fuzzy wavelet networks for function learning inspired by the theory of multiresolution analysis mra of wavelet transforms and fuzzy concepts a fuzzy wavelet network fwn is proposed for approximating arbitrary nonlinear functions the fwn consists of a set of fuzzy rules each rule corresponding to a sub wavelet neural network wnn consists of single scaling wavelets through efficient bases selection the dimension of the approximated function does not cause the bottleneck for constructing fwn especially by learning the translation parameters of the wavelets and adjusting the shape of membership functions the model accuracy and the generalization capability of the fwn can be remarkably improved furthermore an algorithm for constructing and training the fuzzy wavelet networks is proposed simulation examples are also given to illustrate the effectiveness of the method

radial basis function based adaptive fuzzy systems and their applications to system identification and prediction abstract in this paper we describe a neuro fuzzy system with adaptive capability to extract fuzzy if then rules from input and output sample data through learning the proposed system called radial basis function rbf based adaptive fuzzy system afs employs the gaussian functions to represent the membership functions of the premise part of fuzzy rules three architectural deviations of the rbf based afs are also presented according to different consequence types such as constant first order linear function and fuzzy variable these provide versatility of the network to handle arbitrary fuzzy inference schemes we present examples of system identification and time series prediction to illustrate how to solve these problems and to demonstrate its validity and effectiveness using the rbf based afs

on the associated cycles of discrete series representations let g k be a classical symmetric pair defined by the involution ong let g k be the corresponding lie algebras given a stable borel subalgebra b we determine a densek orbit ink b k in the case when g k is of type aiii or bdi we use this information to compute the harmonic polynomial determined by the associated cycle of a large discrete series representation

fuzzy wavelet neural network models for prediction and identification of dynamical systems this paper presents fuzzy wavelet neural network fwnn models for prediction and identification of nonlinear dynamical systems the proposed fwnn models are obtained from the traditional takagi sugeno kang fuzzy system by replacing the then part of fuzzy rules with wavelet basis functions that have the ability to localize both in time and frequency domains the first and last model use summation and multiplication of dilated and translated versions of single dimensional wavelet basis functions respectively and in the second model then parts of the rules consist of radial function of wavelets gaussian type of activation functions are used in if part of the fuzzy rules a fast gradient based training algorithm i e the broyden fletcher goldfarb shanno method is used to find the optimal values for unknown parameters of the fwnn models simulation examples are also given to compare the effectiveness of the models with the other known methods in the literature according to simulation results we see that the proposed fwnn models have impressive generalization ability

global convergence of a cass of quasi newton methods on convex problems we study the global convergence properties of the restricted broyden class of quasi newton methods when applied to a convex objective function we assume that the line search satisfies a standard sufficient decrease condition and that the initial hessian approximation is any positive definite matrix we show global and superlinear convergence for this class of methods except for dfp this generalizes powell s well known result for the bfgs method the analysis gives us insight into the properties of these algorithms in particular it shows that dfp lacks a very desirable self correcting property possessed by bfgs

a novel parallel hybrid intelligence optimization algorithm for a function approximation problem a novel parallel hybrid intelligence optimization algorithm phioa is proposed based on combining the merits of particle swarm optimization with genetic algorithms the phioa uses the ideas of selection crossover and mutation from genetic algorithms gas and the update velocity and situation of particle swarm optimization pso under the independence of pso and gas the proposed algorithm divides the individuals into two equation groups according to their fitness values the subgroup of the top fitness values is evolved by gas and the other subgroup is evolved by the pso algorithm the optimal number is selected as a global optimum at every circulation which shows better results than both pso and gas then improves the overall performance of the algorithm the phioa is used to optimize the structure and parameters of the fuzzy neural network finally the experimental results have demonstrated the superiority of the proposed phioa to search the global optimal solution the phioa can improve the error accuracy while speeding up the convergence process and effectively avoid the premature convergence to compare with the existing methods

endoproperties of modules and local duality abstract let r be any ring and n i i n i be a direct sum of finitely presented left r modules n i suppose that d n and d n i are the local duals of n and n i for each i i we prove that the lattice of endosubmodules of n is anti isomorphic to the lattices of matrix subgroups of d n and of m i i d n i as consequences n is endoartinian if and only if m or d n is endonoetherian and n is endonoetherian if and only if m or d n is pure injective we obtain in particular that if r is a krull schmidt ring and m is an indecomposable pure injective endonoetherian right r module which is the source of a left almost split morphism in mod r then m is endofinite as an application a ring r is of finite representation type if and only if every pure injective right r module is endonoetherian

fuzzy modeling of high dimensional systems complexity reduction and interpretability improvement fuzzy modeling of high dimensional systems is a challenging topic this paper proposes an effective approach to data based fuzzy modeling of high dimensional systems an initial fuzzy rule system is generated based on the conclusion that optimal fuzzy rules cover extrema redundant rules are removed based on a fuzzy similarity measure then the structure and parameters of the fuzzy system are optimized using a genetic algorithm and the gradient method during optimization rules that have a very low firing strength are deleted finally interpretability of the fuzzy system is improved by fine training the fuzzy rules with regularization the resulting fuzzy system generated by this method has the following distinct features 1 the fuzzy system is quite simplified 2 the fuzzy system is interpretable and 3 the dependencies between the inputs and the output are clearly shown this method has successfully been applied to a system that has 11 inputs and one output with 20 000 training data and 80 000 test data

classes of modules with the exchange property in searching for isomorphic refinements of direct sum decompositions of modules9 crawley and jonsson introduced an exchange property for modules that is strongly reminiscent of steinitz exchange lemma for vector spaces an r module m where r is an associative ring with identity is said to have the finite exchange property if m can be fitted into any finite sum grid as follows whenever a4 occurs as a direct summand of a finite direct sum a bielai then a m ci for suitable submodules ci of the ai 2 this concept led to very general extensions of the classical refinement theorems see e g 2 3 171 many of the problems suggested by crawley and jonsson in their pioneering paper are still open the most salient one does the finite exchange property imply the unrestricted exchange property we show that the answer is yes for modules which possess decompositions into indecomposable summands in the background of this observation stands the following

differential operators on homogeneous spaces iii characteristic varieties of harish chandra modules and of primitive ideals letg be a semi simple complex algebraic group with lie algebra and flag varietyx g b for each primitive idealj with trivial central character in the enveloping algebrau we define a characteristic variety in the cotangent bundle ofx which projects under the springer resolution mapt x onto the closure of a nilpotent orbit we prove that this characteristic variety is theg saturation of the characteristic variety of a highest weight module with annihilatorj we conjecture that it is irreducible forg sl n our conjecture would provide a geometrical explanation for the classification of primitive ideals in terms of weyl group representations as achieved by a joseph the presentation of these ideas here is simultaneously used to some extent as an opportunity to continue our more general systematic discussion of differential operators on a complete homogeneous space and to study more generally characteristic varieties of harish chandra modules

finite splitness and finite projectivity let r be a ring let a c be left r modules and f a c an epimorphism f is called pure if hom m f hom m a hom m c is an epimorphism for all finitely presented left r modules m let b be the kernel off then by a theorem of fieldhouse and warfield f is pure if and only if b is pure in a in the sense that the natural homomorphism n or b n or a derived from the inclusion map b a is a monomorphism for all right r modules n and moreover by cohn s theorem this is equivalent to the condition that if a finite system of linear equations c aixj bi i 1 2 m with aye r and bie b has a solution x x2 x in a then it has a solution in b i e there exist y y y b such that j aii y bj i 1 2 m in the present paper we attempt to generalize this situation by replacing the class of finitely presented modules with the class of finitely generated modules to yield a series of some meaningful results we call the epimorphism f finitely split if hom m f is an epimorphism for all finitely generated left rmodules m or what is the same thing if for any finitely generated submodule c of c there exists a homomorphism cp co a such that f 0 cp is the identity map of co in terms of the kernel b off this is equivalent to the condition that b is a direct summand of every submodule a of a such that a 3 b and the factor module a b is finitely generated we say in this case that b is finitely split in a we can show that this is also equivalent to the following condition if a finite or infinite system of linear equations c 1 a x bi i e i with au e r and bi e b has a solution x x2 x in a then it has a solution in b let a4 be a left r module m is called pure projective if every pure epimorphism onto m splits while a4 is called pure injective if m is a direct 114 0021 8693 87 3 00

structurally dynamic wavelet networks for adaptive control of robotic systems the practical applicability of recently developed adaptive neurocontrol algorithms for poorly modelled robotic systems depends crucially upon the accuracy and efficiency of the neural network used

bayesian wavelet networks for nonparametric regression radial wavelet networks have been proposed previously as a method for nonparametric regression we analyze their performance within a bayesian framework we derive probability distributions over both the dimension of the networks and the network coefficients by placing a prior on the degrees of freedom of the model this process bypasses the need to test or select a finite number of networks during the modeling process predictions are formed by mixing over many models of varying dimension and parameterization we show that the complexity of the models adapts to the complexity of the data and produces good results on a number of benchmark test series

ten years of genetic fuzzy systems current framework and new trends fuzzy systems have demonstrated their ability to solve different kinds of problems in various application domains currently there is an increasing interest to augment fuzzy systems with learning and adaptation capabilities two of the most successful approaches to hybridise fuzzy systems with learning and adaptation methods have been made in the realm of soft computing neural fuzzy systems and genetic fuzzy systems hybridise the approximate reasoning method of fuzzy systems with the learning capabilities of neural networks and evolutionary algorithms the objective of this paper is to provide an account of genetic fuzzy systems with special attention to genetic fuzzy rule based systems after a brief introduction to models and applications of genetic fuzzy systems the field is overviewed new trends are identified a critical evaluation of genetic fuzzy systems for fuzzy knowledge extraction is elaborated and open questions that remain to be addressed in the future are raised the paper also includes some of the key references required to quickly access implementation details of genetic fuzzy systems

a new class of wavelet networks for nonlinear system identification a new class of wavelet networks wns is proposed for nonlinear system identification in the new networks the model structure for a high dimensional system is chosen to be a superimposition of a number of functions with fewer variables by expanding each function using truncated wavelet decompositions the multivariate nonlinear networks can be converted into linear in the parameter regressions which can be solved using least squares type methods an efficient model term selection approach based upon a forward orthogonal least squares ols algorithm and the error reduction ratio err is applied to solve the linear in the parameters problem in the present study the main advantage of the new wn is that it exploits the attractive features of multiscale wavelet decompositions and the capability of traditional neural networks by adopting the analysis of variance anova expansion wns can now handle nonlinear identification problems in high dimensions

an algorithmic approach for fuzzy inference to apply fuzzy logic two major tasks need to be performed the derivation of production rules and the determination of membership functions these tasks are often difficult and time consuming this paper presents an algorithmic method for generating membership functions and fuzzy production rules the method includes an entropy minimization for screening analog values membership functions are derived by partitioning the variables into the desired number of fuzzy terms and production rules are obtained from minimum entropy clustering decisions in the rule derivation process rule weights are also calculated this algorithmic approach alleviates many problems in the application of fuzzy logic to binary classification

injective modules and fp injective modules over valuation rings abstract it is shown that each almost maximal valuation ring r such that every indecomposable injective r module is countably generated satisfies the following condition c each fp injective r module is locally injective the converse holds if r is a domain moreover it is proved that a valuation ring r that satisfies this condition c is almost maximal the converse holds if spec r is countable when this last condition is satisfied it is also proved that every ideal of r is countably generated new criteria for a valuation ring to be almost maximal are given they generalize the criterion given by e matlis in the domain case necessary and sufficient conditions for a valuation ring to be an if ring are also given

decomposition properties of strict mittag leffler modules we show that a not necessarily unitary ring with enough idempotents is left perfect if and only if there exists a cardinal number such that every flat strict mittag leffler module is a direct sum of generated modules several applications are given to the decomposition properties of modules into direct summands

fuzzy wavelet network identification of optimum operating point of non crystalline silicon solar cells the emerging non crystalline silicon c si solar cell technologies are starting to make significant inroads into solar cell markets most of the researchers have focused on c si solar cell in maximum power points tracking applications of photovoltaic pv systems however the characteristics of non c si solar cell technologies at maximum power point mpp have different trends in current voltage characteristics for this reason determining the optimum operating point is very important for different solar cell technologies to increase the efficiency of pv systems in this paper it has been shown that the use of fuzzy system coupled with a discrete wavelet network in takagi sugeno type model structure is capable of identifying the mpp voltage of different non c si solar cells with very high accuracy the performance of the fuzzy wavelet network fwn method has been compared with other ann structures such as radial basis function rbf adaptive neuro fuzzy inference system anfis and three layered feed forward neural network tffn the simulation results show that the single fwn architecture has superior approximation accuracy over the other methods and a very good generalization capability for different operating conditions and different technologies

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

single hidden layer fuzzy recurrent wavelet neural network when a fuzzy wavelet neural network fwnn has a large number of neurons in its consequent part it may not be able to effectively follow fast variations in the process this paper aims to develop a single hidden layer fuzzy recurrent wavelet neural network slfrwnn for the function approximation and identification of dynamic systems in the proposed framework the consequent part of each fuzzy rule is developed by a single neuron with the capability of storing the past data of the network to guarantee the convergence and to speed up the process of the on line training algorithm the optimal learning rate olr is introduced based on lyapunov stability theory the modifications allow the slfrwnn to be much faster than fwnn and hence it is more appropriate in real time applications the efficiency of the modified model is investigated using three different types of wavelet families in approximating a benchmark piecewise function furthermore two nonlinear dynamic plants are considered to demonstrate the feasibility of the slfrwnn in the system identification the results indicate that slfrwnn achieves higher accuracy and needs a lower number of parameters than the other models

stable adaptive fuzzy control of nonlinear systems a direct adaptive fuzzy controller that does not require an accurate mathematical model of the system under control is capable of incorporating fuzzy if then control rules directly into the controllers and guarantees the global stability of the resulting closed loop system in the sense that all signals involved are uniformly bounded is developed the specific formula for the bounds is provided so that controller designers can determine the bounds based on their requirements the direct adaptive fuzzy controller is used to regulate an unstable system to the origin and to control the duffing chaotic system to track a trajectory the simulation results show that the controller worked without using any fuzzy control rules and that after fuzzy control rules were incorporated the adaptation speed became much faster it is shown explicitly how the supervisory control forces the state to remain within the constraint set and how the adaptive fuzzy controller learns to regain control

every ℵ1 σ cs module is σ cs abstract it is proved that if m is a uniform module such that m 1 is cs then its endomorphism ring is local as a consequence it is shown that every 1 cs module is cs this solves open questions asked in contemp math 259 2000 467 j algebra 262 2003 194 on the way to these results it is also shown that the endomorphism ring of a uniform module m is local provided that every local summand of m 0 is a direct summand

lattice dynamical wavelet neural networks implemented using particle swarm optimization for spatio temporal system identification in this brief by combining an efficient wavelet representation with a coupled map lattice model a new family of adaptive wavelet neural networks called lattice dynamical wavelet neural networks ldwnns is introduced for spatio temporal system identification a new orthogonal projection pursuit opp method coupled with a particle swarm optimization pso algorithm is proposed for augmenting the proposed network a novel two stage hybrid training scheme is developed for constructing a parsimonious network model in the first stage by applying the opp algorithm significant wavelet neurons are adaptively and successively recruited into the network where adjustable parameters of the associated wavelet neurons are optimized using a particle swarm optimizer the resultant network model obtained in the first stage however may be redundant in the second stage an orthogonal least squares algorithm is then applied to refine and improve the initially trained network by removing redundant wavelet neurons from the network an example for a real spatio temporal system identification problem is presented to demonstrate the performance of the proposed new modeling framework

modules with indecomposable decompositions that complement maximal direct summands generalizing a fundamental property of semisimple modules anderson w x and fuller 1 introduced the following important concept for direct decompositions of modules a decomposition m s m is said to ig i i complement direct summands in case for each direct summand a of m w there is a subset h i such that m s a m cf also 2 p ig h i x 141 such a decomposition is necessarily an indecomposable decomposition and it is an interesting problem to study under which conditions an indecomposable decomposition complements direct summands there is w x an extensive literature concerning this problem by 1 theorem 6 right perfect rings can be characterized by the property that all projective right modules have decompositions that complement direct summands fuller w x 7 showed that over a generalized uniserial ring every module has a decomposition that complements direct summands thus providing a first class of non semisimple rings satisfying this property more generally w x tachikawa 14 proved that every left and right module over a ring of finite representation type has a decomposition that complements direct summands and that the converse is also true was established by fuller and w x w x reiten 9 restricting just to one side fuller 8 showed that rings over which every right module has a decomposition that complements direct summands are precisely the rings over which every right module is a direct sum of finitely generated modules they are also called right pure semisim

wavelet neural networks for function learning a wavelet based neural network is described the structure of this network is similar to that of the radial basis function rbf network except that in the present paper the radial basis functions are replaced by orthonormal scaling functions that are not necessarily radial symmetric the efficacy of this type of network in function learning and estimation is demonstrated through theoretical analysis and experimental results in particular it has been shown that the wavelet network has universal and l sup 2 approximation properties and is a consistent function estimator convergence rates associated with these properties are obtained for certain function classes where the rates avoid the curse of dimensionality in the experiments the wavelet network performed well and compared favorably to the mlp and rbf networks

a solution to the baer splitting problem let r be a commutative domain we prove that an r module b is projective if and only if ext 1 r b t 0 for any torsion module t this answers in the affirmative a question raised by kaplansky in 1962

design of fuzzy wavelet neural networks using the ga approach for function approximation and system identification in this paper an efficient method is proposed to design fuzzy wavelet neural network fwnn for function learning and identification by tuning fuzzy membership functions and wavelet neural networks the structure of fwnn is based on the basis of fuzzy rules including wavelet functions in the consequent parts of rules in order to improve the function approximation accuracy and general capability of the fwnn system an efficient genetic algorithm ga approach is used to adjust the parameters of dilation translation weights and membership functions by minimizing a quadratic measure of the error derived from the output of the system the design problem can be characterized by the proposed ga formulation moreover the solution is directly obtained without any need for complicated computations the performance of our approximation is superior to that of existing methods several numerical design examples are likewise presented to demonstrate the design flexibility and usefulness of this presented approach

nonlinear control via approximate input output linearization the ball and beam example approximate input output linearization of nonlinear systems which fail to have a well defined relative degree is studied for such systems a method for constructing approximate systems that are input output linearizable is provided the analysis presented is motivated through its application to a common undergraduate control laboratory experiment the ball and beam where it is shown to be more effective for trajectory tracking than the standard jacobian linearization

evolutionary algorithm based learning of fuzzy neural networks part 2 recurrent fuzzy neural networks fuzzy neural networks fnn as opposed to neuro fuzzy systems whose main task is to process numerical relationships can process both numerical measurement based information and perception based information in spite of great importance of fuzzy feed forward and recurrent neural networks for solving wide range of real world problems today there are no effective training algorithm for them currently there are two approaches for training of fnn first approach is based on application of the level sets of fuzzy numbers and the back propagation bp algorithm the second approach involves using evolutionary algorithms to minimize error function and determine the fuzzy connection weights and biases the method based on the second approach was proposed by the authors and published in part 1 of this paper r a aliev b fazlollahi r vahidov genetic algorithm based learning of fuzzy neural networks part 1 feed forward fuzzy neural networks fuzzy sets and systems 118 2001 351 358 in contrast to the bp and other supervised learning algorithms evolutionary algorithms do not require nor use information about differentials and hence they are most effective in case where the derivative is very difficult to obtain or even unavailable however the main deficiency of the existing fnn based on the feed forward architecture is its adherence to static problems in case of dynamic or temporal problems there is a need for recurrent fuzzy neural networks rfnn designing efficient training algorithms for rfnn has recently become an active research direction in this paper we propose an effective differential evolution optimization deo based learning algorithm for rfnn with fuzzy inputs fuzzy weights and biases and fuzzy outputs the effectiveness of the proposed method is illustrated through simulation of benchmark forecasting and identification problems and comparisons with the existing methods the suggested approach has also been used for real applications in an oil refinery plant for petrol production forecasting

fuzzy basis functions universal approximation and orthogonal least squares learning fuzzy systems are represented as series expansions of fuzzy basis functions which are algebraic superpositions of fuzzy membership functions using the stone weierstrass theorem it is proved that linear combinations of the fuzzy basis functions are capable of uniformly approximating any real continuous function on a compact set to arbitrary accuracy based on the fuzzy basis function representations an orthogonal least squares ols learning algorithm is developed for designing fuzzy systems based on given input output pairs then the ols algorithm is used to select significant fuzzy basis functions which are used to construct the final fuzzy system the fuzzy basis function expansion is used to approximate a controller for the nonlinear ball and beam system and the simulation results show that the control performance is improved by incorporating some common sense fuzzy control rules

sigma cotorsion rings abstract it is proved that a ring r is right perfect if and only if it is cotorsion as a right module over itself several other conditions are shown to be equivalent for example that every pure submodule of a free right r module is strongly pure essential in a direct summand or that the countable direct sum c r 0 of the cotorsion envelope of r r is cotorsion if c r is a flat cotorsion module then c r admits a decomposition into a direct sum of indecomposable modules with a local endomorphism ring the jacobson radical j s of the endomorphism ring s end r c is characterized as the maximum ideal that acts locally t nilpotently on c r if r is semilocal and c c r then the radical consists of those endomorphisms f c c whose image is contained in cj

classification of admissible nilpotent orbits in the classical real lie algebras m duflo introduced the notion of admissibility of a linear form on a real lie algebra and constructed certain unitary representations from admissible linear forms with good polarization in d d vogan has wanted to find a notion of unipotent representations of real reductive groups which corresponds to the one of lusztig s unipotent representations of finite reductive groups he pointed out that a unipotent representation should be a constituent of a representation attached to an admissible nilpotent coadjoint orbit by some orbit method cf vl v2 but for real reductive groups there have not yet been found the correct definition of unipotent representations and hence the orbit method which should exist i e a correspondence between admissible nilpotent coadjoint orbits and representations which contain unipotent representations as constituents however it seems that these notions must play an important role for the classification of unitary representations the purpose of this paper is to determine all the admissible nilpotent orbits in real classical non compact lie groups here a real classical lie group means a lie group in the following list rg

adaptive fuzzy wavelet network control design for nonlinear systems this paper presents a new adaptive fuzzy wavelet network controller a fwnc for control of nonlinear affine systems inspired by the theory of multiresolution analysis mra of wavelet transforms and fuzzy concepts the proposed adaptive gain controller which results from the direct adaptive approach has the ability to tune the adaptation parameter in the then part of each fuzzy rule during real time operation each fuzzy rule corresponds to a sub wavelet neural network sub wnn and one adaptation parameter each sub wnn consists of wavelets with a specified dilation value the degree of contribution of each sub wnn can be controlled flexibly orthogonal least square ols method is used to determine the number of fuzzy rules and to purify the wavelets for each sub wnn since the efficient procedure of selecting wavelets used in the ols method is not very sensitive to the input dimension the dimension of the approximated function does not cause the bottleneck for constructing fwn fwn is constructed based on the training data set of the nominal system and the constructed fuzzy rules can be adjusted by learning the translation parameters of the selected wavelets and also determining the shape of membership functions then the constructed adaptive fwn controller is employed such that the feedback linearization control input can be best approximated and the closed loop stability is guaranteed the performance of the proposed a fwnc is illustrated by applying a second order nonlinear inverted pendulum system and compared with previously published methods simulation results indicate the remarkable capabilities of the proposed control algorithm it is worth noting that the proposed controller significantly improves the transient response characteristics and the number of fuzzy rules and on line adjustable parameters are reduced

forecasting time series with genetic fuzzy predictor ensemble this paper proposes a genetic fuzzy predictor ensemble gfpe for the accurate prediction of the future in the chaotic or nonstationary time series each fuzzy predictor in the gfpe is built from two design stages where each stage is performed by different genetic algorithms ga the first stage generates a fuzzy rule base that covers as many of training examples as possible the second stage builds fine tuned membership functions that make the prediction error as small as possible these two design stages are repeated independently upon the different partition combinations of input output variables the prediction error will be reduced further by invoking the gfpe that combines multiple fuzzy predictors by an equal prediction error weighting method applications to both the mackey glass chaotic time series and the nonstationary foreign currency exchange rate prediction problem are presented the prediction accuracy of the proposed method is compared with that of other fuzzy and neural network predictors in terms of the root mean squared error rmse

characteristic cycles of discrete series for rank one groups we determine the characteristic cycles of the discrete series representations for connected r rank one linear groups the computation is made through the moment maps we determine their fibers and the cohomology in question case by case the multiplicity of the discrete series in terms of their harish chandra parameters is given by recursive formulae for groups of type a and b closed formulae are obtained

baer and mittag leffler modules over tame hereditary algebras we develop a structure theory for two classes of infinite dimensional modules over tame hereditary algebras the baer modules and the mittag leffler ones a right r module m is called baer if rm ext 1 r m t 0 for all torsion modules t and m is mittag leffler in case the canonical map m otimes r prod i in i q i to prod i in i m otimes rq i is injective where q i i in i are arbitrary left r modules we show that a module m is baer iff m is p filtered where p is the preprojective component of the tame hereditary algebra r we apply this to prove that the universal localization of a baer module is projective in case we localize with respect to a complete tube using infinite dimensional tilting theory we then obtain a structure result showing that baer modules are more complex then the infinite dimensional preprojective modules in the final section we give a complete classification of the mittag leffler modules

an identification algorithm in fuzzy relational systems abstract the paper presents an effective identification method in fuzzy relational systems we propose an algorithm for constructing models on the basis of fuzzy and nonfuzzy data with the aid of fuzzy discretization and clustering techniques the usefulness of the method provided is demonstrated by means of two numerical examples also a possible way of generating a linguistic decision making algorithm is discussed

trajectory priming with dynamic fuzzy networks in nonlinear optimal control fuzzy logic systems have been recognized as a robust and attractive alternative to some classical control methods the application of classical fuzzy logic fl technology to dynamic system control has been constrained by the nondynamic nature of popular fl architectures many difficulties include large rule bases i e curse of dimensionality long training times etc these problems can be overcome with a dynamic fuzzy network dfn a network with unconstrained connectivity and dynamic fuzzy processing units called feurons in this study dfn as an optimal control trajectory priming system is considered as a nonlinear optimization with dynamic equality constraints the overall algorithm operates as an autotrainer for dfn a self learning structure and generates optimal feed forward control trajectories in a significantly smaller number of iterations for this dfn encapsulates and generalizes the optimal control trajectories by the algorithm the time varying optimal feedback gains are also generated along the trajectory as byproducts this structure assists the speeding up of trajectory calculations for intelligent nonlinear optimal control for this purpose the direct descent curvature algorithm is used with some modifications called modified descend controller mdc algorithm for the nonlinear optimal control computations the algorithm has numerically generated robust solutions with respect to conjugate points the minimization of an integral quadratic cost functional subject to dynamic equality constraints which is dfn is considered for trajectory obtained by mdc tracking applications the adjoint theory whose computational complexity is significantly less than direct method has been used in the training of dfn which is as a quasilinear dynamic system the updating of weights identification of dfn parameters are based on broyden fletcher goldfarb shanno bfgs method simulation results are given for controlling a difficult nonlinear second order system using fully connected three feuron dfn

efficient self evolving evolutionary learning for neurofuzzy inference systems this study proposes an efficient self evolving evolutionary learning algorithm seela for neurofuzzy inference systems nfiss the major feature of the proposed seela is that it is based on evolutionary algorithms that can determine the number of fuzzy rules and adjust the nfis parameters the seela consists of structure learning and parameter learning the structure learning attempts to determine the number of fuzzy rules a subgroup symbiotic evolution is adopted to yield several variable fuzzy systems and an elite based structure strategy is adopted to find a suitable number of fuzzy rules for solving a problem the parameter learning is to adjust parameters of the nfis it is a hybrid evolutionary algorithm of cooperative particle swarm optimization cpso and cultural algorithm called cultural cpso ccpso the ccpso which uses cooperative behavior among multiple swarms can increase the global search capacity using the belief space experimental results demonstrate that the proposed method performs well in predicting time series and solving nonlinear control problems

a hybrid learning algorithm for a class of interval type 2 fuzzy neural networks in real life information about the world is uncertain and imprecise the cause of this uncertainty is due to deficiencies on given information the fuzzy nature of our perception of events and objects and on the limitations of the models we use to explain the world the development of new methods for dealing with information with uncertainty is crucial for solving real life problems in this paper three interval type 2 fuzzy neural network it2fnn architectures are proposed with hybrid learning algorithm techniques gradient descent backpropagation and gradient descent with adaptive learning rate backpropagation at the antecedents layer a interval type 2 fuzzy neuron it2fn model is used and in case of the consequents layer an interval type 1 fuzzy neuron model it1fn in order to fuzzify the rule s antecedents and consequents of an interval type 2 takagi sugeno kang fuzzy inference system it2 tsk fis it2 tsk fis is integrated in an adaptive neural network in order to take advantage the best of both models this provides a high order intuitive mechanism for representing imperfect information by means of use of fuzzy if then rules in addition to handling uncertainty and imprecision on the other hand neural networks are highly adaptable with learning and generalization capabilities experimental results are divided in two kinds in the first one a non linear identification problem for control systems is simulated here a comparative analysis of learning architectures it2fnn and anfis is done for the second kind a non linear mackey glass chaotic time series prediction problem with uncertainty sources is studied finally it2fnn proved to be more efficient mechanism for modeling real world problems

a hammerstein recurrent neurofuzzy network with an online minimal realization learning algorithm this paper presents a hammerstein recurrent neurofuzzy network associated with an online minimal realization learning algorithm for dealing with nonlinear dynamic applications we fuse the concept of states in linear systems into a neurofuzzy framework so that the whole structure can be expressed by a state space representation an online minimal realization learning algorithm has been developed to find a controllable and observable state space model of minimal size from the input output measurements of a given system such an idea can simultaneously resolve the problem of the determination of a minimal structure and the difficulty of network stability analysis the advantages of our approach include 1 our recurrent network is capable of translating the complicated dynamic behavior of a nonlinear system into a minimal set of linguistic fuzzy dynamical rules and into state space representation as well and 2 an online minimal realization learning algorithm unifies an order determination algorithm a hybrid parameter initialization method and a recursive recurrent learning algorithm into a systematic procedure to identify a minimal structure with satisfactory performance performance evaluations on benchmark examples as well as real world applications have successfully validated the effectiveness of our approach

a key module over pure semisimple hereditary rings abstract let r be a hereditary indecomposable left pure semisimple ring inspired by i reiten c m ringel infinite dimensional representations of canonical algebras canad j math 58 2006 180 224 we investigate the perfect cotorsion pair c d in r mod generated by the preinjective component q we show that there is a finitely generated product complete tilting and cotilting left r module w such that c cogen w and d gen w the finite subcategory w of r mod given by the indecomposable summands of w stores important information on r for example if we assume r of infinite representation type then by b zimmermann huisgen strong preinjective partitions and representation type of artinian rings proc amer math soc 109 1990 309 322 there are non preinjective indecomposable modules occurring as direct summands of products of preinjective modules and it turns out that w is precisely the class of such modules moreover we prove that r has finite representation type if and only if every module in w is source of a left almost split map in r mod finally we address the question when w is endofinite