1 t i t 0 1 with t a continuous t norm and i t its residual implicator in this paper we clear out some misunderstandings concerning fuzzified normal forms and explore for which continuous de morgan triplets the disjunctive fuzzified normal form is smaller than or equal to the conjunctive fuzzified normal form furthermore we figure out to what extent their mutual distance depends on the original boolean function special attention is drawn to the lukasiewicz triplet as it is the only continuous de morgan triplet for which the difference between both fuzzified normal forms is independent of the underlying boolean function

rotation invariant t norm solutions of a system of functional equations the generalization of the disjunctive and conjunctive boolean normal forms to fuzzy set theory obtained by interpreting as a t norm as a t conorm and as a negator often provides a kind of standard fuzzification procedure a system of functional equations turns up if some functional independence of the difference between both generalizations is demanded in this paper we explore which de morgan triplets based on a left continuous t norm t solve this system imposing some extra continuity conditions on t these t norm solutions can be obtained by the rotation construction of jenei the cauchy equation plays a key role in the reasoning process

sparls the sparse rls algorithm we develop a recursive l1 regularized least squares sparls algorithm for the estimation of a sparse tap weight vector in the adaptive filtering setting the sparls algorithm exploits noisy observations of the tap weight vector output stream and produces its estimate using an expectation maximization type algorithm we prove the convergence of the sparls algorithm to a near optimal estimate in a stationary environment and present analytical results for the steady state error simulation studies in the context of channel estimation employing multipath wireless channels show that the sparls algorithm has significant improvement over the conventional widely used recursive least squares rls algorithm in terms of mean squared error mse moreover these simulation studies suggest that the sparls algorithm with slight modifications can operate with lower computational requirements than the rls algorithm when applied to tap weight vectors with fixed support

a characterization of truth functions in the nilpotent minimum logic abstract by introducing a new family of partitions into the n cube 0 1 n the problem of characterizing truth tables of formulas in the nilpotent minimum logic is solved and their normal forms are presented so far only this kind of fuzzy truth functions have normal forms among all fuzzy propositional calculi which are based on left continuous but discontinuous t norm

approximation of uncertain functional relationships in this paper we consider methods for the linguistic modelling of vague functional relationships where the linguistic model is supposed to be given as a set of rules two approaches for deriving a fuzzy valued function from such models are proposed it is argued that both approaches can be interpreted as a generalization of ordinary methods for the interpolation and approximation of functions mathematical properties of fuzzy functions associated with a set of rules are investigated particularly for the second approach a universal approximation property is shown

stability and the fuzzy controller abstract this paper corrects a part of the main result theorem 1 in buckley fuzzy sets and systems 77 1996 167 173

can fuzzy neural nets approximate continuous fuzzy functions abstract we first argue that regular fuzzy neural nets based on standard fuzzy arithmetic and the extension principle cannot be universal approximators this negative result is surprising since regular neural nets are universal approximators we then argue that hybrid fuzzy neural nets not necessarily based on standard fuzzy arithmetic can be universal approximators