Recent years have witnessed a widespread in the use of interval type-2 fuzzy logic systems (IT2 FLSs) in real-world applications. It has been shown recently that interval type-2 fuzzy sets (IT2 FSs) are more general than interval-valued fuzzy sets (IV FSs) [1]. Hence, there is a need to explore the capabilities of the more general forms of IT2 FSs (beyond IV FSs) and the applications areas they will be more suitable for. In addition, there is a need to develop the theory of the general forms of IT2 FLSs (gfIT2 FLSs), which employ IT2 FSs that are not equivalent to IV FSs and can have nonconvex secondary membership functions (MFs). Although these systems could be considered within the scope of general type-2 FLSs (GT2 FLSs), the practical implementation of GT2 FLSs has traditionally required the secondary MFs to be convex and normal type-1 fuzzy sets (T1 FSs). In addition, the type-reduction operation still presents a challenge for GT2 FLSs because of its computational complexity. In this paper, we present a complete framework for a type-2 FLS that uses the most recent perception of IT2 FSs (the so called general forms of interval type-2 fuzzy sets, gfIT2 FSs), whose secondary grades can be nonconvex T1 FSs. This framework includes new equations for the meet and join operations of gfIT2 FSs, as well as a new type reduction procedure for the type-2 FLS involving gfIT2 FSs. In addition, we present the type-2 FLS operation for singleton and nonsingleton fuzzification. We will introduce the various operations employed within a gfIT2 FLSs, from fuzzification (including singleton and nonsingleton) to inference, type-reduction, and defuzzification. We will also present two examples in which these gfIT2 FSs arise naturally when modeling sonar sensors input noise and the antecedents/consequents from a survey including different users.

Recently, the theory regarding interval type-2 fuzzy sets and fuzzy logic systems has been further developed. In the first instance, the concepts of interval type-2 fuzzy sets were broadened, proving that this class of sets include some which are different from interval-valued sets. In a later work, the set theoretic operations of union and intersection on these sets were studied and presented under the framework of general type-2 fuzzy sets. This stimulated and motivated the further study of fuzzy logic systems using these new sets, which have been referred to as the general forms of interval type-2 fuzzy sets. However, as usual when a new fuzzy logic framework is presented, only the singleton version of these systems was introduced. In this work we aim to generalise that work, introducing the non-singleton general forms of interval type-2 fuzzy logic systems. We will present a real example on how to use these non-singleton fuzzy logic systems in real world applications.

Recently, it has been shown that interval type-2 fuzzy sets (IT2FSs) are more general than interval-valued fuzzy sets (IVFSs), and some of these IT2FSs can actually be non-convex. Although these IT2FSs could be considered within the general type-2 fuzzy sets' (GT2FSs) scope, this latter have always been studied and developed under certain conditions considering the convexity and normality of their secondary grades. In recent works the operations of intersection and union for GT2FSs have been extended to include non-convex and non-normal secondary grades. Hence, there is a need to develop the theory for those general forms of interval type-2 fuzzy logic systems (gfIT2FLSs) which use IT2FSs that are not equivalent to IVFSs and can have non-convex secondary grades. Furthermore, we will present the mathematical tools to define the inference engine. This work aims to introduce the basic structure of such gfIT2FLSs, paying special attention to those blocks presenting significant differences with the already well known type-2 FLSs which employ IT2FSs which are equivalent to IVFSs (we will term IVFLSs).

The rapid growth of social networks has led many companies to use mobile payment systems as business sales tools. As these platforms have an increasing acceptance among the consumers, the main goal of this research is to analyze the individuals’ use intention of these systems in a social network environment. The data used were collected after performing an experiment using the Zong Payment tool. The paper includes a comparative analysis of several machine learning methods applied to the variable selection problem considering strategic, sociodemographic, and behavioral variables. The methods were applied isolatedly and, in a novel approach, using multiobjective optimization criteria. The results obtained by these algorithms were validated by an expert committee, who ranked them on the basis of their quality. The proposed methodology obtained the best results in terms of optimization as well as the highest scores from the experts.

In this paper we will present two theorems for the join and meet operations for general type-2 fuzzy sets with arbitrary secondary memberships, which can be non-convex and/or non-normal type-1 fuzzy sets. These results will be used to derive the join and meet operations of the more general descriptions of interval type-2 fuzzy sets presented in [1], where the secondary grades can be non-convex. Hence, this work will help to explore the potential of type-2 fuzzy logic systems which use the general forms of interval type-2 fuzzy sets which are not equivalent to interval valued fuzzy sets. Several examples for both general type-2 and the more general forms of interval type-2 fuzzy sets are presented.

There are currently several biological databases related to proteins depending on the information we are interested to extract. Therefore, since a heterogeneous set of features will be needed (domains, structures, ontology terms, etc), several quite different databases should be consulted. The handling of different databases can become difficult, as each database could provide a different nomenclature for the same proteins. Anyway, these databases usually provides some mapping tools in order to determine the correspondence among the different nomenclatures used for the same protein. The main goal of this paper is to provide a biological database including a huge amount of protein information in order to be used for different purposes in bioinformatics. This database will be designed as a flexible and extensible tool and it could be extended and updated when new proteins are annotated or the included ones are modified.

Smoothing b-splines constitute a powerful and popular methodology for performing nonparametric regression with high accuracy. It is well known that the placement of the knots in spline smoothing approximation has an important and considerable effect on the behavior of the final approximation. For this purpose, in this paper a novel methodology is presented for optimal placement and selections of knots, in order to approximate or fit curves to data, using smoothing splines. A new method based on improved clustering algorithm is used to optimally select a reduced number of knots for constructing the base of the b-spline, while ensuring the best accuracy.

This work presents a Color Fuzzy Set Design procedure, or similarly a color naming procedure, based on the VITA Classical dental color shade guide, for composite color matching applications in direct restorations in aesthetic dentistry. For that purpose, a psychophysical experience based on a set of visual assessments by a panel of observers was performed, with the objective of identifying the areas of the CIELAB color space which can be associated to each shade of the VITA guide. A number of composite sets from four different manufacturing companies were used in the experiment. This information was processed and a set of nonparametric Fuzzy Sets was obtained for the VITA shades, with the aid of an acceptability dental color threshold taken from previous studies. The designed Fuzzy Set System was applied for the identification of the VITA shade of different dentine and enamel composite samples (bilaminar technique) from two different manufacturing companies, with the subsequent clinical applicability. Results show a high level of accuracy in VITA shade identification of the operated dental samples, when compared with visual assessment performed by experts.

The electrocardiogram (ECG) is a noninvasive technique used to reflect underlying heart conditions by measuring the electrical activity of the heart, and nowadays it is possible with just a few derivation (with just only two), obtain important information in order than an expert can recognize abnormal heart rhythms (the heart rate is very fast, very slow, or irregular) or a heart attack (myocardial infarction), and if it was recent or some time ago. In this paper, several intelligent classifiers are developed, focusing on the problem of diagnosing cardiac diseases based on the electrocardiogram (ECG), or more precisely, on the differentiation of several arrhythmia using a large data set. We will study and imitate the ECG treatment methodologies and the features extracted from the electrocardiograms used by the researchers, which obtained the best results in the PhysioNet Challenge (www.physionet.org/). We will extract a great amount of features, partly those used by these researchers and some additional others we considered to be important for the distinction previously mentioned. A new method based on different paradigms of intelligent computation (such as extreme learning machine, support vector machine, decision trees, genetic algorithms and feature selection) will be used to select the most relevant characteristics and to obtain a classifier capable of autonomously distinguishing the different types arrhythmia from the ECG signal.

MOTIVATION: Multiple sequence alignments (MSAs) are widely used approaches in bioinformatics to carry out other tasks such as structure predictions, biological function analyses or phylogenetic modeling. However, current tools usually provide partially optimal alignments, as each one is focused on specific biological features. Thus, the same set of sequences can produce different alignments, above all when sequences are less similar. Consequently, researchers and biologists do not agree about which is the most suitable way to evaluate MSAs. Recent evaluations tend to use more complex scores including further biological features. Among them, 3D structures are increasingly being used to evaluate alignments. Because structures are more conserved in proteins than sequences, scores with structural information are better suited to evaluate more distant relationships between sequences. RESULTS: The proposed multiobjective algorithm, based on the non-dominated sorting genetic algorithm, aims to jointly optimize three objectives: STRIKE score, non-gaps percentage and totally conserved columns. It was significantly assessed on the BAliBASE benchmark according to the Kruskal-Wallis test (P < 0.01). This algorithm also outperforms other aligners, such as ClustalW, Multiple Sequence Alignment Genetic Algorithm (MSA-GA), PRRP, DIALIGN, Hidden Markov Model Training (HMMT), Pattern-Induced Multi-sequence Alignment (PIMA), MULTIALIGN, Sequence Alignment Genetic Algorithm (SAGA), PILEUP, Rubber Band Technique Genetic Algorithm (RBT-GA) and Vertical Decomposition Genetic Algorithm (VDGA), according to the Wilcoxon signed-rank test (P < 0.05), whereas it shows results not significantly different to 3D-COFFEE (P > 0.05) with the advantage of being able to use less structures. Structural information is included within the objective function to evaluate more accurately the obtained alignments. AVAILABILITY: The source code is available at http://www.ugr.es/~fortuno/MOSAStrE/MO-SAStrE.zip.

Singleton interval type-2 fuzzy logic systems (FLSs) have been widely applied in several real-world applications, where it was shown that the singleton interval type-2 FLSs outperform their singleton type-1 counterparts in applications with high uncertainty levels. However, one of the main criticisms of singleton interval type-2 FLSs is the fact that they outperform singleton type-1 FLSs solely based on their use of extra degrees of freedom (extra parameters) and that type-1 FLSs with a sufficiently large number of parameters may provide the same performance as interval type-2 FLSs. In addition, most works on type-2 FLSs only compare their results with singleton type-1 FLSs but fail to consider nonsingleton type-1 systems. In this paper, we aim to directly address and investigate this criticism. In order to do so, we will perform a comparative study between optimized singleton type-1, nonsingleton type-1, and singleton interval type-2 FLSs under the presence of noise. We will also present a multiobjective evolutionary algorithm (MOEA) for the optimization of singleton type-1, nonsingleton type-1, and singleton interval type-2 fuzzy systems for function approximation problems. The MOEA will aim to satisfy two objectives to maximize the accuracy of the FLS and minimize the number of rules in the FLS, thus improving its interpretability. Furthermore, we will present a methodology to obtain “optimal” consequents for the FLSs. Hence, this paper has two main contributions: First, it provides a common methodology to learn the three types of FLSs (i.e., singleton type-1, nonsingleton type-1, and singleton interval type-2 FLSs) from data samples. The second contribution is the creation of a common framework for the comparison of type-1 and type-2 FLSs that allows us to address the aforementioned criticism. We provide details of a series of experiments and include statistical analysis showing that the type-2 FLS is able to handle higher levels of noise than its nonsingleton and singleton type-1 counterparts.

Multiple sequence alignment (MSA) is one of the most studied approach in Bioinformatics to carry out other outstanding tasks like structural predictions, biological function analysis or next-generation sequencing. However, MSA algorithms do not achieve consistent results in all cases, as alignments become difficult when sequences have low similarity. In other words, each algorithm is focused in specific features of sequences and their results depend on them. For this reason, each approach could align better those sections of sequences that include such features, obtaining partially optimal solutions. In this work, a multiobjective evolutionary algorithm based on NSGA-II will be implemented in order to assemble previously aligned sequences, trying to avoid suboptimal alignments.

In this paper, a new approach for Self-evolving PArameter-free fuzzy Rule-based Controller (SPARC) is proposed. Two illustrative examples are provided aiming a proof of concept. The proposed controller can start with no pre-defined fuzzy rules, and does not need to pre-define the range of the output or control variables. This SPARC learns autonomously from its own actions while performing the control of the plant. It does not use any parameters, explicit membership functions, any off-line pre-training nor the explicit model (e.g. in a form of differential equations) of the plant. It combines the relative older concept of indirect adaptive control with the newer concepts of (self-)evolving fuzzy rule-based systems (and controllers, in particular) and with the very recent concept of parameter-free, data cloud and data density based fuzzy rule based systems (and controllers in particular). It has been demonstrated that a fully autonomously and in an unsupervised manner (based only on the data density and selecting representative prototypes/focal points from the control hyper-surface acting as a data space) it is possible generate a parameter-free control structure and evolve it in on-line mode. Moreover, the results demonstrate that this autonomous controller is effective (has comparative error and performance characteristics) to other known controllers, including self-learning ones, but surpasses them with its flexibility and extremely lean structure (small number of prototypes/focal points which serve as seeds to form parameter-free and membership function-free fuzzy rules based on them). The illustrative examples aim primarily proof of concept.

This work introduces an open benchmark dataset to investigate inertial sensor displacement effects in activity recognition. While sensor position displacements such as rotations and translations have been recognised as a key limitation for the deployment of wearable systems, a realistic dataset is lacking. We introduce a concept of gradual sensor displacement conditions, including ideal, self-placement of a user, and mutual displacement deployments. These conditions were analysed in the dataset considering 33 fitness activities, recorded using 9 inertial sensor units from 17 participants. Our statistical analysis of acceleration features quantified relative effects of the displacement conditions. We expect that the dataset can be used to benchmark and compare recognition algorithms in the future.

The automatic recognition of postures, movements and physical exercises has being recently applied to several healthcare related fields, with a special interest in chronic disease management and prevention. In this work we describe a complete method to define an accurate activity recognition system, stressing on the classification stage. As binary classifiers can be, in general, considered more efficient than direct multiclass classifiers, and looking for an appropriate multiclass extension schema, a hierarchical weighted classification model with a special application for multi-sensed problems is presented. Remarkable accuracy results are obtained for a particular activity recognition problem in contrast to a traditional multiclass majority voting algorithm.

In function approximation problems, one of the most common ways to evaluate a learning algorithm consists in partitioning the original data set (input/output data) into two sets: learning, used for building models, and test, applied for genuine out-of-sample evaluation. When the partition into learning and test sets does not take into account the variability and geometry of the original data, it might lead to non-balanced and unrepresentative learning and test sets and, thus, to wrong conclusions in the accuracy of the learning algorithm. How the partitioning is made is therefore a key issue and becomes more important when the data set is small due to the need of reducing the pessimistic effects caused by the removal of instances from the original data set. Thus, in this work, we propose a deterministic data mining approach for a distribution of a data set (input/output data) into two representative and balanced sets of roughly equal size taking the variability of the data set into consideration with the purpose of allowing both a fair evaluation of learning's accuracy and to make reproducible machine learning experiments usually based on random distributions. The sets are generated using a combination of a clustering procedure, especially suited for function approximation problems, and a distribution algorithm which distributes the data set into two sets within each cluster based on a nearest-neighbor approach. In the experiments section, the performance of the proposed methodology is reported in a variety of situations through an ANOVA-based statistical study of the results.

In this study, a novel fuzzy controller, which is able to self-design from scratch, while working online, is proposed. The controller does not use the information regarding the differential equations that govern the plant's behavior or any of their bounds. The algorithm presented is able to determine the most-adequate topology for the fuzzy controller based on the data obtained during the system's normal operation. Therefore, the controller can start operating with an empty set of fuzzy rules and needs no offline training. The proposed methodology comprises two phases: adaptation of the consequents for every selected topology and online addition of new membership functions (MFs). Some of the main advantages of this method are its robustness under changes on the plant's dynamics, good performance in noisy situations, and the ability to perform variable selection among a group of candidate variables. Unlike other online methods, the modification of the topology is based on the analysis of the whole operating region of the plant, thus providing higher robustness. Several simulation examples are used to show these features.

This paper presents a self-organizing adaptive fuzzy controller that works online. No prior knowledge about the differential equations governing the plant nor offline training is needed. Starting from very simple topologies, the algorithm uses the data obtained online during the normal operation of the system to modify the structure of the fuzzy controller. This is achieved in two phases: first, the consequents of the current fuzzy rules are adapted; in the second phase, new membership functions are added online. To show its capabilities, a real experiment with a nonlinear servo system has been carried out with satisfactory results.

E-health and e-monitoring have become an increasingly important area during recent years, being the recognition of motion, postures and physical exercises one of the main topics. In this kind of problem is common to work with a huge training data set in a multidimensional space, so feature selection is absolutely necessary. Most works are based on knowledge extraction using features which permit to make decisions about the activity realized, being feature selection the most critical stage. Conventional feature selection procedures based on wrapper methods or `branch and bound' are highly computationally expensive. In this work, we propose an alternative filter method using a feature-set ranking via a couple of two statistical criteria, which achieves remarkable accuracy rates in the classification process. We demonstrate the usefulness of our method on both laboratory and seminaturalistic activity ambient living datasets for real problems.

Affymetrix High Oligonucleotide expression arrays are widely used for the high-throughput assessment of gene expression of thousands of genes simultaneously. Although disputed by several authors, there are non-biological variations and systematic biases that must be removed as much as possible through the pre-processing step before an absolute expression level for every gene is assessed. It is important to evaluate microarray pre-processing procedures not only to the detection of differentially expressed genes, but also to classification, since a major use of microarrays is the expression-based phenotype classification. Thus, in this paper, we use several cancer microarray datasets to assess the influence of five different pre-processing methods in Support Vector Machine-based classification methodologies with different kernels: linear, Radial Basis Functions (RBFs) and polynomial.

Marital dissolutions, that include divorces and separations, are considered one of the most adverse events that can influence the health, life quality and welfare of the adults and infants implied. There have been several researches in the sanitary and sociological field that show how these processes of breaking a life in common can deteriorate the health in both, the physic and the psychological, aspect. This paper presents the application of machine learning methods to be able to predict if a marriage, that has started a dissolution process, will end up in a friendly agreement or it will be taken to the court. In order to accomplish this task, Radial Basis Function Neural Networks in combination with Mutual Information will be able to determine which elements should be considered to make a prediction. As the experiments will show, the methodology applied is able to classify with a high accuracy and robustness a real data base. The results could be applied in order to prevent some traumas to the people involved in the dissolution in the medical aspect and to perform a better management in the legal aspects.

This paper presents a first approach to try to determine if a newborn will be macrosomic before the labor, using a set of data taken from the mother. The problem of determining if a newborn is going to be macrosomic is important in order to plan cesarean section and other problems during the labor. The proposed model to classify the weight is a neural network whose design is based recent algorithms that will allow the networks to focus on a concrete class. Before proceeding with the design methodology to obtain the models, a previous step of variable selection is performed in order to indentify the risk factors and to avoid the curse of dimensionality. Another study is made regarding the missing values in the database since the data were not complete for all the patients. The results will show how useful the addition of the missing values into the original data set can be in order to identify new risk factors.

Tooth bleaching is receiving an increasing interest by patients and dentists since it is a relatively non-invasive approach for whitening and lightening teeth. Instrument designed for tooth color measurements and visual assessment with commercial shade guides are nowadays used to evaluate the tooth color. However, the degree of color change after tooth bleaching varied substantially among studies and currently, there are no objective guidelines to predict the effectiveness of a tooth bleaching treatment. Fuzzy Logic is a well known paradigm for data modelling; their main advantage is their ability to provide an interpretable set of rules that can be later used by the scientists. However these models have the problem that the global approximation optimization can lead to a deficient rule local modelling. This work proposes a modified fuzzy model that performs a simultaneous global and local modelling. This property is reached thanks to a special partitioning of the input space in the fuzzy system. The proposed approach is used to approximate a set of color measurements taken after a bleaching treatment using the pre-bleaching measurements. The system uses as rule antecedents the colorimetric values of the VITA commercial shade guide. The expected post-bleaching colorimetric values are immediately obtained from the local models (rules) of the system thanks to the proposed modified fuzzy model. Additionally, these post-bleaching CIELAB coordinate values have been associated with VITA shades through the evaluation of their respective membership functions, approximating which VITA shades are expected after the treatment for each pre-bleaching VITA shade.

Selective attention to visual or auditory stimuli that elicits steady-state visual or auditory responses (SSVEP or ASSR respectively) amplifies the power of those flickering frequencies of the stimuli measured in the electro-encephalography (EEG). The design of brain-computer interfaces (BCI) based on selective attention to auditory stimuli that elicits ASSRs has two major advantages: First, no much training is needed as selective attention is an inherent skill of human beings. Second, as the human hearing system behaves as an amplitude modulated (AM) envelope detector, if the auditory stimuli are previously AM modulated, a steady-state response signal can be easily elicited. As EEG signals are considered to be non stationary, this is an interesting approach to EEG analysis as the feature of our interest can be considered stationary, hence Fourier analysis applied. In this paper we study the behavior of a Perceptron as a classifier of a BCI system where the features for classification are extracted from EEG as responses to AM modulated auditory stimuli and how we can use it in a BCI system.

Radial basis function neural networks (RBFNNs) are well known because, among other applications, they present a good performance when approximating functions although their design still remains as a difficult task. The function approximation problem arises in the construction of a control system to optimize the process of the mineral reduction. In order to regulate the temperature of the ovens and other parameters, a module to predict the final concentration of mineral that will be obtained from the source materials is necessary. In a previous work, this problem was successfully solved by designing an RBFNN using a MultiObjective genetic algorithm (MOGA). However, the more samples are obtained from the system, the more difficult it becomes to design the RBFNN due to the high dimensionality of the problem. Therefore, a new algorithm that addresses the dimensionality reduction has been developed, allowing to obtain more accurate RBFNNs, deciding which input parameters must be considered. Another important element incorporated in the algorithm is the concept of fuzzy dominance, the algorithm, when performing the sorting of the population dividing it in subsets of non-dominated individuals, uses a fuzzy criteria to decide if an individual dominates another. As the experimental results will show, the new version of the algorithm generates RBFNNs with smaller approximation errors and less complexity due to the reduction in the number of input variables and neurons.

Radial basis function neural networks (RBFNNs) have been applied to solve problems of classification, function approximation and time series prediction. In the design of an RBFNN it is necessary to set the values for the positions of the centers and the radii for each RBF. In the literature it is usually performed an initialization step to set the positions of the centers and, once they are placed, the radii are calculated using a heuristic. In this paper, a new algorithm to set the value of those two parameters is presented. This new algorithm uses a supervised learning in such a way that the position of the centers will be constrained by the output of the function to be approximated. Since each center represents a neuron that is activated by the input vectors, the radii are initialized using the center's positions and their activation grades. In this way, the calculation of the radii is also influenced by the output of the target function, not like in other heuristics where only the positions of the centers or the input vectors are considered. As the experiments show, the new algorithm outperforms other algorithms previously used for this problem.

The goal of this paper is to achieve real time control of a monotonic system which, in general, may be non-linear and whose differential equations are unknown. We assume that there is no model of the plant available so there cannot be any off-line pre-training of the main controller parameters. We propose a both adaptive and self-learning algorithm capable of starting from a "void" fuzzy controller and, in real time, optimizing the fuzzy controller's rules (both antecedents and consequents) in order to translate the state of the plant to the desired value in the shortest possible time.

In this paper, the multigrid-based fuzzy system (MGFS) approach is applied for the CATS time series prediction benchmark. The MGFS architecture overcomes the problem inherent to all grid-based fuzzy systems when dealing with high dimensional input data, thus keeping low computational cost and high performance. A greedy algorithm for MGFS structure identification allows to perform the input variable selection for the time series prediction problem, while identifying the pseudo-optimal architecture according to the provided dataset.

A novel approach to achieve real-time global learning in fuzzy controllers is proposed. Both the rule consequents and the membership functions defined in the premises of the fuzzy rules are tuned using a one-step algorithm, which is capable of controlling nonlinear plants with no prior offline training. Direct control is achieved by means of two auxiliary systems: The first one is responsible for adapting the consequents of the main controller's rules to minimize the error arising at the plant output, while the second auxiliary system compiles real input-output data obtained from the plant. The system then learns in real time from these data taking into account, not the current state of the plant but rather the global identification performed. Simulation results show that this approach leads to an enhanced control policy thanks to the global learning performed, avoiding overfitting.

This paper presents a multiobjective evolutionary algorithm to optimize radial basis function neural networks (RBFNNs) in order to approach target functions from a set of input-output pairs. The procedure allows the application of heuristics to improve the solution of the problem at hand by including some new genetic operators in the evolutionary process. These new operators are based on two well-known matrix transformations: singular value decomposition (SVD) and orthogonal least squares (OLS), which have been used to define new mutation operators that produce local or global modifications in the radial basis functions (RBFs) of the networks (the individuals in the population in the evolutionary procedure). After analyzing the efficiency of the different operators, we have shown that the global mutation operators yield an improved procedure to adjust the parameters of the RBFNNs.

This paper presents an innovative approach to self-adaptation of the structure of a fuzzy controller in real time. Without any off-line pretraining, the algorithm achieves very high control performance through the iteration of a three-stage algorithm. In the first stage, coarse tuning of the fuzzy rules (both rule consequents and membership functions of the premises) is accomplished using the sign of the dependency of the plant output with respect to the control signal and an overall analysis of the main operating regions. In stage two, fine tuning of the fuzzy rules is achieved based on the controller output error using a gradient-based method. Finally, the third stage is responsible of modifying the structure of the fuzzy controller, proposing that input variable which should get a new membership function in order to improve the control policy in an optimum way.

The identification of a model is one of the key issues in the field of fuzzy system modeling and function approximation theory. There are numerous approaches to the issue of parameter optimization within a fixed fuzzy system structure but no reliable method to obtain the optimal topology of the fuzzy system from a set of input-output data. This paper presents a reliable method to obtain the structure of a complete rule-based fuzzy system for a specific approximation accuracy of the training data, i.e., it can decide which input variables must be taken into account in the fuzzy system and how many membership functions (MFs) are needed in every selected input variable in order to reach the approximation target with the minimum number of parameters.

The Web newspaper pagination problem consists of optimizing the layout of a set of articles extracted from several Web newspapers and sending it to the user as the result of a previous query. This layout should be organized in columns, as in real newspapers, and should be adapted to the client Web browser configuration in real time. This paper presents an approach to the problem based on simulated annealing (SA) that solves the problem on-line, adapts itself to the client's computer configuration, and supports articles with different widths.

Most genetic algorithm (GA) users adjust the main parameters of the design of a GA (crossover and mutation probability, population size, number of generations, crossover, mutation, and selection operators) manually. Nevertheless, when GA applications are being developed it is very important to know which parameters have the greatest influence on the behavior and performance of a GA. The purpose of this study was to analyze the dynamics of GAs when confronted with modifications to the principal parameters that define them, taking into account the two main characteristics of GAs; their capacity for exploration and exploitation. Therefore, the dynamics of GAs have been analyzed from two viewpoints. The first is to study the best solution found by the system, i.e., to observe its capacity to obtain a local or global optimum. The second viewpoint is the diversity within the population of GAs; to examine this, the average fitness was calculated. The relevancy and relative importance of the parameters involved in GA design are investigated by using a powerful statistical tool, the analysis of the variance (ANOVA).

An enhanced self-organizing controller (E-SOC) is presented to achieve real time global learning in fuzzy controllers. Direct control is achieved by means of two auxiliary systems: the first one is responsible for adapting the consequents of the main controller's rules to minimize the error arising at the plant output, while the second auxiliary system compiles real input/output data obtained from the plant. The system then learns in real time from these data taking into account, not the current state of the plant but rather the global identification performed. Simulation results show that this approach leads to an enhanced control policy thanks to the global learning performed.

A new approach is presented to fine tune a fuzzy controller based on very limited information on the nonlinear plant to be controlled. Without any off-line pre-training, the algorithm achieves very high control performance through a two-stage algorithm. In the first stage, coarse tuning of the fuzzy rules (both rule consequents and membership functions of the premises) is accomplished in real time using a small amount of information about the plant and an overall analysis of the main operating regions. In stage two, fine tuning of the fuzzy rules is achieved based on the controller output error using a gradient-based method.

This paper presents a reliable method to obtain the structure of a complete rule-based fuzzy system for a specific approximation accuracy of the training data, i.e. it can decide which input variables must be taken into account in the fuzzy system and how many membership functions are needed in every selected input variable in order to reach the approximation target with the minimum number of parameters.

This paper proposes a framework for constructing and training a radial basis function (RBF) neural network, which is an example of fuzzy system. For this purpose, a sequential learning algorithm is presented to adapt the structure of the network, in which it is possible to create a new hidden unit (rule) and also to detect and remove inactive units. The structure of the gaussian functions (membership functions) is modified using a pseudo-Gaussian function (PG) in which two sealing parameters /spl sigma/ are introduced, which eliminates the symmetry restriction and provides the neurons in the hidden layer with greater flexibility with respect to function approximation. Other important characteristics of the proposed neural system is that instead of using a single parameter for the output weights, these are functions of the input variables which leads to a significant reduction in the number of hidden units compared with the classical RBF network Finally, we examine the result of applying the proposed algorithm to time series prediction.

In this paper we propose a genetic algorithm (GA) that is capable of simultaneously optimizing the structure of the system and tuning the parameters that define the fuzzy system. For this purpose, we use the concept of multiple-deme GAs, in which several populations with different structures (number of input variables) evolve and compete with each other. In each of these populations, the element also has different numbers of membership functions in the input spaces and different numbers of rules. Instead of the normal coding system used to represent a fuzzy system, in which all the parameters are represented in vector form, we performed coding by means of multidimensional matrices, in which the elements are real-valued numbers, rather than the traditional binary or gray coding.

Abstract The parallelization of complex planning and control problems arising in diverse application areas in the industrial, services and commercial environments not only allows the determination of control variables in the required times but also improves the performance of the control procedure as more processors are involved in the execution of the parallel program. In this paper we describe a scheduling application in a water supply network to demonstrate the benefits of parallel processing. The procedure we propose combines dynamic programming with genetic algorithms and time series prediction in order to solve problems in which decisions are made in stages, and the states and control belong to a continuous space. Taking into account the computational complexity of these applications and the time constraints that are usually imposed, the procedure has been implemented by a parallel program in a cluster of computers, an inexpensive and widely extended platform that can make parallelism a practical means of tackling complex problems in many different environments. Copyright © 2001 John Wiley & Sons, Ltd.

Describes a structure to create a RBF neural network. This structure has 4 main characteristics. The first one is that the special RBF network architecture uses regression weights to replace the constant weights normally used. These regression weights are assumed to be functions of input variables. The second characteristic is the normalization of the activation of the hidden neurons (weighted average) before aggregating the activations, which, as observed by various authors, produces better results than the classical weighted sum architecture. The third aspect is that a new type of nonlinear function is proposed, the pseudo-gaussian function (PGBF). With this, the neural system gains flexibility, as the neurons possess an activation field that does not necessarily have to be symmetric with respect to the centre or to the location of the neuron in the input space. In addition to this new structure, we propose, as the fourth and final feature, a sequential learning algorithm, which is able to adapt the structure of the network, with this, it is possible to create new hidden units and also to detect and remove inactive units.

In the synthesis of a fuzzy system two steps are generally employed: the identification of a structure and the optimization of the parameters defining it. The paper presents a methodology to automatically perform these two steps in conjunction using a three-phase approach to construct a fuzzy system from numerical data. Phase 1 outlines the membership functions and system rules for a specific structure, starting from a very simple initial topology. Phase 2 decides a new and more suitable topology with the information received from the previous step; it determines for which variable the number of fuzzy sets used to discretize the domain must be increased and where these new fuzzy sets should be located. This, in turn, decides in a dynamic way in which part of the input space the number of fuzzy rules should be increased. Phase 3 selects from the different structures obtained to construct a fuzzy system the one providing the best compromise between the accuracy of the approximation and the complexity of the rule set. The accuracy and complexity of the fuzzy system derived by the proposed self-organized fuzzy rule generation procedure (SOFRG) are studied for the problem of function approximation. Simulation results are compared with other methodologies such as artificial neural networks, neuro-fuzzy systems, and genetic algorithms.

In this paper, a systematic design is proposed to determine fuzzy system structure and learning its parameters, from a set of given training examples. In particular, two fundamental problems concerning fuzzy system modeling are addressed: 1) fuzzy rule parameter optimization and 2) the identification of system structure (i.e., the number of membership functions and fuzzy rules). A four-step approach to build a fuzzy system automatically is presented: Step 1 directly obtains the optimum fuzzy rules for a given membership function configuration. Step 2 optimizes the allocation of the membership functions and the conclusion of the rules, in order to achieve a better approximation. Step 3 determines a new and more suitable topology with the information derived from the approximation error distribution; it decides which variables should increase the number of membership functions. Finally, Step 4 determines which structure should be selected to approximate the function, from the possible configurations provided by the algorithm in the three previous steps. The results of applying this method to the problem of function approximation are presented and then compared with other methodologies proposed in the bibliography.