a ga based fuzzy modeling approach for generating tsk models this paper proposes a new genetic based modeling method for building simple and well defined tsk models with scatter type input partitions our approach manages all attributes characterizing the structure of a tsk model simultaneously particularly it determines the number of rules the input partition the participating inputs in each rule and the consequent parameters the model building process is divided into two phases in phase one the structure learning task is formulated as a multi objective optimization problem which is resolved using a novel genetic based structure learning gbsl scheme apart from the mean square error mse and the number of rules three additional criteria are introduced in the fitness function for measuring the quality of the partitions optimization of these measures leads to models with representative rules small overlapping and efficient data cover in order to obtain models with accurate data fitting and good local performance the consequent parameters are determined using a local mse function while the overall model is evaluated on the basis of a global mse function the search capabilities of the suggested structure learning scheme are significantly enhanced by including a highly effective local search operator implemented by a micro genetic algorithm and four problem specific operators finally a genetic based parameter learning gbpl scheme is suggested in phase two which performs fine tuning of the initial models obtained after structure learning the performance of the proposed modeling approach is evaluated using a static example and a well known dynamic benchmark problem simulation results demonstrate that our models outperform those suggested by other methods with regard to simplicity model structure and accuracy

on the characterization of graphs by star complements abstract let g be a graph of order n and be an adjacency eigenvalue of g with multiplicity k 1 a star complement for in g is an induced subgraph of g of order n k with no eigenvalue in this paper all the regular graphs with k 1 1 t as a star complement are determined also the maximal graphs with k 1 1 t t 8 9 as a star complement for the eigenvalue 1 and k 7 as a star complement for the eigenvalue 2 are described

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

selecting fuzzy if then rules for classification problems using genetic algorithms this paper proposes a genetic algorithm based method for selecting a small number of significant fuzzy if then rules to construct a compact fuzzy classification system with high classification power the rule selection problem is formulated as a combinatorial optimization problem with two objectives to maximize the number of correctly classified patterns and to minimize the number of fuzzy if then rules genetic algorithms are applied to this problem a set of fuzzy if then rules is coded into a string and treated as an individual in genetic algorithms the fitness of each individual is specified by the two objectives in the combinatorial optimization problem the performance of the proposed method for training data and test data is examined by computer simulations on the iris data of fisher

structure optimization of fuzzy neural network by genetic algorithm abstract this paper presents an auto tuning method of fuzzy inference using genetic algorithm and delta rule fuzzy inference is applied to various problems however the determination of membership functions of the fuzzy inference depends on human experts which is a difficult problem and time consuming therefore some auto tuning methods have been proposed to reduce the time consuming operations however the convergence of the tuning by the conventional methods depends on the initial conditions of the fuzzy model so we propose an auto tuning method for the fuzzy neural network by genetic algorithm the new tuning method realizes to construct minimal and optimal structure of the fuzzy model this paper shows effectiveness of the tuning system by simulations compared with the conventional method

improving the interpretability of tsk fuzzy models by combining global learning and local learning the fuzzy inference system proposed by takagi sugeno and kang known as the tsk model in fuzzy system literature provides a powerful tool for modeling complex nonlinear systems unlike conventional modeling where a single model is used to describe the global behavior of a system tsk modeling is essentially a multimodel approach in which simple submodels typically linear models are combined to describe the global behavior of the system most existing learning algorithms for identifying the tsk model are based on minimizing the square of the residual between the overall outputs of the real system and the identified model although these algorithms can generate a tsk model with good global performance i e the model is capable of approximating the given system with arbitrary accuracy provided that sufficient rules are used and sufficient training data are available they cannot guarantee the resulting model to have a good local performance often the submodels in the tsk model may exhibit an erratic local behavior which is difficult to interpret since one of the important motivations of using the tsk model also other fuzzy models is to gain insights into the model it is important to investigate the interpretability issue of the tsk model we propose a new learning algorithm that integrates global learning and local learning in a single algorithmic framework this algorithm uses the idea of local weighed regression and local approximation in nonparametric statistics but remains the component of global fitting in the existing learning algorithms the algorithm is capable of adjusting its parameters based on the user s preference generating models with good tradeoff in terms of global fitting and local interpretation we illustrate the performance of the proposed algorithm using a motorcycle crash modeling example

a fuzzy logic based approach to qualitative modeling this paper discusses a general approach to quali tative modeling based on fuzzy logic the method of qualitative modeling is divided into two parts fuzzy modeling and linguistic approximation it proposes to use a fuzzy clustering method fuzzy c means method to identify the structure of a fuzzy model to clarify the advantages of the proposed method it also shows some examples of modeling among them a model of a dynamical process and a model of a human operator s control action

a gmdh based fuzzy modeling approach for constructing ts model in this paper a new learning algorithm based on group method of data handling gmdh is proposed for the identification of takagi sugeno fuzzy model different from existing methods the new approach called ts gmdh starts from simple elementary ts fuzzy models and then uses the mechanism of gmdh to produce candidate fuzzy models of growing complexity until the ts model of optimal complexity has been created the main characteristic of the new approach is its ability to identify the structure of ts model automatically experiments on box jenkins gas furnace data and uci datasets have shown that the proposed method can achieve satisfactory results and is more robust to noise in comparison with other ts modeling techniques such as anfis

adaptive fuzzy output tracking control of mimo nonlinear uncertain systems in this paper the adaptive fuzzy tracking control problem is discussed for a class of uncertain multiple input multiple output mimo nonlinear systems with the block triangular structure the fuzzy logic systems are used to approximate the unknown nonlinear functions by using the backstepping technique the adaptive fuzzy tracking control design scheme is developed which has minimal learning parameterizations the adaptive fuzzy tracking controllers guarantee that the outputs of systems converge to a small neighborhood of the reference signals and all the signals in the closed loop system are semiglobally uniformly ultimately bounded two examples are used to show the effectiveness of the approach

star complements and switching in graphs star complements are used to construct switching equivalent graphs which share an eigenvalue of the same multiplicity a variant of the construction is used to obtain a characterization of the mclaughlin graph

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

fuzzy instrumental variable approach for nonlinear discrete time systems identification in a noisy environment nonlinear discrete time systems identification based on instrumental variable iv method and takagi sugeno ts fuzzy model is proposed in this paper the ivs statistically uncorrelated with noise are adequately chosen and mapped to fuzzy sets partitioning the input space of the nonlinear plant in subregions for unbiased estimates of the ts fuzzy model consequent parameters in a noisy environment the fuzzy instrumental variable fiv concept is proposed so that consistency and unbias properties of the fiv algorithm are derived from lemmas and theorem simulation results show the efficiency of the fiv algorithm for nonlinear system identification in a noisy environment and its application for modeling of an aluminium beam with free free configuration which is commonly used for active vibration control design in aircrafts and aerospace vehicles

ga fuzzy modeling and classification complexity and performance the use of genetic algorithms gas and other evolutionary optimization methods to design fuzzy rules for systems modeling and data classification have received much attention in recent literature authors have focused on various aspects of these randomized techniques and a whole scale of algorithms have been proposed we comment on some recent work and describe a new and efficient two step approach that leads to good results for function approximation dynamic systems modeling and data classification problems first fuzzy clustering is applied to obtain a compact initial rule based model then this model is optimized by a real coded ga subjected to constraints that maintain the semantic properties of the rules we consider four examples from the literature a synthetic nonlinear dynamic systems model the iris data classification problem the wine data classification problem and the dynamic modeling of a diesel engine turbocharger the obtained results are compared to other recently proposed methods

parameter identification of tsk neuro fuzzy models abstract in the framework of the tsk neuro fuzzy model a combination of the two well known identification methods are employed for parameter estimation of the neuro fuzzy inference system namely the series parallel and the parallel configurations the presented paper proposes two new possible configurations for identifying the parameters of the tsk neuro fuzzy model using the combinations of these two existing configurations one of the proposed configurations constitutes the series parallel configuration to the premise part and the parallel configuration to the consequent part of the neuro fuzzy model termed as ps p configuration the second one is composed of the series parallel configuration to the consequent part and the parallel configuration to the premise part of the neuro fuzzy model termed as cs p configuration the presented work mainly deals with a comparative study of the proposed configurations and the existing configurations in the context of parameter identification of the tsk neuro fuzzy model on three different benchmark examples moreover it investigates upper bound of the learning rates using the lyapunov stability theorem to assure the stability and the convergence of the model learning process implementation of the modified mountain clustering mmc and the cluster validity function yields initial models to restrict the upper bound during the learning process it also presents a two phase adaptive learning rate

self tuning fuzzy modeling with adaptive membership function rules and hierarchical structure based on genetic algorithm abstract recently fuzzy systems have been used in many fields and places in order to apply the fuzzy system to the various fields the tuning and optimizing method of the fuzzy system is the key issue some self tuning methods have been proposed so far however these conventional self tuning methods do not have sufficient capability of learning in this paper we propose a new supervised self tuning fuzzy modeling which consist of some membership function expressed by the radial basis function with insensitive region learning is carried out by the genetic algorithms the descent method is also utilized for tuning the shapes of the membership function and consequent parts the effectiveness of the proposed methods is shown by some numerical examples

optifel a convergent heterogeneous particle swarm optimization algorithm for takagi sugeno fuzzy modeling data driven design of accurate and reliable takagi sugeno t s fuzzy systems has attracted a lot of attention where the model structures and parameters are important and often solved in an optimization framework the particle swarm optimization pso algorithm is widely applied in the field however the classical pso suffers from premature convergence and it is trapped easily into local optima which will significantly affect the model accuracy to overcome these drawbacks we have developed a new t s fuzzy system parameters searching strategy called optifel with a heterogeneous multiswarm pso mspso to enhance the searching performance mspso groups the whole population into multiple cooperative subswarms which perform different search behaviors for the potential solutions we have found that the multiple subswarms strategy proposed in this paper is greatly helpful for finding the optimal parameters suitable for the subspaces of the t s fuzzy model our theoretical proof has also demonstrated that the cooperation among the subswarms can maintain a balance between exploration and exploitation to ensure the particles converge to stable points experimental results show that mspso performs significantly better than traditional pso algorithms on six benchmark functions with the improved mspso optifel can generate a good fuzzy system model with high accuracy and strong generalization ability

a genetic based neuro fuzzy approach for modeling and control of dynamical systems linguistic modeling of complex irregular systems constitutes the heart of many control and decision making systems and fuzzy logic represents one of the most effective algorithms to build such linguistic models in this paper a linguistic qualitative modeling approach is proposed the approach combines the merits of the fuzzy logic theory neural networks and genetic algorithms gas the proposed model is presented in a fuzzy neural network fnn form which can handle both quantitative numerical and qualitative linguistic knowledge the learning algorithm of a fnn is composed of three phases the first phase is used to find the initial membership functions of the fuzzy model in the second phase a new algorithm is developed and used to extract the linguistic fuzzy rules in the third phase a multiresolutional dynamic genetic algorithm mrd ga is proposed and used for optimized tuning of membership functions of the proposed model two well known benchmarks are used to evaluate the performance of the proposed modeling approach and compare it with other modeling approaches

on bipartite graphs with complete bipartite star complements abstract let g be a bipartite graph with as an eigenvalue of multiplicity k 1 we show that if g has k r s 1 r s as a star complement for then k s 1 moreover if is non main then k s 2 for large enough s we provide examples of graphs in which various bounds on k or s are attained we also describe the bipartite graphs with k 1 s as a star complement for a non main eigenvalue of multiplicity s 1 1

eigenvalue multiplicity in triangle free graphs abstract let g be a connected triangle free graph of order n 5 with 1 0 as an eigenvalue of multiplicity k 1 we show that if d is the maximum degree in g then k n d 1 moreover if k n d 1 then either a g is non bipartite and k 2 3 1 2 2 1 with equality only if g is strongly regular or b g is bipartite and k d 1 with equality only if g is a bipolar cone in each case we discuss the extremal graphs that arise

a multilayered neuro fuzzy classifier with self organizing properties a novel self organizing neuro fuzzy multilayered classifier sonefmuc is suggested in this paper which is composed of small scale interconnected fuzzy neuron classifiers fncs arranged in layers the model provides a different perspective for generating a new class of hierarchical classifiers with multilevel classifiers combination at each layer parent fncs are combined to construct a descendant fnc at the next layer with enhanced classification qualities the generic fncs exhibit an original structure including four modules 1 the fuser aggregates the decision support outputs of the parent fncs using a fusion operator 2 the data splitting module divides data into correctly classified patterns with high degree of confidence which are handled by the fuser and ambiguous ones 3 the last two modules are realized by fuzzy rule based systems and implement a neuro fuzzy classifier within each fnc used to improve the classification accuracy of ambiguous patterns the former performs feature transformations to an intermediate output space while the latter provides the decision supports of non confident patterns unlike traditional classifiers the classification mapping is accomplished in sonefmuc by performing successive decision fusions and feature transformations sonefmuc structure is determined sequentially via a self constructing learning algorithm structure learning inherently implements feature selection considering the most informative attributes as model inputs to improve classification accuracy the models obtained after structure learning are optimized using a parameter learning scheme based on genetic algorithms the effectiveness of our approach is tested on a set of benchmark classification problems experimental results show that the proposed neuro fuzzy classifier is favorably compared to other well known classification techniques of the literature

the number of regular semisimple conjugacy classes in the finite classical groups abstract using generating functions we enumerate regular semisimple conjugacy classes in the finite classical groups for the general linear unitary and symplectic groups this gives a different approach to known results for the special orthogonal groups the results are new

on degrees of irreducible brauer characters based on a large amount of examples which we have checked so far we conjecture that g p 1 2 where p is a prime and the sum runs through the set of irreducible brauer characters in characteristic p of the finite group g we prove the conjecture simultaneously for p solvable groups and groups of lie type in the defining characteristic in non defining characteristics we give asymptotically an affirmative answer in many cases

regular graphs with a prescribed complete multipartite graph as a star complement abstract let g be a simple graph of order n and let be an adjacency eigenvalue with multiplicity k 1 a star complement h for in g is an induced subgraph of order n k with no eigenvalue in this paper the regular graphs with the complete multipartite graph s k 1 k t s 2 as a star complement are investigated more precisely when is a main eigenvalue we prove that g k s 2 when is a non main eigenvalue we determine the regular graphs with s k 1 k t as a star complement for t 1 or s 3 we show that the complete multipartite graph s 1 k 2 s 2 is the only possible graph under a certain condition and we raise a conjecture for the general case

application of neural networks incorporated with real valued genetic algorithms in knowledge acquisition abstract often a major difficulty in the design of rule based systems is the process of acquiring the requisite knowledge in the form of if then rules this paper presents a class of fuzzy degraded hyperellipsoidal composite neural networks fdhecnns that are trained to provide appealing solutions to the problem of knowledge acquisition the values of the network parameters after sufficient training are then utilized to generate if then rules on the basis of preselected meaningful features in order to avoid the risk of getting stuck in local minima during the training process a real valued genetic algorithm is proposed to train fdhecnns the effectiveness of the method is demonstrated on two problems namely the truck backer upper problem as well as real world application of a hypothesis regarding the pathophysiology of diabetes

star complements in regular graphs old and new results we survey results concerning star complements in finite regular graphs and note the connection with designs and strongly regular graphs in certain cases we include improved proofs along with new results on stars and windmills as star complements

on graphs with prescribed star complements abstract let be an eigenvalue of a simple graph g with multiplicity k 1 a star complement for in g is an induced subgraph of g of order n k with no eigenvalue in this paper we study the maximal graphs with the star s m as a star complement for 2 the maximal graphs with s 3 s 4 s 13 and s 21 as a star complement for 2 are described we also describe the regular graphs with k 2 s s 2 as a star complement for an eigenvalue

an iv qr algorithm for neuro fuzzy multivariable online identification in this paper a new algorithm for neuro fuzzy identification of multivariable discrete time nonlinear dynamic systems more specifically applied to consequent parameters estimation of the neuro fuzzy inference system is proposed based on a decomposed form as a set of coupled multiple input and single output miso takagi sugeno ts neuro fuzzy networks an on line scheme is formulated for modeling a nonlinear autoregressive with exogenous input narx recurrent neuro fuzzy structure from input output samples of a multivariable nonlinear dynamic system in a noisy environment the adaptive weighted instrumental variable wiv algorithm by qr factorization based on the numerically robust orthogonal householder transformation is developed to modify the consequent parameters of the ts multivariable neuro fuzzy network

a design of genetically oriented fuzzy relation neural networks frnns based on the fuzzy polynomial inference scheme in this paper we introduce new architectures of genetically oriented fuzzy relation neural networks frnns and offer a comprehensive design methodology that supports their development the proposed frnns are based on ldquoif thenrdquo rule based networks with the extended structure of the premise and the consequence parts of the individual rules we consider two types of the frnn topologies which are called frnn i and frnn ii here depending upon the usage of inputs in the premise and the consequence of fuzzy rules three different forms of regression polynomials namely constant linear and quadratic are used to construct the consequence of the rules in order to develop optimal frnns the structure and the parameters are optimized using genetic algorithms gas the proposed methodology is compared when the two development strategies with separate and simultaneous optimization schemes that involve structure and parameters are carried out given the large search space associated with these frnn models we enhance the search capabilities of the gas by introducing the dynamic variants of genetic optimization it fully exploits the processing capabilities of the frnns by supporting their structural and parametric optimization to evaluate the performance of the proposed frnns we exploit a suite of several representative numerical examples a comparative analysis shows that the frnns exhibit higher accuracy and predictive capabilities as well as better modeling stability when compared with some other models that exist in the literature

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

building sugeno type models using fuzzy discretization and orthogonal parameter estimation techniques this paper develops a new approach to building sugeno type models the essential idea is to separate the premise identification from the consequence identification while these are mutually related in the previous methods a fuzzy discretization technique is suggested to determine the premise of the model and an orthogonal estimator is provided to identify the consequence of the model the orthogonal estimator can provide information about the model structure or which terms to include in the model and final parameter estimates in a very simple and efficient manner the well known gas furnace data of box and jenkins is used to illustrate the proposed modeling approach and to compare its performance with other statistical and fuzzy modeling approaches it shows that the performance of the new approach compares favorably with these existing techniques

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 graphs with complete bipartite star complements abstract let be an eigenvalue of the graph g with multiplicity m a star complement for in g is an induced subgraph g x such that x m and is not an eigenvalue of g x some general observations concerning graphs with the complete bipartite graph k r s r s 2 as a star complement are followed by a complete analysis of the case r 2 s 5 the results include a characterization of the schlafli graph and the construction of all the regular graphs which have k 2 5 as a star complement

fuzzy adaptive observer backstepping control for mimo nonlinear systems in this paper a fuzzy adaptive backstepping output feedback control approach is developed for a class of multi input and multi output mimo nonlinear systems with unmeasured states using fuzzy logic systems to approximate the unknown nonlinear functions a fuzzy adaptive observer is designed for state estimation as well as system identification combining with the backstepping design techniques a fuzzy adaptive output feedback control is constructed recursively it is proved that the proposed fuzzy adaptive control approach can guarantee the semi global uniform ultimate boundedness for all the signals and the tracking error to a small neighborhood of the origin simulation studies illustrate the effectiveness of the proposed approach

a new approach to fuzzy modeling this paper proposes a new approach to fuzzy modeling the suggested fuzzy model can express a given unknown system with a few fuzzy rules as well as takagi and sugeno s model 1985 because it has the same structure as that of takagi and sugeno s model it is also as easy to implement as sugeno and yasukawa s model 1993 because its identification mimics the simple identification procedure of sugeno and yasukawa s model the suggested algorithm is composed of two steps coarse tuning and fine tuning in coarse tuning fuzzy c regression model fcrm clustering is used which is a modified version of fuzzy c means fcm in fine tuning gradient descent algorithm is used to precisely adjust parameters of the fuzzy model instead of nonlinear optimization methods used in other models finally some examples are given to demonstrate the validity of this algorithm