adaptive fuzzy rule based classification systems this paper proposes an adaptive method to construct a fuzzy rule based classification system with high performance for pattern classification problems the proposed method consists of two procedures an error correction based learning procedure and an additional learning procedure the error correction based learning procedure adjusts the grade of certainty of each fuzzy rule by its classification performance that is when a pattern is misclassified by a particular fuzzy rule the grade of certainty of that rule is decreased on the contrary when a pattern is correctly classified the grade of certainty is increased because the error correction based learning procedure is not meaningful after all the given patterns are correctly classified we cannot adjust a classification boundary in such a case to acquire a more intuitively acceptable boundary we propose an additional learning procedure we also propose a method for selecting significant fuzzy rules by pruning unnecessary fuzzy rules which consists of the error correction based learning procedure and the concept of forgetting we can construct a compact fuzzy rule based classification system with high performance

state dependent scaling design for a unified approach to robust backstepping global robust stabilization of nonlinear systems is characterized as a state dependent scaling problem by choosing scaling functions recursively one can construct robust control laws for an extended class of strict feedback systems

fuzzy semistar operations on overrings abstract in this paper we reinvestigate the notion of fuzzy semistar operation introduced in 5 we show how a fuzzy semistar operation on an integral domain r induces canonically a fuzzy semistar operation on an overring t of r and conversely how a fuzzy semistar operation on t induces canonically a semistar operation on r as an application new characterizations of prufer domains and complete description of the set of all fuzzy semistar operations of finite character on prufer domains are obtained we also characterize conducive domains

utility of multiple choices in detecting ill defined roadlike structures a multivalued recognition system has been formulated recently by mandal murthy and pal which is capable of handling various imprecise inputs and in providing multiple choices of classes corresponding to any input in the present work we have demonstrated an application of the recognition system for detecting the ill defined roadlike structures from an indian remote sensing irs satellite image the concept of multiple choices of the recognition system is found to be very effective in the detection procedure the results are found to be quite satisfactory when the scenes of calcutta and bombay were considered as input

tl subrings and tl ideals part 4 radicals of tl ideals abstract in this paper the notion of the radicals of l subsets and tl ideals of a ring is introduced and studied where t is an infinitely distributive t norm on a given complete brouwerian lattice l our main objective is to present basic properties about the radicals of tl ideals in preparation for the forthcoming two papers

stationary fuzzy fokker planck learning and stochastic fuzzy filtering the application of nonlinear optimization to the estimation of fuzzy model parameters is well known to do the reverse of this the concept of stationary fuzzy fokker planck learning sffpl is introduced i e sffpl applies the fuzzy modeling technique in nonlinear optimization problems sffpl is based on the fuzzy approximation of the stationary cumulative distribution function of a stochastic search process associated with the nonlinear optimization problem a carefully designed algorithm is suggested for sffpl to locate the optimum point this paper also considers the variational bayes vb based inference of a stochastic fuzzy filter whose consequents as well as antecedents are random variables the problem of vb inference of stochastic antecedents because of the nonlinearity of the likelihood function is analytically intractable the sffpl algorithm for high dimensional nonlinear optimization that does not require the derivative of the objective function can be used to numerically solve the stochastic fuzzy filtering problem

operations on fuzzy ideals in this paper we give suitable definitions of the operations of l fuzzy ideals in a ring as intersection addition multiplication and residual division and we prove some fundamental properties of the operations analogous to those that hold for the operations of ordinary ideals see 3

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

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

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

on line incremental feature weighting in evolving fuzzy classifiers in this paper we present an approach for addressing the problem of dynamic dimension reduction during on line training evolution and updating of evolving fuzzy classifiers efc the basic idea of our approach is that instead of permanently changing the list of most important features with newly loaded data blocks we generalize the concept of incremental feature selection to an incremental feature weighting approach features are assigned weights in 0 1 according to their importance level these weights are permanently updated during on line mode and guarantee a smooth learning process in the evolving fuzzy classifiers as they change softly and continuously over time in some cases when the weights become approximately 0 an automatic switching off of some features and therefore a soft dimension reduction is achieved two novel incremental feature weighting strategies are proposed in this paper one based on a leave one feature out the other based on a feature wise separability criterion we will describe the integration concept of the feature weights in the evolving fuzzy classifiers using single and multi model architecture where flexfis class sm and flexfis class mm serve as training engines the whole approach of integrated incremental feature weighting in evolving fuzzy classifiers will be evaluated based on high dimensional on line real world classification scenarios and based on data from the internet the results will show that incremental feature weighting in efc in fact helps to reduce curse of dimensionality and therefore guides the evolving fuzzy classifiers to a higher on line predictive power

completeness and consistency conditions for learning fuzzy rules the completeness and consistency conditions were introduced in order to achieve acceptable concept recognition rules in real problems we can handle noise affected examples and it is not always possible to maintain both conditions moreover when we use fuzzy information there is a partial matching between examples and rules therefore the consistency condition becomes a matter of degree in this paper a learning algorithm based on soft consistency and completeness conditions is proposed this learning algorithm combines in a single process rule and feature selection and it is tested on different databases

robust h sub spl infin control of uncertain nonlinear system via state feedback this technical note presents a solution of robust h sub spl infin control problem for an affine nonlinear system with gain bounded uncertainty it is shown that the l sub 2 induced norm of a closed loop system with the uncertainty is less than one if an extended nonlinear system with no uncertainty is dissipative with respect to a supply rate in consequence of this result a state feedback law such that the closed loop system has h sub spl infin robust performance is derived based on the hamilton jacobi inequality it is also shown that the existing results for linear systems are special cases of the presented results

voting in fuzzy rule based systems for pattern classification problems in this paper we examine two kinds of voting schemes in fuzzy rule based systems for pattern classification problems one is the voting by multiple fuzzy if then rules in a single fuzzy rule based classification system the other is the voting by multiple fuzzy rule based classification systems first we discuss the voting by multiple fuzzy if then rules which is used as a fuzzy reasoning method for classifying input patterns in a single fuzzy rule based classification system the performance of the voting by multiple fuzzy if then rules is examined by computer simulations on the iris data next we discuss the voting by multiple fuzzy rule based classification systems three voting methods i e a perfect unison rule a majority rule and a weighted voting rule are used for combining classification results by multiple fuzzy rule based classification systems finally we compare the performance of fuzzy rule based classification systems with that of other classification methods such as neural networks and statistical techniques by computer simulations on some well known test problems

robust control for nonlinear systems with structured l 2 gain bounded uncertainty abstract this paper focuses on the problem of robust control design for uncertain nonlinear systems with l 2 gain bounded dynamic uncertainty and periodically time varying memoryless uncertainty the robust performance problem is solved via nonlinear h control with scaling factors it is shown that the scaling factors can be functions of state variables in contrast with linear robust control

necessary and sufficient conditions of stability a multiloop generalization of the circle criterion a linear time invariant system with a vector output and a vector input is described this system is closed by an uncertain nonlinear time varying feedback the only information on this feedback is given by several integral quadratic inequalities i e the uncertainties under consideration generalize the so called conic nonlinearities necessary and sufficient frequency domain conditions of stability are obtained an advanced version of the s procedure losslessness theorem and some other tools of the absolute stability theory are used

including a simplicity criterion in the selection of the best rule in a genetic fuzzy learning algorithm learning algorithms can obtain very useful descriptions of several problems many different alternative descriptions can be generated in many cases a simple description is preferable since it has a higher possibility of being valid in unseen cases and also it is usually easier to understand by a human expert thus the main idea of this paper is to propose simplicity criteria and to include them in a learning algorithm in this case the learning algorithm will reward the simplest descriptions we study simplicity criteria in the selection of fuzzy rules in the genetic fuzzy learning algorithm called slave

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 primary representations of fuzzy ideals abstract let r be a commutative ring with identity and let a be a fuzzy ideal of r then a is said to have a fuzzy primary representation if a is the intersection of a finite number of fuzzy primary ideals we show that every fuzzy ideal a of r such that a 0 1 has a fuzzy primary representation if and only if r is artinian we show that uniqueness properties for reduced primary representations of ideals in the usual sense carry over to fuzzy ideals

some comments on spectrums of prime fuzzy ideals of a ring abstract common and distinctive features of two prime spectrums one obtained by kumar and kohli using 2 valued prime fuzzy ideals and the other obtained by the author using not so restrictive definition of prime fuzzy ideals are discussed it is also shown that some results claimed by kumar and kohli regarding spectrum of 2 valued prime fuzzy ideals need some corrections

on fuzzy ideals of a ring 1 abstract the aim of this paper is to study fuzzy ideals of a ring to characterise regular rings and noetherian rings by fuzzy ideals and to determine all fuzzy prime ideals of the ring z of integers

fuzzy subrings and ideals redefined abstract v q fuzzy subrings and ideals of a ring are defined the concepts of v q fuzzy semiprime prime semi primary primary and maximal ideals are introduced and characterization of such fuzzy ideals are obtained v q fuzzy cosets determined by v q fuzzy ideals and v q fuzzy radicals of v q fuzzy ideals are discussed

a learning process for fuzzy control rules using genetic algorithms abstract the purpose of this paper is to present a genetic learning process for learning fuzzy control rules from examples it is developed in three stages the first one is a fuzzy rule genetic generating process based on a rule learning iterative approach the second one combines two kinds of rules experts rules if there are and the previously generated fuzzy control rules removing the redundant fuzzy rules and the thrid one is a tuning process for adjusting the membership functions of the fuzzy rules the three components of the learning process are developed formulating suitable genetic algorithms

distributed representation of fuzzy rules and its application to pattern classification abstract this paper introduces the concept of distributed representation of fuzzy rules and applies it to classification problems distributed representation is implemented by superimposing many fuzzy rules corresponding to different fuzzy partitions of a pattern space this means that we simulatenously employ many fuzzy rule tables corresponding to different fuzzy partitions in fuzzy inference in order to apply distributed representation of fuzzy rules to pattern classification problems we first propose an algorithm to generate fuzzy rules from numerical data next we propose a fuzzy inference method using the generated fuzzy rules the classification power of distributed representation is compared with that of ordinary fuzzy rules which can be viewed as local representation

weighting fuzzy classification rules using receiver operating characteristics roc analysis in fuzzy rule based classification systems rule weight has often been used to improve the classification accuracy in past research a number of heuristic methods for rule weight specification have been proposed in this paper a method of fuzzy rule weight specification using receiver operating characteristic roc analysis is proposed in order to specify the weight of a fuzzy rule using 2 class roc analysis the threshold that the rule achieves its maximum accuracy is found this threshold is used as the weight of the rule the proposed method is compared with existing ones through computer simulations on some well known classification problems with continuous attributes simulation results show that the proposed method performs better than existing methods of fuzzy rule weight specification

coevolutionary genetic fuzzy systems a hierarchical collaborative approach abstract in this paper a coevolutionary genetic approach is devised to support hierarchical collaborative relations between individuals representing different parameters of takagi sugeno fuzzy models the coevolutionary approach assumes species to mean partial solutions of fuzzy modeling problems organized into four hierarchical levels individuals at each hierarchical level encode membership functions individual rules rule bases and fuzzy systems respectively a shared fitness evaluation scheme is used to measure the performance of each individual constraints are observed and particular targets are defined throughout the hierarchical levels with the purpose of promoting the occurrence of valid individuals and inducing rule compactness rule base consistency and partition set visibility the performance of the approach is evaluated via an example of function approximation with noisy data and a nonlinearly separable classification problem

parameterized lmis in control theory a wide variety of problems in control system theory fall within the class of parameterized linear matrix inequalities lmis that is lmis whose coefficients are functions of a parameter confined to a compact set such problems though convex involve an infinite set of lmi constraints and hence are inherently difficult to solve numerically this paper investigates relaxations of parameterized lmi problems into standard lmi problems using techniques relying on directional convexity concepts an in depth discussion of the impact of the proposed techniques in quadratic programming lyapunov based stability and performance analysis mu analysis and linear parameter varying control is provided illustrative examples are given to demonstrate the usefulness and practicality of the approach

fuzzy maximal radical and primary ideals of a ring we introduce the concepts of fuzzy maximal ideal the fuzzy radical of a fuzzy ideal and fuzzy primary ideal of a ring we show that a fuzzy left right ideal a of a ring r is a fuzzy maximal ideal if and only a 0 1 and a x r a x a 0 is a maximal left right ideal of r we also show that a fuzzy ideal a of a commutative ring r with unity is a fuzzy primary ideal of r if and only a 0 1 a is two valued and a is a primary ideal of r

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

an inductive learning procedure to identify fuzzy systems abstract in many real cases a system may not be described by a functional input output description and the only way to describe it is through a finite set of fuzzy rules even in some cases where exact identification is possible looking for that rule description may be useful for the sake of ease and effectiveness the automatic identification of a system through the analysis of an input output data set is the aim of this work in order to identify a system from raw data obtained in repeated instances of its own system the frequency of appearance of some kind of patterns may be particularly interesting nevertheless when the base domain is fuzzy and the data can be crisp statistical methods are not very appropriate and it is necessary to study a new model for frequencies on fuzzy domains the proposed model for identifying systems is based on this definition

inferring descriptive and approximate fuzzy rules for credit scoring using evolutionary algorithms generating both accurate as well as explanatory classification rules is becoming increasingly important in a knowledge discovery context in this paper we investigate the power and usefulness of fuzzy classification rules for data mining purposes we propose two evolutionary fuzzy rule learners an evolution strategy that generates approximate fuzzy rules whereby each rule has its own specific definition of membership functions and a genetic algorithm that extracts descriptive fuzzy rules where all fuzzy rules share a common linguistically interpretable definition of membership functions in disjunctive normal form the performance of the evolutionary fuzzy rule learners is compared with that of nefclass a neurofuzzy classifier and a selection of other well known classification algorithms on a number of publicly available data sets and two real life benelux financial credit scoring data sets it is shown that the genetic fuzzy classifiers compare favourably with the other classifiers in terms of classification accuracy furthermore the approximate and descriptive fuzzy rules yield about the same classification accuracy across the different data sets

state dependent scaling problems and stability of interconnected iiss and iss systems this paper addresses the problem of establishing stability of nonlinear interconnected systems this paper introduces a mathematical formulation of the state dependent scaling problems whose solutions directly provide lyapunov functions proving stability properties of interconnected dissipative systems in a unified manner stability criteria are interpreted as sufficient conditions for the existence of solutions to the state dependent scaling problems computing solutions to the problems is straightforward for systems covered by classical stability criteria it however could be too difficult for systems with strong nonlinearity the main purpose of this paper is to demonstrate the effectiveness beyond formal applicability by focusing on interconnected integral input to state stable iiss systems and input to state stable iss systems this paper derives small gain type theorems for interconnected systems involving iiss systems from the state dependent scaling formulation this paper provides solutions and lyapunov functions explicitly the new framework seamlessly generalizes the iss small gain theorem and classical stability criteria such as the lp small gain theorem the passivity theorems the circle and popov criteria state dependence of the scaling is crucial for effective treatment of essential nonlinearities while constants are sufficient for classical nonlinearities

multipolar aggregation operators in reasoning methods for fuzzy rule based classification systems the reasoning methods in fuzzy rule based classification systems are studied and their relation to multipolar aggregation operators is discussed we describe the change in the output of the classification system based on the change of the fuzzy reasoning method we propose a new fuzzy reasoning method based on multipolar fusion owa operator which can control the transition between the maximum rule method and the maximum vote method by a weighting vector this new method uses principles of owa operators and assigns the rule weight according to the strength of activation of the rule we compare different fuzzy reasoning methods in case studies

ifs coco instance and feature selection based on cooperative coevolution with nearest neighbor rule feature and instance selection are two effective data reduction processes which can be applied to classification tasks obtaining promising results although both processes are defined separately it is possible to apply them simultaneously this paper proposes an evolutionary model to perform feature and instance selection in nearest neighbor classification it is based on cooperative coevolution which has been applied to many computational problems with great success the proposed approach is compared with a wide range of evolutionary feature and instance selection methods for classification the results contrasted through non parametric statistical tests show that our model outperforms previously proposed evolutionary approaches for performing data reduction processes in combination with the nearest neighbor rule

some new qualitative insights into quality of fuzzy rule based models rules in fuzzy rule based models convey essential knowledge about the system under discussion as such they capture the essence of relationships occurring among input and output variables while the quality of such fuzzy models is predominantly related with the accuracy and eventual interpretability of rules although to a limited extent the quality of rules being regarded as generic pieces of knowledge has not been studied so far in this study we formulate and investigate this problem by looking at the quality of rules including aspects of a stability b generalizability and c conflict we identify a concept of rule multiplicity conflict and study an emergence of rule generalization a number of pertinent performance indices are developed and their usage is presented through a series of experimental studies

a min max approach to fuzzy clustering estimation and identification this study for any unknown physical process y f x1 xn is concerned with the 1 fuzzy partition of n dimensional input space x x1timesmiddotmiddotmiddottimesxn into k different clusters 2 estimating the process behavior ycirc f xcirc for a given input xcirc xcirc1 middotmiddotmiddot xcircn isinx and 3 fuzzy approximation of the process with uncertain input output identification data x k plusmndeltaxk y k plusmnvk k 1 using a sugeno type fuzzy inference system a unified min max approach that attempts to minimize the worst case effect of data uncertainties and modeling errors on estimation performance is suggested to provide robustness against data uncertainties and modeling errors the proposed method of min max fuzzy parameters estimation does not make any assumption and does not require a priori knowledge of upper bounds statistics and distribution of data uncertainties and modeling errors to show the feasibility of the approach simulation studies and a real world application of physical fitness classification based on the fuzzy interpretation of physiological parameters have been provided

a genetic algorithm for generating fuzzy classification rules abstract fuzzy classification systems based on fuzzy logic are capable of dealing with cognitive uncertainties such as vagueness and ambiguity involved in classification problems to build a fuzzy classification system the key is to find an optimal set of fuzzy rules machine learning methods such as fuzzy neural networks and fuzzy decision tree induction have been applied to learn fuzzy rules but they may be trapped into local optimal based on the principle of natural evolution and global searching a genetic algorithm is promising in obtaining better results but it is usually less efficient in this paper a fuzzy genetic algorithm fga is developed to generate fuzzy classification rules several techniques such as multi value logic coding composite fitness function viability check and rule extraction are used to improve the efficiency and the effectiveness of the algorithm two experiments are conducted to demonstrate the performance of fga and to compare fga with other machine learning algorithms

on radicals of fuzzy submodules and primary fuzzy submodules we define in this paper the concepts of the radical of fuzzy submodules and the primary fuzzy submodules and prove some of their properties

fuzzy prime ideals of a ring abstract this paper characterizes all fuzzy prime ideals p of an arbitrary ring r we show that a nonconstant fuzzy ideal p of r is prime if and only if p0 x r p x p 0 is a prime ideal of r p is two valued and p 0 1 examples are given showing that p0 is a prime ideal is not sufficient for p to be a fuzzy prime ideal and that p0 may be a prime ideal of r with the image of p being of arbitrary finite cardinality or being countably infinite

fuzzy prime ideals of rings abstract the notions of fuzzy ideal and fuzzy prime ideal of a ring with truth values in a complete lattice satisfying the infinite meet distributive law are introduced which generalize the existing notions with truth values in the unit interval of real numbers a procedure to construct any fuzzy ideal from a family of ideals with certain conditions is established all fuzzy prime maximal ideals of a given ring are determined by establishing a one to one correspondence between fuzzy prime maximal ideals and the pairs p where p is a prime maximal ideal of the ring and is a prime element dual atom in the complete lattice

robust stability with time varying structured uncertainty considers the problem of assessing robust stability in the presence of block diagonally structured time varying dynamic uncertainty it is shown that robust stability holds only if there exist constant scalings which lead to a small gain condition the notion of stability here is finite gain stability over finite energy signals in sharp contrast to the case of time invariant dynamic uncertainty this result is not limited by the number uncertainty blocks these results parallel previous results regarding finite gain stability over persistent bounded signals

linguistic recognition system based on approximate reasoning a linguistic recognition system based on approximate reasoning has been described which is capable of handling various imprecise input patterns and of providing a natural decision the input feature is considered to be of either linguistic form or quantitative form or mixed form or set form an input has been viewed as consisting of various combinations of the three primary properties small medium and high possessed by its different features to some degree the various uncertainty ambiguity in the input statement has been managed by providing modifying membership values heuristically to a great extent unlike the conventional fuzzy set theoretic approach the sets small and high have been represented here by functions the weight matrices corresponding to various properties and classes have been taken into account in the composition rule of inference in order to make the analysis more effective the natural output decision is associated with a confidence factor denoting the degree of certainty of the decision thus providing a low rate of misclassification as compared to the conventional two state system the effectiveness of the algorithm has been demonstrated on the speech recognition problem

hybridizing genetic algorithms with sharing scheme and evolution strategies for designing approximate fuzzy rule based systems genetic algorithms and evolution strategies are combined in order to build a multi stage hybrid evolutionary algorithm for learning constrained approximate mamdani type knowledge bases from examples the genetic algorithm niche concept is used in two of the three stages composing the learning process with the purpose of improving the accuracy of the designed fuzzy rule based systems the proposed genetic fuzzy rule based system is used to solve an electrical engineering problem and the results obtained are compared with other methods presenting different characteristics

solving multi class problems with linguistic fuzzy rule based classification systems based on pairwise learning and preference relations this paper deals with multi class classification for linguistic fuzzy rule based classification systems the idea is to decompose the original data set into binary classification problems using the pairwise learning approach confronting all pair of classes and to obtain an independent fuzzy system for each one of them along the inference process each fuzzy rule based classification system generates an association degree for both of its corresponding classes and these values are encoded into a fuzzy preference relation our analysis is focused on the final step that returns the predicted class label specifically we propose to manage the fuzzy preference relation using a non dominance criterion on the different alternatives contrasting the behaviour of this model with both the classical weighted voting scheme and a decision rule that combines the fuzzy relations of preference conflict and ignorance by means of a voting strategy our experimental study is carried out using two different linguistic fuzzy rule learning methods for which we show that the non dominance criterion is a good alternative in comparison with the previously mentioned aggregation mechanisms this empirical analysis is supported through the corresponding statistical analysis using non parametrical tests

variational bayes for a mixed stochastic deterministic fuzzy filter this study under the variational bayes vb framework infers the parameters of a takagi sugeno fuzzy filter having deterministic antecedents and stochastic consequents the aim of this study is to take advantages of the vb framework to design fuzzy filtering algorithms which include an automated regularization incorporation of statistical noise models and model comparison capability the vb method can be easily applied to the linear in parameters models this paper applies the vb method to the nonlinear fuzzy filters without using taylor expansion for a linear approximation of some nonlinear function it is assumed that the nonlinear parameters i e antecedents of the fuzzy filter are deterministic while linear parameters are stochastic the vb algorithm by maximizing a strict lower bound on the data evidence makes the approximate posterior of linear parameters as close to the true posterior as possible the nonlinear deterministic parameters are tuned in a way to further increase the lower bound on data evidence the vb paradigm can be used to design an algorithm that automatically selects the most suitable fuzzy filter out of the considered finite set of fuzzy filters this is done by fitting the observed data as a stochastic combination of the different takagi sugeno fuzzy filters such that the individual filters compete with one another to model the data

a fast genetic method for inducting descriptive fuzzy models under certain inference mechanisms fuzzy rule bases can be regarded as extended additive models this relationship can be applied to extend some statistical techniques to learn fuzzy models from data the interest in this parallelism is twofold theoretical and practical first extended additive models can be estimated by means of the matching pursuit algorithm which has been related to support vector machines boosting and radial basis neural networks learning this connection can be exploited to better understand the learning of fuzzy models in particular the technique we propose here can be regarded as the counterpart to boosting fuzzy classifiers in the field of fuzzy modeling second since matching pursuit is very efficient in time we can expect to obtain faster algorithms to learn fuzzy rules from data we show that the combination of a genetic algorithm and the backfitting process learns faster than ad hoc methods in certain datasets

a proposed method for learning rule weights in fuzzy rule based classification systems in fuzzy rule based classification systems frbcss rule weighting has often been used as a simple mechanism to tune the classifier in past research a number of heuristic rule weight specification methods have been proposed for this purpose a learning algorithm based on reward and punishment has also been proposed to adjust the weights of each fuzzy rule in the rule base in this paper a new method of learning rule weight in frbcss is proposed the method can be used when single winner or weighted vote methods of reasoning is used compared with reward and punishment scheme the proposed method is much faster and more effective another advantage of the proposed method is that during the learning process redundant rules are removed i e by setting their weights to zero the final rule base usually contains much fewer rules than the initial one this feature is very useful since a compact rule base is usually desired from the point of efficiency and interpretability a number of uci data sets are used to assess the performance of the proposed method in comparison with reward and punishment scheme

radicals of fuzzy ideals abstract there are several natural ways to fuzzify the concepts of prime ideal primary ideal the radical of an ideal and the primary representation of an ideal in a commutative ring in this paper we introduce some new approaches and compare them with known ones our main goal is to unify the various possible fuzzy primary representations of a fuzzy ideal to prepare the way for the study of fuzzy nonlinear systems of equations

the complex structured singular value a tutorial introduction to the complex structured singular value is presented with an emphasis on the mathematical aspects of the based methods discussed here have been useful for analysing the performance and robustness properties of linear feedback systems several tests for robust stability and performance with computable bounds for transfer functions and their state space realizations are compared and a simple synthesis problem is studied uncertain systems are represented using linear fractional transformations lfts which naturally unify the frequency domain and state space methods

a novel generic hebbian ordering based fuzzy rule base reduction approach to mamdani neuro fuzzy system there are two important issues in neuro fuzzy modeling 1 interpretability the ability to describe the behavior of the system in an interpretable way and 2 accuracy the ability to approximate the outcome of the system accurately as these two objectives usually exert contradictory requirements on the neuro fuzzy model certain compromise has to be undertaken this letter proposes a novel rule reduction algorithm namely hebb rule reduction and an iterative tuning process to balance interpretability and accuracy the hebb rule reduction algorithm uses hebbian ordering which represents the degree of coverage of the samples by the rule as an importance measure of each rule to merge the membership functions and hence reduces the number of the rules similar membership functions mfs are merged by a specified similarity measure in an order of hebbian importance and the resultant equivalent rules are deleted from the rule base the rule with a higher hebbian importance will be retained among a set of rules the mfs are tuned through the least mean square lms algorithm to reduce the modeling error the tuning of the mfs and the reduction of the rules proceed iteratively to achieve a balance between interpretability and accuracy three published data sets by nakanishi nakanishi turksen sugeno 1993 the pat synthetic data set pal mitra mitra 2003 and the traffic flow density prediction data set are used as benchmarks to demonstrate the effectiveness of the proposed method good interpretability as well as high modeling accuracy are derivable simultaneously and are suitably benchmarked against other well established neuro fuzzy models

prime fuzzy ideals over noncommutative rings in this paper we introduce prime fuzzy ideals over a noncommutative ring this notion of primeness is equivalent to level cuts being crisp prime ideals it also generalizes the one provided by kumbhojkar and bapat in 1993 which lacks this equivalence in a noncommutative setting semiprime fuzzy ideals over a noncommutative ring are also defined and characterized as intersection of primes this allows us to introduce the fuzzy prime radical and contribute to establish the basis of a fuzzy noncommutative ring theory

certain fuzzy ideals of rings redefined abstract an attempt is made to redefine fuzzy semiprimary fuzzy primary fuzzy prime and fuzzy maximal ideals of rings these fuzzy ideals are characterized by their level ideals fuzzy analogues of various results concerning semiprimary primary prime and maximal ideals are obtained the concept of a fuzzy nil radical of a fuzzy ideal is also formulated and discussed

prime l fuzzy ideals and primary l fuzzy ideals abstract in this paper the concepts of a primary l fuzzy ideal and a prime l fuzzy ideal and p primary are introduced and some fundamental propositions proved in particular a structural theorem for a primary l fuzzy ideal belonging to a prime l fuzzy ideal is given

reduction of fuzzy rule base via singular value decomposition introduces a singular value based method for reducing a given fuzzy rule set the method conducts singular value decomposition of the rule consequents and generates certain linear combinations of the original membership functions to form new ones for the reduced set the present work characterizes membership functions by the conditions of sum normalization sn nonnegativeness nn and normality no algorithms to preserve the sn and nn conditions in the new membership functions are presented preservation of the no condition relates to a high dimensional convex hull problem and is not always feasible in which case a closed to no solution may be sought the proposed method is applicable regardless of the adopted inference paradigms with product sum gravity inference and singleton support fuzzy rule base output errors between the full and reduced fuzzy set are bounded by the sum of the discarded singular values the work discusses three specific applications of fuzzy reduction fuzzy rule base with singleton support fuzzy rule base with nonsingleton support which includes the case of missing rules and the takagi sugeno kang tsk model numerical examples are presented to illustrate the reduction process

genetic learning of fuzzy rules based on low quality data genetic fuzzy systems gfs are based on the use of genetic algorithms for designing fuzzy systems and for providing them with learning and adaptation capabilities in this context fuzzy sets represent linguistic granules of information contained in the antecedents and consequents of the rules whereas the data used in the genetic learning is assumed to be crisp gfs seldom deal with fuzzy valued data in this paper we address this problem and propose a set of techniques that can be incorporated to different gfs in order to learn a knowledge base kb from interval and fuzzy data for regression problems details will be given about the representation of non standard data with fuzzy sets about the needed changes in the reasoning method of the fuzzy rule based system and also about a new generalization of the mean squared error to vague data in addition we will show that the learning process requires a genetic algorithm that must be capable of optimizing a multicriteria fitness function containing both crisp and interval valued criteria lastly we benchmark our procedures with some machine learning related datasets and a real world problem of marketing and the techniques proposed here are shown to improve the generalization properties of other kbs obtained from crisp training data

robust disturbance attenuation of nonlinear systems using output feedback and state dependent scaling this paper presents an approach to output feedback stabilization with l 2 disturbance attenuation for nonlinear systems in the presence of dynamic uncertainties a new formulation of state dependent scaling is introduced into the output feedback design which unifies treatment of nonlinear and linear gains the effect of disturbance on the controlled output which is allowed to be any function of output measurements can be always attenuated to an arbitrarily small level with global asymptotic stability if the plant belongs to a wide class of triangular systems whose uncertainties do not necessarily have finite linear gains the uncertain dynamics is not limited to input to state stable systems either the approach is not only a natural extension of popular approaches in robust linear control but also advantageous to numerical computation which is applicable to non triangular systems as well as triangular systems

genetic feature selection in a fuzzy rule based classification system learning process for high dimensional problems abstract the inductive learning of a fuzzy rule based classification system frbcs is made difficult by the presence of a large number of features that increases the dimensionality of the problem being solved the difficulty comes from the exponential growth of the fuzzy rule search space with the increase in the number of features considered in the learning process in this work we present a genetic feature selection process that can be integrated in a multistage genetic learning method to obtain in a more efficient way frbcss composed of a set of comprehensible fuzzy rules with high classification ability the proposed process fixes a priori the number of selected features and therefore the size of the search space of candidate fuzzy rules the experimentation carried out using sonar example base shows a significant improvement on simplicity precision and efficiency achieved by adding the proposed feature selection processes to the multistage genetic learning method or to other learning methods

local examination of fuzzy intersection equations abstract we extend the primary representation theory for a fuzzy ideal of a commutative ring with identity in order to apply primary representation theory to a local examination of fuzzy intersection equations we show that a system of fuzzy intersection equations can be examined locally to obtain the general solution to the crisp part of the system

combining boosting and evolutionary algorithms for learning of fuzzy classification rules this paper presents a novel boosting algorithm for genetic learning of fuzzy classification rules the method is based on the iterative rule learning approach to fuzzy rule base system design the fuzzy rule base is generated in an incremental fashion in that the evolutionary algorithm optimizes one fuzzy classifier rule at a time the boosting mechanism reduces the weight of those training instances that are classified correctly by the new rule therefore the next rule generation cycle focuses on fuzzy rules that account for the currently uncovered or misclassified instances the weight of a fuzzy rule reflects the relative strength the boosting algorithm assigns to the rule class when it aggregates the casted votes the approach is compared with other classification algorithms for a number problem sets from the uci repository

radicals of tl ideals in this paper we first introduce several different definitions of radicals of tl ideals in a commutative ring with identity and study their basic properties then discuss several kinds of primary tl ideals where t is an arbitrary infinitely distributive t norm on a given complete brouwerian lattice l

robust stabilization of nonlinear systems with pointwise norm bounded uncertainties a control lyapunov function approach the authors give a necessary and sufficient condition for globally stabilizing a nonlinear system robustly with respect to unstructured uncertainties spl phi spl tilde u x t norm bounded for each fixed x and u this condition requires one to find a smooth proper and positive definite solution v x of a suitable partial differential inequality depending only on the system data a procedure based on the knowledge of v x is outlined for constructing almost smooth robustly stabilizing controllers our approach based on lyapunov functions generalizes previous results for linear uncertain systems and establishes a precise connection between robust stabilization on one hand and h sub spl infin control sector conditions and input to state stabilization on the other

a neuro fuzzy method to learn fuzzy classification rules from data abstract neuro fuzzy systems have recently gained a lot of interest in research and application neuro fuzzy models as we understand them are fuzzy systems that use local learning strategies to learn fuzzy sets and fuzzy rules neuro fuzzy techniques have been developed to support the development of e g fuzzy controllers and fuzzy classifiers in this paper we discuss a learning method for fuzzy classification rules the learning algorithm is a simple heuristics that is able to derive fuzzy rules from a set of training data very quickly and tunes them by modifying parameters of membership functions our approach is based on nefclass a neuro fuzzy model for pattern classification we also discuss some results obtained by our software implementation of nefclass which is freely available on the internet

primary tl submodules and p primary tl submodules abstract in this paper we introduce the concepts of primary tl submodules and p primary tl submodules of m where m is a module i e left module over a given commutative ring with identity and t an arbitrary infinitely distributive t norm on a given complete brouwerian lattice l we also give complete characterization of primary tl submodules and study the primary decomposition of tl submodules

a robust design criterion for interpretable fuzzy models with uncertain data we believe that nonlinear fuzzy filtering techniques may be turned out to give better robustness performance than the existing linear methods of estimation h sup 2 and h sup spl infin filtering techniques because of the fact that not only linear parameters consequents but also the nonlinear parameters membership functions attempt to identify the uncertain behavior of the unknown system however the fuzzy identification methods must be robust to data uncertainties and modeling errors to ensure that the fuzzy approximation of unknown system s behavior is optimal in some sense this study presents a deterministic approach to the robust design of fuzzy models in the presence of unknown but finite uncertainties in the identification data we consider online identification of an interpretable fuzzy model based on the robust solution of a regularized least squares fuzzy parameters estimation problem the aim is to resolve the difficulties associated with the robust fuzzy identification method due to lack of a priori knowledge about upper bounds on the data uncertainties the study derives an optimal level of regularization that should be provided to ensure the robustness of fuzzy identification strategy by achieving an upper bound on the value of energy gain from data uncertainties and modeling errors to the estimation errors a time domain feedback analysis of the proposed identification approach is carried out with emphasis on stability robustness and steady state issues the simulation studies are provided to show the superiority of the proposed fuzzy estimation over the classical estimation methods

r primary l representations of l ideals we examine the basic properties of prime l ideals primary l ideals and r radicals of l ideals where l is a completely distributive lattice we determine to what extent every l ideal has an r primary l representation