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 regular hilbert space representation of a moyal quantization it is shown that in the regular viz phase space representation of a moyal quantization real polynomials in the phase space variables become essentially self adjoint operators and that functions in the positive cone of monomials of even power in the phase space variables yield positive operators conditions on the boundedness of moyal operators are given the classical limit of a moyal operator is defined and used to relate classical with quantum entropy

on the relation between classical and quantum thermodynamic entropy we discuss the unresolved problem of proving rigorously that in the classical limit 0 the quantum thermodynamic entropy functional tends to the classical entropy functional we state rather restrictive conditions that define the general problem of finding a complete classical phase space representation of quantum kinematics whether the problem admits of solutions remains an unresolved question we discuss a physically interesting attempt to relate the structure in the classical limit 0 of the well known blokhintzev wigner and wehrl phase space functions to the spectral expansion of the quantum state operator

a ga based neural fuzzy system for temperature control abstract this paper addresses the structure and an associated learning algorithm of a feedforward multilayered connectionist network for realizing the basic elements and functions of a traditional fuzzy logic controller the genetic algorithm based neural fuzzy system ga nfs is based on takagi sugeno kang tsk type model possessing a neural network s learning ability a hybrid learning algorithm is proposed for parameters learning the proposed algorithm combines the genetic algorithm ga and the least squares estimate lse method to construct the ga nfs the genetic algorithm is used to tune membership functions at the precondition part of fuzzy rules while the lse method is used to tune parameters at the consequent part of fuzzy rules the performance of the ga nfs is compared to that of the traditional pid controller and fuzzy logic controller on the water bath temperature control system

new approach using ant colony optimization with ant set partition for fuzzy control design applied to the ball and beam system in this paper we describe the design of a fuzzy logic controller for the ball and beam system using a modified ant colony optimization aco method for optimizing the type of membership functions the parameters of the membership functions and the fuzzy rules this is achieved by applying a systematic and hierarchical optimization approach modifying the conventional aco algorithm using an ant set partition strategy the simulation results show that the proposed algorithm achieves better results than the classical aco algorithm for the design of the fuzzy controller

algorithms for the computation of the matrix logarithm based on the double exponential formula abstract we consider the computation of the matrix logarithm by using numerical quadrature the efficiency of numerical quadrature depends on the integrand and the choice of quadrature formula the gauss legendre quadrature has been conventionally employed however the convergence could be slow for ill conditioned matrices this effect may stem from the rapid change of the integrand values to avoid such situations we focus on the double exponential formula which has been developed to address integrands with endpoint singularity in order to utilize the double exponential formula we must determine a suitable finite integration interval which provides the required accuracy and efficiency in this paper we present a method for selecting a suitable finite interval based on an error analysis as well as two algorithms and one of these algorithms is an adaptive quadrature algorithm

biorthogonal bases of compactly supported wavelets orthonormal bases of compactly supported wavelet bases correspond to subband coding schemes with exact reconstruction in which the analysis and synthesis filters coincide we show here that under fairly general conditions exact reconstruction schemes with synthesis filters different from the analysis filters give rise to two dual riesz bases of compactly supported wavelets we give necessary and sufficient conditions for biorthogonality of the corresponding scaling functions and we present a sufficient condition for the decay of their fourier transforms we study the regularity of these biorthogonal bases we provide several families of examples all symmetric corresponding to linear phase filters in particular we can construct symmetric biorthogonal wavelet bases with arbitrarily high preassigned regularity we also show how to construct symmetric biorthogonal wavelet bases close to a nonsymmetric orthonormal basis

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

image coding using wavelet transform a scheme for image compression that takes into account psychovisual features both in the space and frequency domains is proposed this method involves two steps first a wavelet transform used in order to obtain a set of biorthogonal subclasses of images the original image is decomposed at different scales using a pyramidal algorithm architecture the decomposition is along the vertical and horizontal directions and maintains constant the number of pixels required to describe the image second according to shannon s rate distortion theory the wavelet coefficients are vector quantized using a multiresolution codebook to encode the wavelet coefficients a noise shaping bit allocation procedure which assumes that details at high resolution are less visible to the human eye is proposed in order to allow the receiver to recognize a picture as quickly as possible at minimum cost a progressive transmission scheme is presented it is shown that the wavelet transform is particularly well adapted to progressive transmission

a classical bound on quantum entropy a classical upper bound for quantum entropy is identified and illustrated 0 sq ln e 2 2 involving the variance 2 in phase space of the classical limit distribution of a given system a fortiori this further bounds the corresponding information theoretical generalizations of the quantum entropy proposed by renyi

divisive clustering of symbolic objects using the concepts of both similarity and dissimilarity a new approach to clustering of symbolic objects which makes use of both similarity and dissimilarity measures is proposed the proposed modified new similarity and dissimilarity measures will take into consideration the position span and content of symbolic objects the similarity and dissimilarity measures used are of new type the advantages of the proposed modified measures are presented a divisive clustering algorithm which makes use of both similarity and dissimilarity is proposed the results obtained by the proposed method is compared with other methods

reduction operations in fuzzy or valued constraint satisfaction in the constraint satisfaction problem csp knowledge about a relation on n variables is given in the form of constraints on subsets of the variables a solution to the csp is simply an instantiation of the n variables which satisfies all the constraints the fuzzy constraint satisfaction problem fcsp is a generalisation of the csp to the case in which the constraints are not categorical but represent preferences in the form of fuzzy sets the fcsp is then an optimisation problem in the space of all possible instantiations of the n variables it has potentially many more applications in real world problems than the csp when the aim is to maximise the value of the most violated constraint then the fcsp can be solved by solving a logarithmic number of csps fuzzy k consistency can even be established by an algorithm whose worst case complexity is identical to that of an optimal k consistency algorithm for csps when the operator used to aggregate constraint values is strictly monotonic as is the case in max csp for example the classic operation of arc consistency has to be completely redefined we show that an ordered version of arc consistency exists for all fcsps with a strictly monotonic aggregation operator and that in the case of max csp it can be established by an algorithm whose worst case complexity is identical to that of the optimal arc consistency algorithm for csps neighbourhood substitution in csps can be generalised to fuzzy neighbourhood substitution in fcsps whether the aggregation operator is strictly monotonic or idempotent we give an algorithm for applying fuzzy neighbourhood substitutions until convergence based on the corresponding algorithm for csps

classical information entropy and phase distributions of optical fields the wehrl phase distribution is defined as a phase density of the wehrl classical information entropy the new measure is applied to describe the quantum phase properties of some optical fields including fock states coherent and squeezed states and superposition of chaotic and coherent fields the wehrl phase distribution is compared with both the conventional wehrl entropy and husimi phase distribution the marginal husimi q function it is shown that the wehrl phase distribution is a good measure of the phase space uncertainty noise phase locking and phase bifurcation effects it is also demonstrated that the wehrl phase distribution properly describes phase randomization processes and thus can be used in a description of the quantum optical phase

a comparative study of feature extraction methods and their application to p rbf nns in face recognition problem this study is concerned with a design of a face recognition algorithm realized based on feature extraction with the aid of the 2 directional 2 dimensional linear discriminant analysis referred to as 2d 2lda the 2dlda algorithm yields high accuracy but comes with an unresolved problem of handling large feature matrices present in face recognition problems the proposed 2d 2lda algorithm is computationally more efficient and produces more powerful discrimination decision the proposed p rbf nns is used as a recognition module the architecture of this module consists of three functional components the coefficients of the p rbf nns model are obtained by fuzzy inference method forming the inference part of fuzzy rules the essential design parameters including learning rate momentum fuzzification coefficient and the feature selection mechanism of the networks are optimized by means of differential evolution de the experimental results reported for benchmark face datasets the yale orl database and ic ci dataset demonstrate the effectiveness and efficiency of 2d 2lda algorithm compared with other pre processing approaches such as lpp 2d pca 2d lpp sr pca 2d 2pca and fusion of pca lda the experimental results show that 2d 2lda based p rbf nns achieves higher performance than being reported by other methods

genetic algorithm based optimal fuzzy controller design in the linguistic space in this paper a genetic algorithm ga based optimal fuzzy controller design is proposed the design procedure is accomplished by establishing an index function as the consequent part of the fuzzy control rule the inputs of the controller after scaling are utilized by the index function for computing the output linguistic value this linguistic value can then be used to map the suitable fuzzy control actions this proposed novel fuzzy control rule has crisp input and fuzzified output characteristics the index function plays a role in mapping the desired fuzzy sets for defuzzification resulting in a controlled hypersurface in the linguistic space formed by the input fuzzy variables two types of index functions both linear and nonlinear are introduced for controlling systems with different degrees of nonlinearity the parameters of the index function are obtained by applying a simple ga with a suitable fitness function various controlled systems result in various parameter sets depending on their dynamics under the acquired optimal parameter set the optimal index function can be used to generate the desired control actions several simulation examples are given to verify the performance of the proposed ga based fuzzy controller

a novel radial basis function neural network for discriminant analysis a novel radial basis function neural network for discriminant analysis is presented in this paper in contrast to many other researches this work focuses on the exploitation of the weight structure of radial basis function neural networks using the bayesian method it is expected that the performance of a radial basis function neural network with a well explored weight structure can be improved as the weight structure of a radial basis function neural network is commonly unknown the bayesian method is therefore used in this paper to study this a priori structure two weight structures are investigated in this study i e a single gaussian structure and a two gaussian structure an expectation maximization learning algorithm is used to estimate the weights the simulation results showed that the proposed radial basis function neural network with a weight structure of two gaussians outperformed the other algorithms

face recognition a convolutional neural network approach we present a hybrid neural network for human face recognition which compares favourably with other methods the system combines local image sampling a self organizing map som neural network and a convolutional neural network the som provides a quantization of the image samples into a topological space where inputs that are nearby in the original space are also nearby in the output space thereby providing dimensionality reduction and invariance to minor changes in the image sample and the convolutional neural network provides partial invariance to translation rotation scale and deformation the convolutional network extracts successively larger features in a hierarchical set of layers we present results using the karhunen loeve transform in place of the som and a multilayer perceptron mlp in place of the convolutional network for comparison we use a database of 400 images of 40 individuals which contains quite a high degree of variability in expression pose and facial details we analyze the computational complexity and discuss how new classes could be added to the trained recognizer

renyi entropies characterizing the shape and the extension of the phase space representation of quantum wave functions in disordered systems we discuss some properties of the generalized entropies called renyi entropies and their application to the case of continuous distributions in particular it is shown that these measures of complexity can be divergent however their differences are free from these divergences thus enabling them to be good candidates for the description of the extension and the shape of continuous distributions we apply this formalism to the projection of wave functions onto the coherent state basis i e to the husimi representation we also show how the localization properties of the husimi distribution on average can be reconstructed from its marginal distributions that are calculated in position and momentum space in the case when the phase space has no structure i e no classical limit can be defined numerical simulations on a one dimensional disordered system corroborate our expectations

fuzzy sets as a basis for a theory of possibility the theory of possibility described in this paper is related to the theory of fuzzy sets by defining the concept of a possibility distribution as a fuzzy restriction which acts as an elastic constraint on the values that may be assigned to a variable more specifically if f is a fuzzy subset of a universe of discourse u u which is characterized by its membership function f then a proposition of the form x is f where x is a variable taking values in u induces a possibility distribution tx which equates the possibility of x taking the value u to f u the compatibility of u with f in this way x becomes a fuzzy variable which is associated with the possibility distribution tx in much the same way as a random variable is associated with a probability distribution in general a variable may be associated both with a possibility distribution and a probability distribution with the weak connection between the two expressed as the possibility probability consistency principle a thesis advanced in this paper is that the imprecision that is intrinsic in natural languages is in the main possibilistic rather than probabilistic in nature thus by employing the concept of a possibility distribution a proposition p in a natural language may be translated into a procedure which computes the probability distribution of a set of attributes which are implied by p several types of conditional translation rules are discussed and in particular a translation rule for propositions of the form x is f is possible where is a number in the interval 0 1 is formulated and illustrated by examples

investigations of information quantifiers for the tavis cummings model abstract in this article a system of two two level atoms interacting with a single mode quantized electromagnetic field in a lossless resonant cavity via a multi photon transition is considered the quantum fisher information negativity classical fisher information and reduced von neumann entropy for the two atoms are investigated we found that the number of photon transitions plays an important role in the dynamics of different information quantifiers in the cases of two symmetric and two asymmetric atoms our results show that there is a close relationship between the different quantifiers also the quantum and classical fisher information can be useful for studying the properties of quantum states which are important in quantum optics and information

generalized single hidden layer feedforward networks for regression problems in this paper traditional single hidden layer feedforward network slfn is extended to novel generalized slfn gslfn by employing polynomial functions of inputs as output weights connecting randomly generated hidden units with corresponding output nodes the significant contributions of this paper are as follows 1 a primal gslfn p gslfn is implemented using randomly generated hidden nodes and polynomial output weights whereby the regression matrix is augmented by full or partial input variables and only polynomial coefficients are to be estimated 2 a simplified gslfn s gslfn is realized by decomposing the polynomial output weights of the p gslfn into randomly generated polynomial nodes and tunable output weights 3 both p and s gslfn are able to achieve universal approximation if the output weights are tuned by ridge regression estimators and 4 by virtue of the developed batch and online sequential ridge elm br elm and osr elm learning algorithms high performance of the proposed gslfns in terms of generalization and learning speed is guaranteed comprehensive simulation studies and comparisons with standard slfns are carried out on real world regression benchmark data sets simulation results demonstrate that the innovative gslfns using br elm and osr elm are superior to standard slfns in terms of accuracy training speed and structure compactness

wehrl information entropy and phase distributions of schrodinger cat and cat like states the wehrl information entropy and its phase density the so called wehrl phase distribution are applied to describe schrcat and cat like kitten states the advantages of the wehrl phase distribution over the wehrl entropy in a description of the superposition principle are presented the entropic measures are compared with a conventional phase distribution from the husimi q function compact form formulae for the entropic measures are found for superpositions of well separated states examples of schr odinger cats including even odd and yurke stoler coherent states as well as the cat like states generated in the kerr medium are analysed in detail it is shown that in contrast to the wehrl entropy the wehrl phase distribution properly distinguishes between different superpositions of unequally weighted states with respect to their number and phase space configuration

comments on subband coding of images using asymmetrical filterbanks in the above paper egger and li see ibid vol 4 p 478 85 apr 1995 presented a set of two channel filterbanks asymmetrical filterbanks afb s for image coding applications the basic properties of these filters are linear phase perfect reconstruction asymmetric lengths for dual filters and maximum regularity in this correspondence we point out that the proposed afb s are not new in the sense that the proposed construction is equivalent to the factorization of lagrange halfband filters which has been reported by other researchers in addition we correct an error in the formulation of constructing afbs in their paper

symbolic classification clustering and fuzzy radial basis function network symbolic fuzzy classification is proposed using fuzzy radial basis function network with fuzzy c medoids clustering at the hidden layer symbolic objects include linguistic nominal boolean and interval type of features along with quantitative attributes classification and clustering in this domain involve the use of symbolic dissimilarity between the objects fuzzy memberships are used for appropriately handling uncertainty inherent in real life decisions the fuzzy radial basis function frbf network here comprises an integration of the principles of radial basis function rbf network and fuzzy c medoids clustering for handling non numeric data the optimal number of hidden nodes is determined by using clustering validity indices like normalized modified hubert s statistic and davies bouldin index in the symbolic framework the effectiveness of the symbolic fuzzy classification is demonstrated on real life benchmark data sets comparison is provided with the performance of a decision tree

renyi formulation of the entropic uncertainty principle for povms uncertainty relations for a pair of arbitrary measurements are posed in the form of inequalities using the renyi entropies the formulation deals with povm measurements on finite dimensional hilbert space both the entropic uncertainty relations with state dependent and state independent bounds are presented the results are illustrated on the example of measurements for state discrimination

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

an online self constructing neural fuzzy inference network and its applications a self constructing neural fuzzy inference network sonfin with online learning ability is proposed in this paper the sonfin is inherently a modified takagi sugeno kang tsk type fuzzy rule based model possessing neural network learning ability there are no rules initially in the sonfin they are created and adapted as online learning proceeds via simultaneous structure and parameter identification in the structure identification of the precondition part the input space is partitioned in a flexible way according to an aligned clustering based algorithm as to the structure identification of the consequent part only a singleton value selected by a clustering method is assigned to each rule initially afterwards some additional significant terms selected via a projection based correlation measure for each rule will be added to the consequent part incrementally as learning proceeds the combined precondition and consequent structure identification scheme can set up an economic and dynamically growing network a main feature of the sonfin in the parameter identification the consequent parameters are tuned optimally by either least mean squares or recursive least squares algorithms and the precondition parameters are tuned by a backpropagation algorithm to enhance the knowledge representation ability of the sonfin a linear transformation for each input variable can be incorporated into the network so that much fewer rules are needed or higher accuracy can be achieved

entropy and wigner functions the properties of an alternative definition of quantum entropy based on wigner functions are discussed such a definition emerges naturally from the wigner representation of quantum mechanics and can easily quantify the amount of entanglement of a quantum state it is shown that smoothing of the wigner function induces an increase in entropy this fact is used to derive some simple rules to construct positive definite probability distributions which are also admissible wigner functions

observability of renyi s entropy despite recent claims we argue that renyi s entropy is an observable quantity it is shown that contrary to popular belief the reported domain of instability for renyi entropies has zero measure bhattacharyya measure in addition we show that the instabilities can be easily emended by introducing a coarse graining into an actual measurement we also clear up any doubts regarding the observability of renyi s entropy in multi fractal systems and in systems with absolutely continuous probability density functions

genetic algorithm for the design of a class of fuzzy controllers an alternative approach a simple easy to implement alternative method for designing fuzzy logic controllers flcs with symmetrically distributed fuzzy sets in a universe of discourse is introduced the design parameters include the parameters of the membership functions of the inputs and outputs and the rule base the method is based on a network implementation of the flc with real and binary weights with constraints due to the presence of the binary weights the backpropagation technique cannot be used the learning problem is cast as a mixed integer constrained dynamic optimization problem and solved using the genetic algorithm ga the crossover and mutation are slightly disrupted in order to cope with the constraints on the binary weights training of the controller is carried out in a closed loop simulation with the controller in the loop

zero order tsk type fuzzy system learning using a two phase swarm intelligence algorithm this paper proposes zero order takagi sugeno kang tsk type fuzzy system learning using a two phase swarm intelligence algorithm tpsia the first phase of tpsia learns fuzzy system structure and parameters by on line clustering aided ant colony optimization aco phase two aims to further optimize all of the free parameters in the fuzzy system using particle swarm optimization pso in clustering aided aco caco fuzzy system structure is learned through on line clustering once a new rule is generated by clustering the consequent is selected from a discrete set of candidate values by aco in aco the path of an ant is regarded as a combination of consequent values selected from every rule caco helps to locate good initial fuzzy systems for subsequent phase learning in phase two initial particles in pso are randomly generated according to the best solution found by caco all free parameters in the designed fuzzy system are optimally tuned by pso simulations on fuzzy control of three nonlinear plants are conducted to verify tpsia performance comparisons with other learning algorithms demonstrate tpsia performance

simultaneous design of membership functions and rule sets for fuzzy controllers using genetic algorithms this paper examines the applicability of genetic algorithms ga s in the simultaneous design of membership functions and rule sets for fuzzy logic controllers previous work using genetic algorithms has focused on the development of rule sets or high performance membership functions however the interdependence between these two components suggests a simultaneous design procedure would be a more appropriate methodology when ga s have been used to develop both it has been done serially e g design the membership functions and then use them in the design of the rule set this however means that the membership functions were optimized for the initial rule set and not the rule set designed subsequently ga s are fully capable of creating complete fuzzy controllers given the equations of motion of the system eliminating the need for human input in the design loop this new method has been applied to two problems a cart controller and a truck controller beyond the development of these controllers we also examine the design of a robust controller for the cart problem and its ability to overcome faulty rules

fuzzy radial basis function neural networks with information granulation and its parallel genetic optimization fuzzy modeling of complex systems is a challenging task which involves important problems of dimensionality reduction and calls for various ways of improving the accuracy of modeling the ig frbfnn a hybrid architecture of the ig fis fuzzy inference system and frbfnn fuzzy radial basis function neural networks is proposed to address these problems the paper is concerned with the analysis and design of ig frbfnns and their optimization by means of the hierarchical fair competition based parallel genetic algorithm hfc pga in the proposed network the membership functions of the premise part of the fuzzy rules of the ig based frbfnn model directly rely on the computation of the relevant distance between data points and the use of four types of polynomials such as constant linear quadratic and modified quadratic are considered for the consequent part of fuzzy rules moreover the weighted least square wls learning is exploited to estimate the coefficients of the polynomial forming the conclusion part of the rules since the performance of the ig rbfnn model is affected by some key design parameters such as a specific subset of input variables the fuzzification coefficient of the fcm the number of rules and the order of polynomial of the consequent part of fuzzy rules it becomes beneficial to carry out both structural as well as parametric optimization of the network in this study the hfc pga is used as a comprehensive optimization vehicle the performance of the proposed model is illustrated by means of several representative numerical examples

on training rbf neural networks using input output fuzzy clustering and particle swarm optimization this paper elaborates on the use of particle swarm optimization in training gaussian type radial basis function neural networks under the umbrella of input output fuzzy clustering the problem being investigated concerns the selection of basis function centers that contribute most in network s performance given that the clustering process in the input space is guided by the clustering in the output space to accomplish this task we quantify the effect of the input space fuzzy partition upon network s square error in terms of an objective function that describes the ability of the partition to accurately reconstruct the input training samples we then theoretically prove that the minimization of the above function acts to minimize an upper bound of the network s square error therefore the resulting solution corresponds to a minimal square error while at the same time it maintains the structure of the input data due to the peculiarity of the aforementioned objective function we treat it as the fitness function used by the particle swarm optimizer the proposed methodology encompasses three design steps the first step implements an independent fuzzy clustering in the output space to obtain a set of cluster centers in the second step unlike other approaches the above centers are directly involved in the estimation of the membership degrees in the input output space in the third step these membership degrees are used by the particle swarm optimizer in order to obtain optimal values for the centers to summarize the novelty of our contribution lies in a the way we handle the information flow from output to input space and b the way we handle the effect of the input space partition upon network s performance the experiments indicate that the fitness function decreases as the number of hidden node increases finally a comparison between the proposed method and other sophisticated approaches shows its statistically significant superiority

a self generating method for fuzzy system design abstract in this paper a self generating method based on genetic algorithms is proposed to automatically construct a fuzzy system a parameter structure of fuzzy system is presented along with a fuzzy set elimination method which enables the self generating method not only to determine an appropriate fuzzy system with a high performance but also to favor the selected system with fewer fuzzy rules an inverted pendulum control and a system modeling problem are utilized respective to illustrate the efficiency of the proposed method in the fuzzy system design

symbolic clustering using a new dissimilarity measure abstract a new dissimilarity measure based on position span and content of symbolic objects is proposed for symbolic clustering the dissimilarity measure is new in the sense that it is not just another aspect of a similarity measure in the proposed hierarchical agglomerative clustering methodology composite symbolic objects are formed using a cartesian join operator whenever a mutual pair of symbolic objects is selected for agglomeration based on minimum dissimilarity the minimum dissimilarity values of different merging levels are used to compute the cluster indicator values and hence to determine the number of clusters in the data the results of the application of the algorithm on numeric data of known number of classes are described first so as to show the efficacy of the method subsequently the results of the experiments on two data sets of assertion type of symbolic objects drawn from the domains of fat oil and microcomputers are presented

polynomial based radial basis function neural networks p rbf nns realized with the aid of particle swarm optimization in this study we design polynomial based radial basis function neural networks p rbf nns based on a fuzzy inference mechanism the essential design parameters including learning rate momentum coefficient and fuzzification coefficient of the underlying clustering method are optimized by means of the particle swarm optimization the proposed p rbf nns dwell upon structural findings about training data that are expressed in terms of a partition matrix resulting from fuzzy clustering in this case being the fuzzy c means fcm the network is of functional nature as the weights between the hidden layer and the output are some polynomials the use of the polynomial weights becomes essential in capturing the nonlinear nature of data encountered in regression or classification problems from the perspective of linguistic interpretation the proposed network can be expressed as a collection of if then fuzzy rules the architecture of the networks discussed here embraces three functional modules reflecting the three phases of input output mapping realized in rule based architectures namely condition formation conclusion creation and aggregation the proposed classifier is applied to some synthetic and machine learning datasets and its results are compared with those reported in the previous studies

incremental learning based multiobjective fuzzy clustering for categorical data the problem of clustering categorical data where attribute values cannot be naturally ordered as numerical values has gained more importance in recent time due to the special properties of categorical attributes the clustering of categorical data seems to be more complicated than that of numerical data although a few clustering algorithms that optimize single clustering objective have been proposed it has found that such single measure may not be appropriate for all kind of datasets hence in this article an incremental learning based multiobjective fuzzy clustering for categorical data is proposed for this purpose a multiobjective modified differential evolution based fuzzy clustering algorithm is developed thereafter it integrates with the well known supervised classifier called random forest using incremental learning to propose the aforementioned technique here the multiobjective algorithm produces a set of optimal clustering solutions known as pareto optimal solutions by optimizing two conflicting objectives simultaneously subsequently through incremental learning using random forest classifier final solution is evolved from the ensemble pareto optimal solutions the results of the proposed method are demonstrated quantitatively and visually in comparison with widely used state of the art methods for six synthetic and four real life datasets finally statistical test is conducted to show the superiority of the results produced by the proposed method

fuzzy neural networks a survey abstract in this paper a fuzzy neural network will be a layered feedforward neural net that has fuzzy signals and or fuzzy weights we survey recent results on learning algorithms and applications for fuzzy neural networks