design for self organizing fuzzy neural networks based on genetic algorithms a novel hybrid learning algorithm based on a genetic algorithm to design a growing fuzzy neural network named self organizing fuzzy neural network based on genetic algorithms sofnnga to implement takagi sugeno ts type fuzzy models is proposed in this paper a new adding method based on geometric growing criterion and the epsiv completeness of fuzzy rules is first used to generate the initial structure then a hybrid algorithm based on genetic algorithms backpropagation and recursive least squares estimation is used to adjust all parameters including the number of fuzzy rules this has two steps first the linear parameter matrix is adjusted and second the centers and widths of all membership functions are modified the ga is introduced to identify the least important neurons i e the least important fuzzy rules simulations are presented to illustrate the performance of the proposed algorithm

training anfis as an identifier with intelligent hybrid stable learning algorithm based on particle swarm optimization and extended kalman filter this paper proposes a novel hybrid learning algorithm with stable learning laws for adaptive network based fuzzy inference system anfis as a system identifier the proposed hybrid learning algorithm is based on the particle swarm optimization pso for training the antecedent part and the extended kalman filter ekf for training the conclusion part lyapunov stability theory is used to study the stability of the proposed algorithm comparison results of the proposed approach pso algorithm for training the antecedent part and recursive least squares rlss or ekf algorithm for training the conclusion part with the other classical approaches such as gradient descent resilient propagation quick propagation levenberg marquardt for training the antecedent part and rlss algorithm for training the conclusion part are provided moreover it is shown that applying pso a powerful optimizer to optimally train the parameters of the membership function on the antecedent part of the fuzzy rules in anfis system is a stable approach which results in an identifier with the best trained model stability constraints are obtained and different simulation results are given to validate the results also the stability of levenberg marquardt algorithms for anfis training is analyzed

a new gradient descent approach for local learning of fuzzy neural models the majority of reported learning methods for takagi sugeno kang tsk fuzzy neural models to date mainly focus on improvement of their accuracy however one of the key design requirements in building an interpretable fuzzy model is that each obtained rule consequent must match well with the system local behavior when all the rules are aggregated to produce the overall system output this is one of the distinctive characteristics from black box models such as neural networks therefore how to find a desirable set of fuzzy partitions and hence identify the corresponding consequent models which can be directly explained in terms of system behavior presents a critical step in fuzzy neural modeling in this paper a new learning approach considering both nonlinear parameters in the rule premises and linear parameters in the rule consequents is proposed unlike the conventional two stage optimization procedure widely practiced in the field where the two sets of parameters are optimized separately the consequent parameters are transformed into a dependent set on the premise parameters thereby enabling the introduction of a new integrated gradient descent learning approach thus a new jacobian matrix is proposed and efficiently computed to achieve a more accurate approximation of the cost function by using the second order levenberg marquardt optimization method several other interpretability issues regarding the fuzzy neural model are also discussed and integrated into this new learning approach numerical examples are presented to illustrate the resultant structure of the fuzzy neural models and the effectiveness of the proposed new algorithm and compared with the results from some well known methods

symplectic integration of hamiltonian systems with additive noise hamiltonian systems with additive noise possess the property of preserving symplectic structure numerical methods with the same property are constructed for such systems special attention is paid to systems with separable hamiltonians and to second order differential equations with additive noise some numerical tests are presented

a new fuzzy neural network with fast learning algorithm and guaranteed stability for manufacturing process control in this paper a new fuzzy neural network fnn is presented for manufacturing process control it is different from the conventional fnn in its structure learning algorithm and stability analysis method firstly it utilizes the input and output layer to on line fine tune scaling factors it can also use the hidden layers to realize the fuzzification fuzzy inference defuzzification and tune parameters such as membership functions fuzzy control rules dynamically secondly a new combining learning algorithm cl which combines the gradient based error back propagation algorithm ebp with similar newton sn algorithm is proposed in order to improve the convergence speed and release computational burden during the learning process lastly a convergence condition for determining the stability of fnn is established physical experiments for manufacturing process control are implemented to evaluate the effectiveness of the proposed scheme

some properties of a class of functions related to completely monotonic functions in this article we present several properties of the composition of functions which are related to the completely monotonic and absolutely monotonic functions relevant connections of the results derived in this article with those in earlier investigations are also indicated

successive identification of a fuzzy model and its applications to prediction of a complex system abstract a successive identification method of a fuzzy model is suggested the identification mechanism consists of two levels one is the supervisor level and the other is the adjustment level the supervisor level determines a policy of parameter adjustment using a set of fuzzy adjustment rules the adjustment rules are derived from the fuzzy implications of a fuzzy model and are extended to fuzzy adjustment rules by using an extended concept of zadeh s contrast intensification the adjustment level executes the policy of parameter adjustment determined with the fuzzy adjustment rules the parameter adjustment consists of premise parameter adjustment and consequent parameter adjustment both of them are realized by the weighted recursive least square algorithm finally it is shown from two examples that the method is very useful for modeling complex systems

identifying fuzzy models utilizing genetic programming abstract fuzzy models offer a convenient way to describe complex nonlinear systems moreover they permit the user to deal with uncertainty and vagueness due to these advantages fuzzy models are employed in various fields of applications e g control forecasting and pattern recognition nevertheless it has to be emphasized that the identification of a fuzzy model is a complex optimization task with many local minima genetic programming provides a way to solve such complex optimization problems in this work the use of genetic programming to identify the input variables the rule base and the involved membership functions of a fuzzy model is proposed for this purpose several new reproduction operators are introduced

recurrent neuro fuzzy networks for nonlinear process modeling a type of recurrent neuro fuzzy network is proposed in this paper to build long term prediction models for nonlinear processes the process operation is partitioned into several fuzzy operating regions within each region a local linear model is used to model the process the global model output is obtained through the centre of gravity defuzzification which is essentially the interpolation of local model outputs this modeling strategy utilizes both process knowledge and process input output data process knowledge is used to initially divide the process operation into several fuzzy operating regions and to set up the initial fuzzification layer weights process i o data are used to train the network network weights are such trained so that the long term prediction errors are minimized through training membership functions of fuzzy operating regions are refined and local models are learnt based on the recurrent neuro fuzzy network model a novel type of nonlinear model based long range predictive controller can be developed and it consists of several local linear model based predictive controllers local controllers are constructed based on the corresponding local linear models and their outputs are combined to form a global control action by using their membership functions this control strategy has the advantage that control actions can be calculated analytically avoiding the time consuming nonlinear programming procedures required in conventional nonlinear model based predictive control the techniques have been successfully applied to the modeling and control of a neutralization process

supplements to a class of logarithmically completely monotonic functions associated with the gamma function abstract in this article the authors present a necessary condition a sufficient condition and a necessary and sufficient condition for a class of functions associated with the gamma function to be logarithmically completely monotonic as a consequence of these results supplements to the recent investigation by chen and qi c p chen f qi logarithmically completely monotonic functions relating to the gamma function j math anal appl 321 2006 405 411 are provided and a new keckic vasic type inequality is concluded

stochastic symplectic runge kutta methods for the strong approximation of hamiltonian systems with additive noise abstract in this paper we construct stochastic symplectic runge kutta ssrk methods of high strong order for hamiltonian systems with additive noise by means of colored rooted tree theory we combine conditions of mean square order 1 5 and symplectic conditions to get totally derivative free schemes we also achieve mean square order 2 0 symplectic schemes for a class of second order hamiltonian systems with additive noise by similar analysis finally linear and non linear systems are solved numerically which verifies the theoretical analysis on convergence order especially for the stochastic harmonic oscillator with additive noise the linear growth property can be preserved exactly over long time simulation

fuzzy identification using fuzzy neural networks with stable learning algorithms in general fuzzy neural networks cannot match nonlinear systems exactly unmodeled dynamic leads parameters drift and even instability problem according to system identification theory robust modification terms must be included in order to guarantee lyapunov stability this paper suggests new learning laws for mamdani and takagi sugeno kang type fuzzy neural networks based on input to state stability approach the new learning schemes employ a time varying learning rate that is determined from input output data and model structure stable learning algorithms for the premise and the consequence parts of fuzzy rules are proposed the calculation of the learning rate does not need any prior information such as estimation of the modeling error bounds this offer an advantage compared to other techniques using robust modification

extracting fuzzy rules for system modeling using a hybrid of genetic algorithms and kalman filter abstract this paper proposes a hybrid algorithm for extracting important fuzzy rules from a given rule base to construct a parsimonious fuzzy model with a high generalization ability this algorithm combines the advantages of genetic algorithms strong search capacity and kalman filter s fast convergence merit each random combination of the rules in the rule base is coded into a binary string and treated as a chromosome in genetic algorithms the binary string indicates the structure of a fuzzy model the parameters of the model are then estimated using the kalman filter in order to achieve a trade off between the accuracy and the complexity of a fuzzy model the schwarz rissanen criterion is used as an evaluation function in the hybrid algorithm the practical applicability of the proposed algorithm is examined by computer simulations on a human operator modeling problem and a nonlinear system modeling problem

learning and convergence analysis of neural type structured networks a class of feedforward neural networks structured networks has recently been introduced as a method for solving matrix algebra problems in an inherently parallel formulation a convergence analysis for the training of structured networks is presented since the learning techniques used in structured networks are also employed in the training of neural networks the issue of convergence is discussed not only from a numerical algebra perspective but also as a means of deriving insight into connectionist learning bounds on the learning rate are developed under which exponential convergence of the weights to their correct values is proved for a class of matrix algebra problems that includes linear equation solving matrix inversion and lyapunov equation solving for a special class of problems the orthogonalized back propagation algorithm an optimal recursive update law for minimizing a least squares cost functional is introduced it guarantees exact convergence in one epoch several learning issues are investigated

identification and control of dynamic systems using recurrent fuzzy neural networks proposes a recurrent fuzzy neural network rfnn structure for identifying and controlling nonlinear dynamic systems the rfnn is inherently a recurrent multilayered connectionist network for realizing fuzzy inference using dynamic fuzzy rules temporal relations are embedded in the network by adding feedback connections in the second layer of the fuzzy neural network fnn the rfnn expands the basic ability of the fnn to cope with temporal problems in addition results for the fnn fuzzy inference engine universal approximation and convergence analysis are extended to the rfnn for the control problem we present the direct and indirect adaptive control approaches using the rfnn based on the lyapunov stability approach rigorous proofs are presented to guarantee the convergence of the rfnn by choosing appropriate learning rates finally the rfnn is applied in several simulations time series prediction identification and control of nonlinear systems the results confirm the effectiveness of the rfnn

fuzzy logic for digital phase locked loop filter design the problem of robust phase locked loop design has attracted attention for many years particularly since the advent of the global positioning system this paper proposes and demonstrates the use of a fuzzy pll to estimate the time varying phase of a sinusoidal signal it is shown via simulation results that fuzzy pll s offer performance comparable to analytically derived pll s e g kalman filters and h sub spl infin estimators when the phase exhibits high dynamics and high noise the fuzzy pll rules are optimized using a gradient descent method and a genetic algorithm

sequential adaptive fuzzy inference system safis for nonlinear system identification and prediction in this paper a sequential adaptive fuzzy inference system called safis is developed based on the functional equivalence between a radial basis function network and a fuzzy inference system fis in safis the concept of influence of a fuzzy rule is introduced and using this the fuzzy rules are added or removed based on the input data received so far if the input data do not warrant adding of fuzzy rules then only the parameters of the closest in a euclidean sense rule are updated using an extended kalman filter ekf scheme the performance of safis is compared with several existing algorithms on two nonlinear system identification benchmark problems and a chaotic time series prediction problem results indicate that safis produces similar or better accuracies with less number of rules compared to other algorithms

gurland s ratio for the gamma function we consider the ratio t x y x y 2 x y 2 and its properties related to convexity logarithmic convexity schur convexity and complete monotonicity several new bounds and asymptotic expansions for t are derived sharp bounds for the function x x 1 e x are presented as well as bounds for the trigamma function the results are applied to a problem related to the volume of the unit ball in r n and also to the problem of finding the inverse of the function x t 1 x 3 x which is of importance in applied statistics

numerical methods for stochastic systems preserving symplectic structure stochastic hamiltonian systems with multiplicative noise phase flows of which preserve symplectic structure are considered to construct symplectic methods for such systems sufficiently general fully implicit schemes i e schemes with implicitness both in deterministic and stochastic terms are needed a new class of fully implicit methods for stochastic systems is proposed increments of wiener processes in these fully implicit schemes are substituted by some truncated random variables a number of symplectic integrators is constructed special attention is paid to systems with separable hamiltonians some results of numerical experiments are presented they demonstrate superiority of the proposed symplectic methods over very long times in comparison with nonsymplectic ones

training fuzzy systems with the extended kalman filter the generation of membership functions for fuzzy systems is a challenging problem we show that for mamdani type fuzzy systems with correlation product inference centroid defuzzification and triangular membership functions optimizing the membership functions can be viewed as an identification problem for a nonlinear dynamic system this identification problem can be solved with an extended kalman filter we describe the algorithm and compare it with gradient descent and with adaptive neuro fuzzy inference system anfis based optimization of fuzzy membership functions the methods discussed in this paper are illustrated on a fuzzy filter for motor winding current estimation and are compared with butterworth filtering we demonstrate that the kalman filter can be an effective tool for improving the performance of a fuzzy system

stability analysis and stabilization of fuzzy state space models abstract a new stability test method for linguistic fuzzy state space models is proposed in this paper this method allows the determination of stability of fuzzy models by applying the lyapunov function to each rule a gradient based algorithm is suggested to simplify the stability tests using this algorithm the lyapunov equation can be updated towards the direction where the stability can be determined more correctly an additional gradient based stabilizing algorithm is also derived which allows a systematic approach to find stabilizing controls by updating the lyapunov equations towards the direction where unstable eigenvalues are decreased examples demonstrate the convenience of the stability test and the two suggested gradient based algorithms

a recurrent self organizing neural fuzzy inference network a recurrent self organizing neural fuzzy inference network rsonfin is proposed the rsonfin is inherently a recurrent multilayered connectionist network for realizing the basic elements and functions of dynamic fuzzy inference and may be considered to be constructed from a series of dynamic fuzzy rules the temporal relations embedded in the network are built by adding some feedback connections representing the memory elements to a feedforward neural fuzzy network each weight as well as node in the rsonfin has its own meaning and represents a special element in a fuzzy rule there are no hidden nodes initially in the rsonfin they are created online via concurrent structure identification and parameter identification the structure learning together with the parameter learning forms a fast learning algorithm for building a small yet powerful dynamic neural fuzzy network two major characteristics of the rsonfin can thus be seen 1 the recurrent property of the rsonfin makes it suitable for dealing with temporal problems and 2 no predetermination like the number of hidden nodes must be given since the rsonfin can find its optimal structure and parameters automatically and quickly moreover to reduce the number of fuzzy rules generated a flexible input partition method the aligned clustering based algorithm is proposed various simulations on temporal problems are done and performance comparisons with some existing recurrent networks are also made efficiency of the rsonfin is verified from these results

some properties of completely monotonic sequences and related interpolation in this article we present some properties of completely monotonic sequences based on our result related interpolation problems are then solved

implementation of evolutionary fuzzy systems evolutionary fuzzy systems are discussed in which the membership function shapes and types and the fuzzy rule set including the number of rules inside it are evolved using a genetic evolutionary algorithm in addition the genetic parameters operators of the evolutionary algorithm are adapted via a fuzzy system benefits of the methodology are illustrated in the process of classifying the iris data set possible extensions of the methods are summarized

the fuzzy kalman filter state estimation using possibilistic techniques a new method to implement fuzzy kalman filters is introduced the combination of possibilistic techniques and the extended kalman filter has special application in fields where inaccurate information is involved the novelty of this article comes from the fact that by using possibility distributions instead of gaussian distributions a fuzzy description of the expected state and observation is sufficient to obtain a good estimation some characteristics of this approach are that uncertainty does not need to be symmetric and that a wide region of possible values for the expectations is allowed to implement the algorithm this approach also contributes a method to propagate uncertainty through the process model and the observation model based on trapezoidal possibility distributions finally several examples of a real mobile robot moving through a localization process while using qualitative landmarks are shown

fuzzy kalman filtering the classical kalman filtering kf algorithm has recently been extended to interval linear systems with interval parameters under the same statistical assumptions on noise where the new algorithm is called interval kalman filtering ikf scheme the ikf algorithm has the same structure and preserves the same optimality as the classical kf scheme but provides interval valued estimates if the interval system has confidence description about the distribution of its interval values we can further incorporate the ikf scheme with fuzzy logic inference so as to develop a new filtering algorithm called fuzzy kalman filtering fkf algorithm this algorithm preserves the same recursive mechanism of the kf and ikf but produces a scalar valued rather than an interval valued estimate at each iteration of the filtering process to compare the fkf to the ikf computer simulation is included which shows that the fkf is also robust against system parameter variations

stability analysis of discrete tsk type ii iii systems we propose a new approach for the stability analysis of discrete sugeno types ii and iii fuzzy systems the approach does not require the existence of a common lyapunov function we introduce the concept of fuzzy positive definite and fuzzy negative definite functions this new concept is used to replace classical positive and negative definite functions in arguments similar to those of traditional lyapunov stability theory we obtain the equivalent fuzzy system for a cascade of two type ii iii fuzzy systems we use the cascade of a system and a fuzzy lyapunov function candidate to derive new conditions for stability and asymptotic stability for discrete type ii and type iii fuzzy systems to demonstrate the new approach we apply it to numerical examples where no common lyapunov function exists

a set of practical experiments to validate the fuzzy kalman filter abstract the fuzzy kalman filter fkf was recently reformulated with a number of basic examples included in order to demonstrate its applicability we now look ahead to its practical implementation introducing deep analysis which includes very detailed simulations and complete real applications this will allow us to not only validate the fkf but also to draw important conclusions which will help users in the adjustment of the fuzzy filter parameters and the choosing of possibilistic distributions

automatic design of hierarchical takagi sugeno type fuzzy systems using evolutionary algorithms this paper presents an automatic way of evolving hierarchical takagi sugeno fuzzy systems ts fs the hierarchical structure is evolved using probabilistic incremental program evolution pipe with specific instructions the fine tuning of the if then rule s parameters encoded in the structure is accomplished using evolutionary programming ep the proposed method interleaves both pipe and ep optimizations starting with random structures and rules parameters it first tries to improve the hierarchical structure and then as soon as an improved structure is found it further fine tunes the rules parameters it then goes back to improve the structure and the rules parameters this loop continues until a satisfactory solution hierarchical ts fs model is found or a time limit is reached the proposed hierarchical ts fs is evaluated using some well known benchmark applications namely identification of nonlinear systems prediction of the mackey glass chaotic time series and some classification problems when compared to other neural networks and fuzzy systems the developed hierarchical ts fs exhibits competing results with high accuracy and smaller size of hierarchical architecture

stochastic symplectic methods based on the pade approximations for linear stochastic hamiltonian systems in this article we propose a kind of numerical methods based on the pade approximations for two kinds of stochastic hamiltonian systems for the general linear stochastic hamiltonian systems it is shown that the applied pade approximations p k k produce numerical solutions that are symplectic and the proposed numerical schemes based on p r s are of root mean square convergence order r s 2 for a special kind of linear stochastic hamiltonian systems with additive noises the numerical methods using two kinds of pade approximations p r s and p r 1 possess root mean square convergence order r 2 when r s r 3 and are symplectic if r s these generalize the pade approximation approaches for symplectic integration of linear hamiltonian systems to the stochastic context

logarithmically completely monotonic functions and applications in this article we give a sufficient condition and a necessary and sufficient condition for a function class associated with the gamma function to be logarithmically completely monotonic some applications are also presented

inequalities for zero balanced hypergeometric functions the authors study certain monotoneity and convexity properties of the gaussian hypergeometric function and those of the euler gamma function

on some inequalities for the gamma and psi functions we present new inequalities for the gamma and psi functions and we provide new classes of completely monotonic star shaped and superadditive functions which are related to and