Using self-powered sensors, traffic data may be collected continuously, efficiently, and sustainably once connected autonomous vehicles (CAVs) are a part of metaverse technology. Metaverse self-powered sensors can capture uninterrupted data that allow for activities such as the management of the traffic network, the optimization of transportation facilities, and the management of urban and intercity journeys to be performed. In addition, metaverse technology creates a new field of study. Evaluating the systems involved in current transportation activities together with the metaverse can increase the efficiency and sustainability of transportation. The main purpose of this study is to prioritize four alternatives of CAVs in metaverse with self-powered sensors using a novel decision making model. The proposed hybrid decision making framework includes two stages. In the first stage the fuzzy full consistency method (fuzzy FUCOM) is applied to find the weighting coefficients of criteria. In the second stage, a fuzzy non-linear model based on fuzzy Aczel-Alsina functions (fuzzy Aczel-Alsina weighted assessment - ALWAS method) is defined to rank the alternatives. Four alternatives are defined and evaluated using twelve different criteria under four headings, namely, technical advancement, environmental, implementation, and financial aspects. A case study has been created for the experts to evaluate the alternatives most effectively. The results of the study indicate that using self-powered sensors for integrating real-time traffic management in the metaverse is the most advantageous alternative.

Deep learning has a great impact on advanced real-world problem solving since it can deal with complex and big amount of data. One of the recent successful applications of deep learning is biomedical imaging and there is a remarkable research effort using medical image data (obtained via MR, tomography, X-Ray, pathology, microscopy, breast CAD, etc.) to perform especially diagnosis oriented studies considering vital diseases such as human brain disorders diseases (i.e., Alzheimer's, Parkinson, sleep disorders) or cancer (i.e., breast cancer, lung cancer, skin cancer). The literature often reports effective results, and thus the use of deep learning for biomedical imaging is a research hot topic. Deep learning is essentially a collection of advanced neural networks such as convolutional neural networks (CNN), deep belief networks (DBN), or auto-encoder neural networks. CNN is the most famous among them but all of these deep learning techniques can be successfully applied in biomedical imaging studies. In some cases, it has been also possible to combine them in hybrid-modelled solutions for improved results. Here, the key questions for understanding the performance of such deep neural networks could be (1) How effective can these neural networks detect a disease, via biomedical imaging? (2) How fast and early can they perform a diagnosis? (3) How can they accomplish the same performance for different types of diseases? (4) How can they contribute to the current and future of medicine?, by moving over the biomedical imaging? This special issue focuses on recent advances, challenges, and future perspectives about deep neural networks applied in biomedical studies in different domains of knowledge. From around 90 submitted articles to this particular section, six papers were selected based on the reviews. Each paper was reviewed by at least two reviewers and went through at least two rounds of reviews. The brief contributions of these papers are discussed below. In the first paper of this special issue, the authors (Shah et al., 2022) have used deep-convolutional generative adversarial networks algorithm to address which generates synthetic images for all the classes (Normal, Pneumonia and COVID-19). To validate whether the generated images are accurate, the k-mean clustering technique with three clusters (Normal, Pneumonia and COVID-19) have been used. The selected X-ray images classified in the correct clusters for training. In this way, a synthetic dataset with three classes has been formed. The generated dataset was then fed to The EfficientNetB4 for training and the experiments achieved promising results of 95% in terms of area under the curve (AUC). The authors (Yadav et al., 2022) propose an enhanced DL CNN model with the Leaky ReLU activation function. DermNet NZ's facial acne images dataset is used for the experiments. Three different techniques- K-Means, texture analysis and HSV model-based segmentation, are applied for image segmentation to extract the acne region from skin images. After applying all the above image segmentation methods five times for each method, output images from K-Means and HSV (5 + 5 images) are collected and combined with the dataset. Using that dataset, one SVM model using Scikit-learn and two CNN models- one with the ReLU activation function and another with the LeakyReLU activation function, is trained. Out of these three models, the proposed CNN (LeakyReLU) model achieved a 97.54% accuracy. In this paper by Loh et al. (2022), the short-time Fourier transform (STFT) is first applied to the EEG signals to obtain spectrogram images of MDD patients and healthy subjects. These spectrogram images are then fed to the CNN model for automated detection of MDD patients and healthy subjects. The EEG signals used in this study were obtained from public database with 34 MDD patients and 30 healthy subjects. The highest classification accuracy, precision, sensitivity, specificity and F1-score of 99.58%, 99.40%, 99.70%, 99.48% and 99.55%, respectively, were obtained with hold-out validation. The proposed MDD detection model is highly accurate and needs to be validated with more diverse MDD database before it can be used in clinical settings. In this research, the authors (Mallikarjuna et al., 2022) support deep neural network (DNN) analysis in healthcare and COVID-19 pandemic and gives the smart contract procedure, to identify the feature extracted data (FED) from the existing data. At the same time, the innovation will be useful to analyse future diseases. The proposed method also analyse the existing diseases which had been reported and it is extremely useful to guide physicians in providing appropriate treatment and save lives. To achieve this, the massive data is integrated using Python scripting language under various libraries to perform a wide range of medical and healthcare functions to infer knowledge that assists in the diagnosis of major diseases such as heart disease, blood cancer, gastric and COVID-19. The next paper by Mansour et al. (2022) presents a novel AI based fusion model for CRC disease diagnosis and classification, named AIFM-CRC. The presented AIFM-CRC model primarily undergoes Gaussian filtering based noise removal and contrast enhancement as a pre-processing stage. In addition, a fusion based feature extraction process takes place where the SIFT based handcrafted features and Inception v4 based deep features are fused together. Besides, whale optimization algorithm tuned deep support vector machine model is employed as a classification technique to determine the existence of CRC. In order to highlight the proficient results analysis of the AIFM-CRC model, a comprehensive simulation analysis takes place. The resultant experimental values pointed out the betterment of the AIFM-CRC model by accomplishing a maximum accuracy of 96.18%. The final article by Yuan et al. (2022) explores the adoption value of deep learning combined with computed tomography (CT) imaging omics in the prediction of metastatic lymph nodes of nasopharyngeal carcinoma (NPC). An end-to-end neural network architecture was designed based on the fully convolutional neural network (FCNN), which was applied to the CT image analysis of 52 patients with lymphatic metastasis and 36 patients without lymphatic metastasis. Patient's lymph node volume (V), the largest cross-sectional shortest diameter (d-value) and other macro characteristics were recorded. The microscopic features of its CT imaging omics were extracted. The results showed that the lymph node volume (4.37 ± 0.67) and the shortest diameter of the largest cross section (12.35 ± 2.31) of patients with lymph node metastasis were greatly larger than those without lymph node metastasis (1.84 ± 0.65, 7.98 ± 2.04) (p < 0.05). To conclude, this special issue publishes six papers out of a total of around 90 submitted papers. The guest editors hope that the research contributions and findings in this special issue would benefit the readers in enhancing their knowledge and encouraging them to work on various aspects of deep neural networks for biomedical data and imaging. We want to express our sincere thanks to the Editor-in-Chief and Special Issues & Reviews Editor for allowing us to organise this particular issue. The editorial office staffs are excellent, and thanks for their support. We are also thankful to all the authors who made this special issue possible, and to the reviewers for their thoughtful contributions.

In this article a design methodology for Mamdani interval type-3 fuzzy systems with center-of-sets type reduction is outlined. The methodology utilizes statistical measures, fuzzy c-means clustering and granular computing, to establish the justifiable footprint of uncertainty (JFOU) of the fuzzy granules, as explainable semantic abstractions that form the fuzzy model. The design methodology is presented in three general steps, first we use the principle of justifiable granularity to build a diagram of the justifiable information granule that contains a data structure with the descriptive measures of the experimental evidence of the data set. These measures are obtained from the partition matrix of the utilized clustering process, and these measures are used to evaluate the parameters of membership functions and characterize their JFOU. Second, we use the data structure of the justifiable information granule to characterize and parameterize the asymmetric interval type-3 membership functions. Lastly, the main procedure to obtain all the justifiable information fuzzy granules that define the knowledge base and the inference process of the fuzzy model is presented. Experiments were made with synthetic and real benchmark data from automated learning repositories, computing R adj 2 ${R}_{\mathrm{adj}}^{2}$ and root-mean-squared error to measure the reliability of the methodology, while keeping the justifiable uncertainty of the model.

Traditional mathematical models work with type-0, which means using precise numbers in the models, but since the seminal work of Prof. Zadeh in 1965, type-1 fuzzy models emerged as a powerful way to represent human knowledge and natural phenomena. Later type-2 fuzzy models were also proposed by Prof. Zadeh in 1975 and more recently have been studied and applied in real world problems by many researchers. In addition, as another extension of the original type-1 fuzzy logic, Prof. Atanassov proposed Intuitionistic Fuzzy Logic, which is a very powerful theory in its own right. Previous works of the author and other researchers have shown that certain problems can be appropriately solved by using type-1, and others by interval type-2, while others by using intuitionistic fuzzy logic. Bio-inspired and meta-heuristic optimization algorithms have been commonly used to find the optimal design of type-1, type-2 or intuitionistic fuzzy models for applications in control, robotics, pattern recognition, time series prediction, just to mention a few. However, the question still remains about if even more complex problems may require even higher types, orders or extensions of type-1 fuzzy models to obtain better solutions to real world problems. In this paper a framework for solving this problem of finding the optimal fuzzy model for a particular problem is presented. To the knowledge of the author, this is the first work to propose a systematic approach to solve this problem, and we envision that in the future this approach will serve as a basis for more efficient algorithms for the same task of finding the optimal fuzzy system.

In this paper we propose the use of interval type-2 fuzzy systems to dynamically adjust the parameters of the imperialist competitive algorithm (ICA). A type-1 fuzzy system was taken as a basis, with the input variable as the decades and beta as the output variable, then after that we extended to an interval type-2 fuzzy system, with some variants base on triangular, Gaussian and trapezoidal membership functions. The imperialist competitive algorithm takes as its basis the concept of imperialism, where the strongest countries absorb the weakest and make then their colonies. To measure the performance of the proposed approach 6 benchmark functions are used and finally, a comparison was made between the variants and the results obtained with the type-1 fuzzy system to observe their behavior applied to benchmark mathematical functions.

The main purpose considered in this paper is to maintain a specific location and behavior for a robot that uses type-2 fuzzy logic for controlling its behavior. In this work, we propose a combination of behaviors by following a trajectory without leaving or losing it and avoiding obstacles in an omnidirectional mobile platform. The results of the simulation show the advantages of the proposed approach. We describe the previous knowledge about type-2 fuzzy logic, the virtualization of the mobile robot and its modeling according to real situations. The proposed control system is developed in Matlab/Simulink, the system can model and guide a mobile robot in a successful way in simulated and real environments.

Through the advancement of science and technology, every day new methods or computational techniques are emerging that allow to solve problems in widely different areas, such as medicine, engineering, even in any industrial process. Optimization is of vital importance in applications and in industry, the main objective being to find the best possible solution to a particular problem of interest. In this work we propose to use the Grey Wolf Optimizer (GWO), which is a relatively new meta-heuristic, inspired by the hunting behavior and leadership hierarchy of grey wolves, for the optimization of fuzzy controllers for mobile autonomous robots. In addition to analyzing and explaining the proposed methodology based on GWO we are presenting simulation results for a two wheeled autonomous mobile robot to validate the efficiency of the proposed approach.

Nowadays Takagi Sugeno Fuzzy Inference Systems provide an interesting alternative to solve different kind of problems, and this is because this approach offers versatility and easy design. One of the applications of this kind of Fuzzy Inference Systems is in the classification area, specifically in diagnosis problems, in order to be used as computer aided systems, and this provides interesting results. This paper aims at evaluating the performance of this kind of systems in diagnosis problems, but modifying the order of the Sugeno polynomial. This polynomial is originally a first-order polynomial that relates the inputs with the firing force of the rules. However, with the emergence of high-order Sugeno polynomials is interesting to evaluate how this approach can improve the performance of the Takagi Sugeno Fuzzy Inference Systems. On the other hand, we evaluate the performance by changing the order of the Sugeno polynomial for Type-1, Interval Type-2 and General Type-2 Fuzzy Inference Systems, in order to obtain a tendency of the performance with respect to the order of the Sugeno polynomial.

In this work we propose a variant for the adjustment of parameters in galactic swarm optimization (GSO) using fuzzy logic. GSO is a newly created metaheuristic that uses the movement and distribution of stars and galaxies in the universe as inspiration. In galactic swarm optimization, multiple cycles of exploration and exploitation are used to obtain a better balance between the exploration and the exploitation phases, thus trying to improve the search for the best solutions. In this paper, it is proposed to perform an optimization of the parameters of the membership functions used in an initial fuzzy system called fuzzy galactic swarm optimization 1 (FGSO1) with the aim of improving the results obtained with the FGSO1 using a parameter setting based on experimentation. The proposed method and the original FGSO1 fuzzy system are tested with the CEC-2015 functions with different number of dimensions to be able to appreciate its behavior characteristics from a low number of dimensions to a high number of dimensions.

Themain aim of this paper is to use fuzzy inference systems for controlling the relevant parameters within the equations of the FWA algorithm. In other words, parameters that are considered constant in the traditional FWA and are now made dynamic by using fuzzy logic. It is worth mentioning that we also made a small modification to the algorithm with the goal of having a better performance and the modification was to change the stopping criteria of the algorithm. In the conventional fireworks algorithm (FWA) the stopping criteria is based on the function evaluations, including, some variations or modifications of the FWA but they also manage this in the same way. We propose a stopping criteria based on the iterations with the goal of having a more precise control and consequently, have a better way to control the output variables in a Fuzzy Inference System (FIS) of Mamdani type, since the number of iterations is used as the input variable. To demonstrate the validity of this modification we tested the algorithm with 12 benchmark functions with good results, and we call the proposed algorithm as Iterative Fuzzy Fireworks Algorithm and we denoted as IFFWA.

The software presented in this paper is an implementation of an intuitionistic fuzzy inference system. Such type of fuzzy inference systems provide an extra layer of uncertainty, called indeterminacy, that the user can integrate in the antecedents and consequents of the fuzzy system. The additional calculations required to make an inference in this type of system needs a negligible extra amount of computational resources, making it a low-cost alternative to type-2 fuzzy inference systems. At the current time, no other implementation of such type of system exist that is open source and free of charge. The software is developed in Clojure in order to leverage the Java libraries, the JVM itself, and the capabilities of the programming language to implement concurrency in a convenient manner. However, the goal of this implementation is to provide a language-agnostic interface based in a REST API, which can be used by any programming language capable of handling HTTP requests. A comparison between a traditional type-1 fuzzy inference is provided, where the reader can observe how the indeterminacy affects the outputs of the system.

The main goal of the work presented in the paper is to introduce the use of fuzzy logic in the Grey Wolf Optimizer (GWO) algorithm specifically for dynamic simultaneous adaptation of the key parameters, which are crucial in the performance of the metaheuristic. The proposed approach for this modification of GWO using fuzzy logic is presented. In addition, a brief comparison between the traditional GWO algorithm and the Grey Wolf Optimizer using fuzzy logic for dynamic adaptation of parameters is reported. This research shows the individual dynamic adjustment of two parameters and then a proposal of how to simultaneously adjust both parameters and finally we present the performance of these methods when they are tested with a set of benchmark functions, showing the advantage of using the strategy of simultaneous adaptation of parameters.

The main goal of the paper is the use of fuzzy logic for dynamic parameter adaptation in the Grey Wolf Optimizer (GWO) algorithm. The proposed approach of a fuzzy GWO is compared with the traditional GWO algorithm with a set of benchmark functions. Simulation results show that there is a significant advantage of the proposed fuzzy GWO.

A hybrid system composed by a generalized Type-2 Fuzzy Logic System (GT2FLS) and a fuzzy Bee Colony Optimization (FBCO) algorithm for the dynamic adaptation in the alpha and beta parameters is presented in this paper. The Bee Colony Optimization meta-heuristic belongs to the class of Nature-Inspired Algorithms. The objective of the work is the analysis of the approach with Generalized Type-2 Fuzzy Logic System to find the best beta and alpha parameter values in BCO. We use BCO specifically for tuning the membership functions of the fuzzy controller for trajectory stability in a mobile robot. We implemented IAE, ISE, RMSE and MSE, which are performance indices to measure the controller behavior. We add perturbations in the model with the pulse generator for the Generalized Type-2 Fuzzy Logic System and analyze better the uncertainty and that the FBCO shows better results than the original BCO.

This work describes a method to construct type-1 intuitionistic fuzzy inference systems. This type of systems is able to handle more uncertainty than a type-1 fuzzy inference system and performs faster than a type-2 fuzzy inference system. The concepts of intuitionistic membership, and intuitionistic center of area are proposed, in order to implement a system which is similar in design than the traditional fuzzy inference systems. The proposed method was implemented and compared against type-1 fuzzy inference systems and interval type-2 fuzzy inference systems, with uncertain means and uncertain standard deviations, by using the Mackey-Glass time series benchmark. A genetic algorithm was used to optimize the parameters of each of the methods being compared. This optimization ensures a fair comparison between each of the methods against the proposed method. The results show that the intuitionistic fuzzy inference system performs better than the other methods.

This work presents the design of a hardware architecture of interval type-2 fuzzy edge detector, performing fuzzy edge detection algorithm at high fidelity to the theoretical model and robustness, at a reduced computational time through hardware design strategies as parallelism and pipelining. Edge detection is an important processes in digital processing of images, but its high computational cost limits real-time applications. Fuzzy-Edge detectors have shown better performance than conventional methods, but at an even higher computational cost. The proposed hardware architecture is adaptable to different context of contrast or brightness without modification of the structure, by means of editable registers; it is described in VHDL that is a Hardware Description Language and synthesized in the Xilinx FPGA Spartan 6 through the Xilinx ISE design platform. The described hardware architecture achieves real-time processing for up to 48 frames per second (FPS), for an image of 1280 by 720 pixels, requiring 44.2 million of Fuzzy Logic Inferences per Second (FLIPS). The proposed architecture is tested to document its processing rate, its fidelity is evaluated and compared to the theoretical algorithm, and sample fuzzy edge detection is reported under controlled perturbations.

We describe in this paper the architecture of a modular neural network (MNN) for pattern recognition. More recently, the study of modular neural network techniques theory has been receiving significant attention. The design of a recognition system also requires careful attention. The paper aims to use the Ant Colony paradigm to optimize the architecture of this Modular Neural Network for pattern recognition in order to obtain a good percentage of image identification and in the shortest time possible.

This paper presents the optimization of the antecedent parameters for a system of image edge detection based on the Sobel technique combined with interval type-2 fuzzy logic. The optimal design of fuzzy systems is a difficult task and for this reason the use of meta-heuristic optimization techniques is considered in this paper. For the optimization of the fuzzy inference system the Cuckoo Search (CS) algorithm is applied, and the idea is to find the optimal design parameters of interval type 2 fuzzy systems and achieve better results in applications of edge detection for digital images.

The proposed method in this paper describes the enhancement of the Cuckoo Search (CS) Algorithm via Lévy flights using a fuzzy system to dynamically adapt its parameters. The original CS method is compared with the proposed method called Fuzzy Cuckoo Search (FCS) on a set of benchmark mathematical functions. In this case we consider a fuzzy system to dynamically change parameters during the execution of the algorithm. Simulation results on a set of mathematical functions show that the FCS outperforms the traditional CS. In addition, we demonstrate through statistical tests that the proposed method is better than the original CS algorithm.

We describe in this paper the Bat Algorithm and a proposed enhancement using a fuzzy system to dynamically adapt its parameter, original method is compared with the proposed method and also compared with genetic algorithm, providing a more complete analysis of the effectiveness of the bat algorithm. Simulation results on a set of mathematical functions with the fuzzy bat algorithm outperform the traditional bat algorithm and genetic algorithms.

This paper describes the optimization of interval type-2 fuzzy integrators in Ensembles of ANFIS (adaptive neuro-fuzzy inferences systems) models for the prediction of the Dow Jones time series. The Dow Jones time series is used to the test of performance of the proposed ensemble architecture. We used the interval type-2 and type-1 fuzzy systems to integrate the output (forecast) of each Ensemble of ANFIS models. Genetic Algorithms (GAs) were used for the optimization of membership function parameters of each interval type-2 fuzzy integrator. In the experiments we optimized Gaussian, Generalized Bell and Triangular membership functions parameter for each of the fuzzy integrators, thereby increasing the complexity of the training. Simulation results show the effectiveness of the proposed approach.

In this paper we propose a fuzzy system for parameter adaptation in ant colony optimization (ACO). ACO is a method inspired in the behavior of ant colonies to find food and its objective are discrete optimization problems. We developed various fuzzy systems for parameter adaptation and in this paper a comparison was made between them. The use of a fuzzy system is to control the diversity of the solutions, this is, control the ability of exploration and exploitation of the ant colony.

This paper presents an edge-detection method that is based on the morphological gradient technique and generalized type-2 fuzzy logic. The theory of alpha planes is used to implement generalized type-2 fuzzy logic for edge detection. For the defuzzification process, the heights and approximation methods are used. Simulation results with a type-1 fuzzy inference system, an interval type-2 fuzzy inference system, and with a generalized type-2 fuzzy inference system for edge detection are presented. The proposed generalized type-2 fuzzy edge-detection method was tested with benchmark images and synthetic images. We used the merit of Pratt measure to illustrate the advantages of using generalized type-2 fuzzy logic.

In this paper a new model of a Multi-Objective Hierarchical Genetic Algorithm (MOHGA) based on the Micro Genetic Algorithm (μGA) approach for Modular Neural Networks (MNNs) optimization is proposed. The proposed method can divide the data automatically into granules or sub modules, and chooses which data are for the training and which are for the testing phase. The proposed Multi-Objective Genetic Algorithm is responsible for determining the number of granules or sub modules and the percentage of data for training that can allow to have better results. The proposed method was applied to human recognition and its applicability with good results is shown, although the proposed method can be used in other applications such as time series prediction and classification.

In this paper we propose a new Gravitational Search Algorithm (GSA) using fuzzy logic to change alpha parameter and give a different gravitation and acceleration to each agent in order to improve its performance, we use this new approach for mathematical functions and present a comparison with original approach.

This paper describes an architecture for Ensembles of ANFIS (adaptive network based fuzzy inference system), with integrators of type-1 FLS and interval type-2 FLS (Fuzzy Logic System), with emphasis on its application to the prediction of chaotic time series, where the goal is to minimize the prediction error. The time series that was considered is the Mackey-Glass. The methods used for the integration of the ensembles of ANFIS are: Integration by average, the integration by weighted average, integration by type-1 FLS and integration by interval type-2 FLS. The performance obtained with this architecture overcomes several standard statistical approaches and neural network models reported in the literature by various researchers. In the experiments we changed the type of membership functions and the desired goal error, thereby increasing the complexity of the training.

This paper describes an evolutionary genetic algorithm approach for the optimization of a fuzzy reactive controller applied to the design of a fuzzy controller for a mobile robot. The algorithm will optimize the fuzzy inference system evaluating the performance of each individual with a neuro-fuzzy fitness function that considers the robots covered distance, time used, battery life and the pattern of the trajectory.

Neural Networks (NN), Type-1 Fuzzy Logic Systems (T1FLS) and Interval Type-2 Fuzzy Logic Systems (IT2FLS) are universal approximators, they can approximate any non-linear function. Recent research shows that embedding T1FLS on an NN or embedding IT2FLS on an NN can be very effective for a wide number of non-linear complex systems, especially when handling imperfect information. In this paper we show that an Interval Type-2 Fuzzy Neural Network (IT2FNN) is a universal approximator with some precision using a set of rules and Interval Type-2 membership functions (IT2MF) and the Stone-Weierstrass Theorem.

In this paper a neural network learning method with lower and upper type-2 fuzzy weight adjustment is proposed. The general mathematical analysis of the proposed learning method architecture and the adaptation of the interval type-2 fuzzy weights are presented. The proposed method is based on research of recent methods that manage weight adaptation and especially type-2 fuzzy weights. In this paper the neural network architecture managing lower and upper type-2 fuzzy weights and the obtained lower and upper final results are presented. The proposed approach is applied to a case of Mackey-Glass time series prediction.

This paper describes an architecture for Ensembles of Neuro-Fuzzy models with interval type-2 and type-1 fuzzy integrators, with emphasis on its application to the prediction of time series, where the objective is obtained the goal is to minimize the prediction error. The time series that was considered is the Mackey-Glass. The methods used for the integration of the ensembles of neuro-fuzzy (we used the ANFIS models "adaptive network based fuzzy inference system") are: integration by average, the integration by weighted average, interval type-2 and type-1 fuzzy inference systems (FIS) integrators. The performance obtained with this architecture overcomes several standard statistical approaches and neural network models reported in the literature by various researchers.

In this paper we describe a new methodology to optimize fuzzy logic controllers using Ant Colony Optimization (ACO); in particular, the fuzzy logic controller for the water tank benchmark problem. The proposed methodology is applied in the optimization of membership function parameters and type of membership functions, using a set of constraints for the construction of the solution matrix of an ACO algorithm.

In the paper, it is proposed to use a recurrent neural network model, and a real-time Levenberg-Marquardt algorithm of its learning for centralized data-based modeling, identification and control of an anaerobic digestion bioprocess, carried out in a fixed bed and a recirculation tank of a wastewater treatment system. The analytical model of the digestion bioprocess, used as process data generator, represented a distributed parameter system, which is reduced to a lumped system using the orthogonal collocation method, applied in four collocation points plus one- in the recirculation tank. The paper proposed to use three types of I-term adaptive control: direct adaptive integral plus states neural control, indirect adaptive I-term sliding mode control and real-time I-term optimal control. The comparative graphical simulation results of the digestion wastewater treatment system control, exhibited a good convergence and precise reference tracking, giving slight priority to the direct control with respect to the other methods of control applied.

This paper describes an optimization method for ensemble neural network models with fuzzy aggregation of responses for forecasting complex time series using genetic algorithms. The time series under consideration for testing the hybrid approach is the Mackey-Glass data, and results for the optimization of type-1 fuzzy response aggregation in the ensemble neural network are presented. Simulation results show the effectiveness of the proposed approach.

In this paper we describe the application of a Modular Neural Network (MNN) for iris, ear and voice recognition for a benchmark database. The proposed MNN architecture consists of three modules; iris, ear and voice. Each module is divided into other three sub modules. Each sub module contains different information, this means one third of the database for each sub module. We considered the integration of each biometric measure separately. Later, we proceed to integrate these modules with a fuzzy integrator. Also, we performed optimization of the modular neural networks and the fuzzy integrators using genetic algorithms, and comparisons were made between optimized results and the results without optimization.

This paper presents a new validation index for the Fuzzy C-Means algorithm, which is composed of two metrics, the modified partition entropy index and the sum of the distances between the means of the fuzzy partitions. The modified partition entropy represents the variation of the data in clusters of the dataset, and the sum of the distances between the means of the fuzzy partition represents the separation between clusters in the data set. The proposed index was tested with synthetic and benchmark datasets with good results.

In this paper, a modification of the Sugeno integral with interval type-2 fuzzy logic is proposed. The modification includes changing the original equations of the Sugeno Measures and the Sugeno integral that were initially proposed for type-1 fuzzy logic. The proposed modification enables calculation of the interval type-2 Sugeno integral for combining multiple source of information with a higher degree of uncertainty than with the traditional type-1 Sugeno integral. The advantages of the interval type-2 Sugeno integral are illustrated by reporting improved recognition rates in benchmark face databases. This new concept could also be a useful tool in other areas of applications. Also, the improvement provided by the type-2 integral is verified to be statistically significant in the recognition results for complex face databases (like the FERET database) when compared with the type-1 Sugeno integral. The proposed Sugeno integral is used to combine the modules' outputs of a modular neural network for face recognition. Simulation results show that the interval type-2 Sugeno integral is able to improve the recognition rate for the benchmark face databases. Recognition results are better or comparable to results produced by alternative approaches present in the literature reported for the same benchmark problems.

This paper addresses the analysis and design of an observer in order to ease the difficulty of working with various variables for the design of type-2 fuzzy controllers. In this paper Fuzzy Lyapunov Synthesis, based on the observed system, is extended to the design of type-2 fuzzy logic controllers for nonsmooth mechanical systems. The output regulation problem for a servomechanism with nonlinear backlash is proposed as a case of study. The problem at hand is to design a feedback controller so as to obtain the closed-loop system in which all trajectories are bounded and the load of the driver is regulated to a desired position while also attenuating the influence of external disturbances. The servomotor position is the only measurement available for feedback; the proposed extension is far from trivial because of the nonminimum phase properties of the system.

Agent-based Modeling and Simulation (ABMS) is a new modeling paradigm and is one of the most exciting practical developments in modeling since the invention of relational database. ABMS promises to have far-reaching effects on the way that businesses use computers to support decision-making and researchers use electronic laboratories to support their research. The goals of this paper are to show how ABMS is: - Useful: Why ABMS is a good and even better modeling approach in many cases: a) Usable: How we are progressively advancing to usable ABMS systems, with better software development environments and more application experiences, and, b) Used: How ABMS is being used to solve practical problems. We proposed three types of agents to treat the system in a hierarchical way. In this paper the operation of the Agent Node is designed, and implemented.

This paper describes reactive and tracking control of a mobile robot using integration methods to combine the response of both types of controls based on fuzzy logic. Simulation and experimental results of the complete system demonstrates the effectiveness of the proposed approach.

We describe in this paper a new hybrid approach for mathematical function optimization combining Particle Swarm Optimization (PSO) and Genetic Algorithms (GAs) using Fuzzy Logic for parameter adaptation and integrate the results. The new evolutionary method combines the advantages of the fuzzy logic to give us an improved FPSO+FGA hybrid method. Fuzzy Logic is used to combine the results of the PSO and GA in the best way possible. The new hybrid FPSO+FGA approach is compared with the PSO and GA methods with a set of benchmark mathematical functions. The new hybrid FPSO+FGA method is shown to be superior to the individual evolutionary methods on the set of benchmark functions.

The paper proposed a neural solution to the direct torque vector control of three phase induction motor including real-time trained RNN velocity controller and a hysteresis flux and torque controllers, which permitted the speed up reaction to the variable load. The basic equations and elements of the direct field oriented torque control scheme are given. The control scheme is realized by one RNN learned by a real-time BP algorithm and three FFNNs learned off-line by Levenberg-Marquardt algorithm with data taken from PI-control scheme simulations.

A neuro-fuzzy learning algorithm is applied to design a Takagi-Sugeno type Fuzzy Logic Controller (T-S FLC) for a biped robot walking problem. The control design considers an output function imposed on the feedback and several TS-FLC models are determined each by ANFIS, which represent a piece-wise control inputs that together to perform a walking cycle. Two simulations of the closed-loop system for generation of walking motions are given, where we assume that the joint positions and the whole state of the system are available for controller feedback respectively.

In this paper we describe a hybrid architecture for classification of cardiac arrhythmias taking as a source the ECG records MIT-BIH Arrhythmia database. The Samples were taken from the LBBB, RBBB, PVC and Fusion Paced and Normal arrhythmias, as well as the normal beats. These were segmented and normalized and three methods of classification were used: Fuzzy KNN, Multi Layer Perceptron with Gradient Descent with Momentum Backpropagation, and Multi Layer Perceptron with Scaled Conjugate Gradient Backpropagation. Finally, we used a Mamdani fuzzy inference system to combine the outputs of each classifier, and we achieved a very high classification rate of 98%.

In this paper we describe an evolutionary method for the optimization of a modular neural network for multimodal biometry. The proposed evolutionary method produces the best architecture of the modular neural network (number of modules, layers and neurons) and fuzzy inference systems (memberships functions) as fuzzy integration methods. The integration of responses in the modular neural network is performed by using optimal interval type-2 fuzzy inference systems. The optimization of membership functions of the type-2 fuzzy systems is based on the level of uncertainty with application to fuzzy response integration.

In this paper we propose a feature extraction method based on brightness control of the pixels of an image using a fuzzy logic inference system. The proposed method was used in a hybrid pattern recognition system of the fingerprints, to improve the identification rate. The fuzzy extraction method preprocesses the fingerprint images and adjusts the brightness. The obtained image is input to the ensemble neural network (ENN), the ENN output is based on response integration with type-1 and type-2 fuzzy logic to obtain the fingerprint identification.

Edge detection is a previous step for image recognition systems that helps to extract the most important shapes in an image, ignoring the homogeneous regions and remarking the real object to classify or recognize. Traditional and fuzzy edge detectors can be used, but it's very difficult to demonstrate which one is better before the recognition results are obtained. In this work we present an experiment where several edge detectors were used to preprocess the same image sets. Each resultant image set was used as training data for a neural network recognition system, and the recognition rates were compared. The goal of this experiment is to find the better edge detector that can be used for the training data on a neural network to improve image recognition.

In this paper we describe the application of a Simple ACO (S-ACO) as a method of optimization for the membership functions' parameters of a fuzzy logic controller (FLC) in order to find the optimal intelligent controller for an autonomous wheeled mobile robot. Simulation results show that ACO outperforms a GA in the optimization of FLCs for an autonomous mobile robot.

In this work we describe a fuzzy inference system to determine the relevance of each module in modular neural networks for images recognition. The tests were made with Type 1 and Interval type-2 fuzzy inference system, to compare the performance. In both cases the fusion operator for the modules is the Sugeno integral, and the parameters to estimate are the fuzzy densities.

There exist several ways to model population growth at present time, which are mainly based on mathematics. However we present a new model based on fuzzy cellular theory. An interval type-2 fuzzy logic system (IT2-FLS) is designed to evaluate the population growth parameters based on the environment resources stochasticity, in time and space. Interval type-2 fuzzy sets are used to measure the uncertainties of the environment resources. The main goal of this work is to demonstrate how the IT2-FLS integrated into a population growth model can make a suitable evaluation of the parameters required to make that the population size reach a stable equilibrium level on which it fluctuates into a time interval and after that, population size goes down as consequence of insufficient resources. This behaviour is the fundamental basis of the majority of the mathematical models made through the years in ecology to study the population dynamics.

We describe in this paper a new hybrid approach for mathematical function optimization combining Particle Swarm Optimization (PSO) and Genetic Algorithms (GAs) using Fuzzy Logic to integrate the results. The new evolutionary method combines the advantages of PSO and GA to give us an improved PSO+GA hybrid method. Fuzzy Logic is used to combine the results of the PSO and GA in the best way possible. The new hybrid PSO+GA approach is compared with the PSO and GA methods with a set of benchmark mathematical functions. The new hybrid PSO+GA method is shown to be superior that the individual evolutionary methods. The mathematical functions were evaluated with 2, 4, 8 and 32 variables to validate this approach.

Fuzzy Lyapunov synthesis is extended to the design of type-2 fuzzy logic system controllers for the output regulation problem for a servomechanism with nonlinear backlash. The problem in question is to design a feedback controller so as to obtain the closed-loop system in which all trajectories are bounded and the load of the driver is regulated to a desired position while also attenuating the influence of external disturbances. The servomotor position is the only measurement available for feedback; the proposed extension is far from trivial because of nonminimum phase properties of the system. Performance issues of the type-2 fuzzy logic regulator constructed are illustrated in a simulation study.

We describe in this paper the application of evolutionary methods for the optimization of type-2 fuzzy logic controllers. These optimal type-2 fuzzy logic controllers are used for the trajectory tracking control of autonomous mobile robots. The evolutionary method to consider is the genetic algorithm, presenting simulations results in Simulink©of Matlab.

In this paper we describe the application of a Simple ACO (S-ACO) as an optimization method for the membership functions' parameters of a fuzzy logic controller (FLC) in order to find the optimal intelligent controller for an autonomous wheeled mobile robot. Simulation results show that ACO outperforms a GA in the optimization of FLCs for an autonomous mobile robot.

An interval type-2 fuzzy logic system (IT2-FLS) is designed to evaluate the parameters of a population growth model based on the environment resources stochasticity, in time and space. Interval type-2 fuzzy sets are used to measure the uncertainties of the environment resources. The main goal of this work is to demonstrate how the IT2-FLS integrated into a population growth model can make a suitable evaluation of the parameters required to make that the population size reach a stable equilibrium level on which it fluctuates into a time interval and after that, population size goes down as consequence of insufficient resources. The simulation results are compared against the results of others mathematical models made through the years in Ecology to study the population dynamics.

Soft computing can be used to build hybrid intelligent systems for achieving different goals in real-world applications.Soft computing techniques include, at the moment, fuzzy logic, neural networks, genetic algorithms, chaos theory methods, and similar techniques that have been proposed in recent years.Each of these techniques has advantages and disadvantages, and several real-world problems have been solved, by using one of these techniques.However, many real-world complex problems require the integration of several of these techniques to really achieve the efficiency and accuracy needed in practice.In particular, evolutionary computing can be used to optimize the topology of a fuzzy or a neural system.Also, there are neuro-fuzzy approaches or even neuro-fuzzy-genetic approaches for designing the best intelligent system for a particular application.This special issue consists of five papers that consider the use and integration of different soft computing techniques for the development of hybrid intelligent systems for modeling, simulation, and control of nonlinear dynamical systems.The five papers, of this special issue, describe different applications of soft computing techniques to real-world problems and can be considered a significant contribution to the field of hybrid intelligent systems.The first paper, "An Artificial Bee Hive for Continuous Optimization" by Mario A. Muñoz et al., deals with an artificial bee-hive algorithm for optimization in continuous search spaces based on a model aimed at individual bee behavior.The algorithm defines a set of behavioral rules for each agent to determine what kind of actions must be carried out.In addition, the proposed algorithm includes some adaptations not considered in the biological model to increase the performance in the search for better solutions.To compare the performance of the algorithm to other swarm-based algorithms a statistical analysis was performed.The second paper, "A Levenberg-Marquardt Learning Applied for Recurrent Neural Identification and Control for a Wastewater Treatment Bioprocess" by Ieroham Baruch and Carlos R. Mariaca-Gaspar, describes a new recurrent neural network (RNN) model for systems identification and states estimation of nonlinear plants.The proposed RNN identifier is implemented in direct and indirect adaptive

An integration of a cognitive map and a fuzzy inference engine is presented, as a cognitive–fuzzy model, targeting online fuzzy logic controller (FLC) design and self fine-tuning. The proposed model is different than previous proposed fuzzy cognitive maps in that it presents a hierarchical architecture in which the cognitive map process, available plant, and control objective data on represented knowledge to generate a complete FLC architecture and parameters description. Online assessment of measured data is processed for linguistic characterization of performance to determine the required FLC parameter's adjustments, the process is repeated until the control objective is reached. A mathematical model of the proposed approach is presented, and sample numerical data illustrate the following: (a) cognitive map construction, (b) start-up self fine-tuning, and (c) system's response to error of plant descriptive data. Simulation results demonstrate model interpretability, which suggests that the model is scalable and offers robust capability to generate near optimal controller, emulating human iterative design flow, and fine-tuning within the knowledge domain of cognitive map. © 2009 Wiley Periodicals, Inc.

We describe in this paper a new hybrid approach for mathematical function optimization combining particle swarm optimization (PSO) and genetic algorithms (GAs) using fuzzy logic to integrate the results. The new evolutionary method combines the advantages of PSO and GA to give us an improved PSO+GA hybrid method. Fuzzy logic is used to combine the results of the PSO and GA in the best way possible. The new hybrid PSO+GA approach is compared with the PSO and GA methods with a set of benchmark mathematical functions. The new hybrid PSO+GA method is shown to be superior than the individual evolutionary methods.

In the paper it is proposed a new recurrent fuzzy-neural multi-model (FNMM) identifier applied for decentralized identification of a distributed parameter anaerobic wastewater treatment digestion bioprocess, carried out in a fixed bed and a recirculation tank. The distributed parameter analytical model of the digestion bioprocess is reduced to a lumped system using the orthogonal collocation method, applied in three collocation points (plus the recirculation tank), which are used as centers of the membership functions of the fuzzyfied space variable of the plant. The states of the proposed FNMM identifier are implemented by a direct feedback-feedforward hierarchical fuzzy-neural controller. The comparative graphical simulation results of the digestion wastewater treatment system identification and control, obtained via learning, exhibited a good convergence, and precise reference tracking outperforming the optimal control.

In this paper, a class of Interval Type-2 Fuzzy Neural Networks (IT2FNN) is proposed, which is functionally equivalent to interval type-2 fuzzy inference systems. The computational process envisioned for fuzzy neural systems is as follows: it starts with the development of an ”Interval Type-2 Fuzzy Neuron”, which is based on biological neural morphologies, followed by the learning mechanisms. We describe how to decompose the parameter set such that the hybrid learning rule of adaptive networks can be applied to the IT2FNN architecture for the Takagi-Sugeno-Kang (TSK) type of reasoning.

Cognitive map and fuzzy logic controller hybrid model is presented in this paper. Sample control applications are included to demonstrate incorporation of analytical and empirical knowledge on the fuzzy cognitive map construction with the purpose of generating fuzzy logic controller (FLC) design on-line. Cognitive map state vector includes all FLC-defining concepts. Controller performance concepts are also included in order to automate FLC parameters adjustments. This model targets control applications when only incomplete plant model is available, or for cases where plant parameters values are not known with certainty, or for cases when plant parameters are expected to change while in operation. On these cases, the CM portion designs the FLC, and fine-tunes controller parameters whenever controller performance is unsatisfactory until user-defined control objectives are achieved; this model emulates expert empirical FLC design and fine-tuning within cognitive map knowledge domain.

We describe a tracking controller for the dynamic model of a unicycle mobile robot by integrating a kinematic and a torque controller based on type-2 fuzzy logic theory and genetic algorithms. Computer simulations are presented confirming the performance of the tracking controller and its application to different navigation problems.

This work focuses in the design and implementation of a digital fuzzy controller, that uses a novel tuning technique called simple tuning algorithm (STA) to achieve the desired controllerpsilas response. Improvements over exciting architectures to implement the fuzzy inference systems (FIS) in a field programmable gate array (FPGA) are presented. A methodology that minimizes the test and validation process is given. Experiments were done using a geared direct current (DC) motor; the control goal was to maintain the speed at a given value.

In this paper a genetic-type-2 fuzzy approach is proposed to optimize the parameters of the membership functions (MFs) of a type-2 fuzzy logic system (FLS) applied to control, we design a chromosome to represent the parameters of the MFs of a preestablished type-2 FLS, design a fitness function and select genetic operators. A case of study is proposed to evaluate the optimization process, this is to achieve the output regulation problem of a servomechanism with backlash. The problem is the design of a type-2 fuzzy logic controller which will be optimized by a GA to obtain the closed-loop system in which the load of the driver is regulated to a desired position. Simulations results illustrate the effectiveness of the optimized closed-loop system.

This paper presents the development and design of two software tools for computational intelligence. The software tools include a graphical user interface for construction, edition and observation of the intelligent systems. The software tool are for interval type-2 fuzzy logic and modular neural networks. The interval type-2 fuzzy logic system toolbox (IT2FLS), is an environment for interval type-2 fuzzy logic inference system development. Tools that cover the different phases of the fuzzy system design process, from the initial description phase, to the final implementation phase, build the toolbox. The toolboxpsilas best qualities are the capacity to develop complex systems and the flexibility that permits the user to extend the availability of functions for working with the use of type-2 fuzzy operators, linguistic variables, interval type-2 membership functions, defuzzification methods and the evaluation of interval type-2 fuzzy inference systems. The toolbox for modular neural networks has similar advantages.

We describe in this paper a comparative study of fuzzy inference systems as methods of integration in modular neural networks (MNNpsilas) for multimodal biometry. These methods of integration are based on type-1 and type-2 fuzzy logic. Also, the fuzzy systems are optimized with simple genetic algorithms. First, we considered the use of type-1 fuzzy logic and later the approach with type-2 fuzzy logic. The fuzzy systems were developed using genetic algorithms to handle fuzzy inference systems with different membership functions, like the triangular, trapezoidal and gaussian; since these algorithms can generate the fuzzy systems automatically. Then the response integration of the modular neural network was tested with the optimized fuzzy integration systems. The comparative study of type-1 and type-2 fuzzy inference systems was made to observe the behavior of the two different integration methods of modular neural networks for multimodal biometry.

This paper presents the development and design of a graphical user interface and a command line programming toolbox for construction, edition and observation of interval type-2 fuzzy inference systems. The interval type-2 fuzzy logic system toolbox (IT2FLS), is an environment for interval type-2 fuzzy logic inference system development. Tools that cover the different phases of the fuzzy system design process, from the initial description phase, to the final implementation phase, build the toolbox. The toolbox's best qualities are the capacity to develop complex systems and the flexibility that permits the user to extend the availability of functions for working with the use of type-2 fuzzy operators, linguistic variables, interval type-2 membership functions, defuzzification methods and the evaluation of interval type-2 fuzzy inference systems.

Uncertainty is an inherent part in controllers used for real-world applications. The use of new methods for handling incomplete information is of fundamental importance in engineering applications. We simulated the effects of uncertainty produced by the instrumentation elements in type-1 and type-2 fuzzy logic controllers to perform a comparative analysis of the systems' response, in the presence of uncertainty. We are presenting an innovative idea to optimize interval type-2 membership functions using an average of two type-1 systems with the Human Evolutionary Model, and we show comparative results of the optimized proposed method. We found that the optimized membership functions for the inputs of a type-2 system increases the performance of the system for high noise levels.

We describe in this paper a new method for response integration in modular neural networks using type-2 fuzzy logic. The modular neural networks were used in human person recognition. Biometric authentication is used to achieve person recognition. Three biometric characteristics of the person are used: face, fingerprint, and voice. A modular neural network of three modules is used. Each module is a local expert on person recognition based on each of the biometric measures. The response integration method of the modular neural network has the goal of combining the responses of the modules to improve the recognition rate of the individual modules. We show in this paper the results of a type-2 fuzzy approach for response integration that improves performance over type-1 fuzzy logic approaches.

Uncertainty is an inherent part of intelligent systems used in real-world applications. The use of new methods for handling incomplete information is of fundamental importance. Type-1 fuzzy sets used in conventional fuzzy systems cannot fully handle the uncertainties present in intelligent systems. Type-2 fuzzy sets can handle such uncertainties in a better way because they provide us with a more complete model of real-world uncertainty. Experimental results are also presented for forecasting chaotic time series in which interval type-2 fuzzy logic outperforms some hybrid intelligent approaches. Neural networks provide a comparable result with type-2 fuzzy systems.

We describe in this paper the evolution of modular neural networks using hierarchical genetic algorithms for pattern recognition. Modular neural networks (MNN) have shown significant learning improvement over single neural networks (NN). For this reason, the use of MNN for pattern recognition is well justified. However, network topology design of MNN is at least an order of magnitude more difficult than for classical NNs. We describe in this paper the use of a hierarchical genetic algorithm (HGA) for optimizing the topology of each of the neural network modules of the MNN. The HGA is clearly needed due to the fact that topology optimization requires that we are able to manage both the layer and node information for each of the MNN modules. Simulation results prove the feasibility and advantages of the proposed approach.

We describe in this paper a new method for response integration in modular neural networks using type-2 fuzzy logic. The modular neural networks were applied to human person recognition. Biometric authentication is used to achieve person recognition. Three biometric characteristics of the person are used: face, fingerprint, and voice. A modular neural network of three modules is used. Each module is a local expert on person recognition based on each of the biometric measures. The response integration method of the modular neural network has the goal of combining the responses of the modules to improve the recognition rate of the individual modules. We show in this paper the results of a type-2 fuzzy logic approach for response integration that improves performance over type-1 fuzzy logic approaches.

Stability is one of the more important aspects in the traditional knowledge of automatic control. Type-2 fuzzy logic is an emerging and promising area for intelligent control (in this case, fuzzy control) applications. We present a design methodology based on the work by Margaliot (2000) for the design of stable Mamdani type-2 fuzzy logic controllers.

This paper presents a general procedure for fuzzy logic controller (FLC) synthesis on field programmable gate arrays (FPGA) devices; the hardware implementation of a simple state machine for data flow control, the VHDL hardware description code of the FLC components, the observed synthesis hardware requirements on a Xilinx Spartan-3 FPGA and executions times achieved, errors due to finite control word length is reported, as well the modifications required in this modular approach to implement a variety of FLC on a readably available FPGA device.

This article presents a new learning methodology based on a hybrid algorithm for interval type-2 TSK fuzzy logic systems (FLS). Using input-output data pairs during the forward pass of the training process, the interval type-2 TSK FLS output is calculated and the consequent parameters are estimated by either recursive least-squares (RLS) or square-root filter (REFIL) method. In the backward pass, the error propagates backward, and the antecedent parameters are estimated by back-propagation (BP) method. The proposed hybrid methodology was used to construct an interval type-2 TSK fuzzy model capable of approximating the behaviour of the steel strip temperature as it is being rolled in an industrial hot strip mill (HSM) and used to predict the transfer bar surface temperature at finishing scale breaker (SB) entry zone. Comparative results show the advantage of the hybrid learning method (RLS-BP or REFIL-BP) over that with only BP

Uncertainty is an inherent part in controllers used for real-world applications. The use of new methods for handling incomplete information is of fundamental importance in engineering applications. This paper deals with the design of controllers using type-2 fuzzy logic for minimizing the effects of uncertainty produced by the instrumentation elements. We simulated type-1 and type-2 fuzzy logic controllers to perform a comparative analysis of the systems' response, in the presence of uncertainty

We describe in this paper the evolution of modular neural networks using hierarchical genetic algorithms. Modular neural networks (MNN) have shown significant learning improvement over single neural networks (NN). For this reason, the use of MNN for pattern recognition is well justified. However, network topology design of MNN is at least an order of magnitude more difficult than for classical NNs. We describe in this paper the use of a hierarchical genetic algorithm (HGA) for optimizing the topology of each of the neural network modules of the MNN. The HGA is clearly needed due to the fact that topology optimization requires that we are able to manage both the layer and node information for each of the MNN modules. Simulation results shown in this paper prove the feasibility and advantages of the proposed approach. The method of integration of response is based on fuzzy integral and Sugeno measures, where parameter /spl lambda/ also is optimized by means of the hierarchical genetic algorithms.

We describe in this paper a new approach for pattern recognition using modular neural networks with a fuzzy logic method for response integration. We proposed a new architecture for modular neural networks for achieving pattern recognition in the particular case of human fingerprints. Also, the method for achieving response integration is based on the fuzzy Sugeno integral. Response integration is required to combine the outputs of all the modules in the modular network. We have applied the new approach for fingerprint recognition with a real database of fingerprints from students of our institution.

We describe in this paper a new approach for pattern recognition using modular neural networks with a fuzzy logic method for response integration. We proposed a new architecture for modular neural networks for achieving pattern recognition in the particular case of human faces. Also, the method for achieving response integration is based on the fuzzy Sugeno integral. Response integration is required to combine the outputs of all the modules in the modular network. We have applied the new approach for face recognition with a real database of faces from students of our institution.

We describe a new approach for face recognition using modular neural networks with a fuzzy logic method for response integration. We proposed a new architecture for modular neural networks for achieving pattern recognition in the particular case of human faces. Also, the method for achieving response integration is based on the fuzzy Sugeno integral. Response integration is required to combine the outputs of all the modules in the modular network. We have applied the new approach for face recognition to a real database of faces of students at our institution. Recognition rates with the modular approach were compared against the monolithic single neural network approach to measure the improvement. The results of the new modular neural network approach were excellent overall and also in comparison to the monolithic approach. © 2005 Wiley Periodicals, Inc. Int J Int Syst 20: 275–291, 2005.

In this article we analyzed the explorative behavior of the Breeder Genetic Algorithm. We tested this algorithm using fuzzy recombination and the classical discrete mutation operator. A general review of the most common linear model structures is given for recommending where to use this type of evolutionary algorithm. We selected for convenience a finite impulse response structure model because it has global optima; we considered this characteristic advisable for analyzing the evolution of the best and poorest individuals in the population through the generations. © 2005 Wiley Periodicals, Inc. Int J Int Syst 20: 293–311, 2005.

We describe A new approach for plant monitoring and diagnostics using type-2 fuzzy logic and fractal theory. The concept of the fractal dimension is used to measure the complexity of the time series of relevant variables for the process. A set of type-2 fuzzy rules is used to represent the knowledge for monitoring the process. In the type-2 fuzzy rules, the fractal dimension is used as a linguistic variable to help in recognizing specific patterns in the measured data. The fuzzy fractal approach has been applied before in problems of financial time series prediction and for other types of problems, but now it is proposed to the monitoring of plants using type-2 fuzzy logic. We also compare the results of the type-2 fuzzy logic approach with the results of using only a traditional type-1 approach. Experimental results show a significant improvement in the monitoring ability with the type-2 fuzzy logic approach.

We describe in this paper the use of type-2 fuzzy logic for achieving adaptive noise cancellation. The objective of adaptive noise cancellation is to filter out an interference component by identifying a model between a measurable noise source and the corresponding un-measurable interference. We propose the use of type-2 fuzzy logic to find this model. The use of type-2 fuzzy logic is justified due to the high level of uncertainty of the process, which makes difficult to find appropriate parameter values for the membership functions.

We describe in this paper a new approach for plant monitoring and diagnostics using type-2 fuzzy logic and fractal theory. The concept of the fractal dimension is used to measure the complexity of the time series of relevant variables for the process. A set of type-2 fuzzy rules is used to represent the knowledge for monitoring the process. In the type-2 fuzzy rules, the fractal dimension is used as a linguistic variable to help in recognizing specific patterns in the measured data. The fuzzy-fractal approach has been applied before in problems of financial time series prediction and for other types of problems, but now it is proposed to the monitoring of plants using type-2 fuzzy logic. We also compare the results of the type-2 fuzzy logic approach with the results of using only a traditional type-1 approach. Experimental results show a significant improvement in the monitoring ability with the type-2 fuzzy logic approach.

We describe in this paper adaptive model-based control of non-linear plants using type-2 fuzzy logic and neural networks. First, the general concept of adaptive model-based control is described. Second, the use of type-2 fuzzy logic for adaptive control is described. Third, a neuro-fuzzy approach is proposed to learn the parameters of the fuzzy system for control. A specific non-linear plant is used to test the hybrid approach for adaptive control. A specific plant was used as test bed in the experiments. The non-linear plant that was considered is the "Pendubot", which is a non-linear plant similar to the two-link robot arm. The results of the type-2 fuzzy logic approach for control were good, both in accuracy and efficiency.

There is a need for shortening the time of formation of the batteries at the production line, and this is due the great demand of this product. In this paper we are proposing a novel technique in this area to optimize the time of manufacturing. This technique uses a fuzzy logic approach to increase the ampere rate in order to minimize the formation time. This paper shows a fuzzy logic system for the formation of batteries using a high scale integration device, such as the FLASH PSD813F1, which is a micro-controller. It includes a CPLD (COMPLEX PLD) embedded, which allows implementing logical functions defined by the user in its 73 inputs 19 outputs AND-OR array. The fuzzy logic algorithm is summarized in a look-up table, described by Boolean equations implemented in the PSD813F1 CPLD. The fuzzy controller, for the formation of batteries for the CPLD of the PSD813F1, basically controls the current intensity applied to the battery depending on its temperature and the change of temperature.

We describe in this paper adaptive model-based control of non-linear plants using type-2 fuzzy logic and neural networks. First, the general concept of adaptive model-based control is described. Second, the use of type-2 fuzzy logic for adaptive control is described. Third, a neuro-fuzzy approach is proposed to learn the parameters of the fuzzy system for control. A specific non-linear plant is used to test the hybrid approach for adaptive control. A specific plant was used as test bed in the experiments. The non-linear plant that was considered is the "Pendubot", which is a non-linear plant similar to the two-link robot arm. The results of the type-2 fuzzy logic approach for control were good, both in accuracy and efficiency.

We describe the application of type-2 fuzzy logic to the problem of automated quality control in sound speaker manufacturing. Traditional quality control has been done by manually checking the quality of sound after production. This manual checking of the speakers is time-consuming and has occasionally been the cause of errors in quality evaluation. For this reason, we developed an intelligent system for automated quality control in sound speaker manufacturing. The intelligent system has a type-2 fuzzy rule base containing the knowledge of human experts in quality control. The parameters of the fuzzy system are tuned by applying neural networks using, as training data, a real time series of measured sounds as given by good sound speakers. We also use the fractal dimension as a measure of the complexity of the sound signal.

We describe in this article a new hybrid fuzzy-fractal approach for plant monitoring. We use the concept of the fractal dimension to measure the complexity of a time series of observed data from the plant. We also use fuzzy logic to represent expert knowledge on monitoring the process in the plant. In the hybrid fuzzy-fractal approach, a set of fuzzy if-then rules are used to classify different conditions of the plant. The fractal dimension is used as an input linguistic variable in the fuzzy system to improve the accuracy in the classification. An implementation of the proposed approach is shown to describe in more detail the method. © 2002 Wiley Periodicals, Inc.

In this paper, we describe a new method for the estimation of the fractal dimension of a geometrical object using fuzzy logic techniques. The fractal dimension is a mathematical concept, which measures the geometrical complexity of an object. The algorithms for estimating the fractal dimension calculate a numerical value using as data a time series for the specific problem. This numerical (crisp) value gives an idea of the complexity of the geometrical object (or time series). However, there is an underlying uncertainty in the estimation of the fractal dimension because we use only a sample of points of the object, and also because the numerical algorithms for the fractal dimension are not completely accurate. For this reason, we have proposed a new definition of the fractal dimension that incorporates the concept of a fuzzy set. This new definition can be considered a weaker definition (but more realistic) of the fractal dimension, and we have named this the "fuzzy fractal dimension." We can apply this new definition of the fractal dimension in conjunction with soft computing techniques for the problem of time series prediction. We have developed hybrid intelligent systems combining neural networks, fuzzy logic, and the fractal dimension, for the problem of time series prediction, and we have achieved very good results.

We describe a new theory of chaos using fuzzy logic techniques. Chaotic behavior in nonlinear dynamical systems is very difficult to detect and control. Part of the problem is that mathematical results for chaos are difficult to use in many cases, and even if one could use them, there is an underlying uncertainty in the accuracy of the numerical simulations of the dynamical systems. For this reason, we can model the uncertainty of detecting the range of values where chaos occurs, using fuzzy set theory. Using fuzzy sets, we can build a new theory of fuzzy chaos, where we can use fuzzy sets to describe the behaviors of a system. We apply this new theory of fuzzy chaos to the case of simulation and control of robotic dynamic systems.

Stepping motors are widely used in robotics and in the numerical control of machine tools, where they have to perform high-precision positioning operations. However, the variations of the mechanical configuration of the drive, which are common to these two applications, can lead to a loss of synchronism for high stepping rates. Moreover, the classical open-loop speed control is weak and a closed-loop control becomes necessary. In this paper, fuzzy logic is applied to control the speed of a stepping motor drive with feedback. A neuro-fuzzy hybrid approach is used to design the fuzzy rule base of the intelligent system for control. In particular, we used the ANFIS (Adaptive Network-based Fuzzy Inference System) methodology to build a Sugeno fuzzy model for controlling the stepping motor drive. An advanced testbed is used in order to evaluate the tracking properties and the robustness capacities of the fuzzy logic controller.

We describe the application of several neural network architectures to the problem of simulating and predicting the dynamic behavior of complex economic time series. We use several neural network models and training algorithms to compare the results and decide which one is best for this application. We also compare the simulation results with fuzzy logic models and the traditional approach of using a statistical model. In this case, we use real time series of prices of consumer goods to test our models. Real prices of tomato and green onion in the US show complex fluctuations in time and are very complicated to predict with traditional statistical approaches. For this reason, we have chosen neural networks and fuzzy logic to simulate and predict the evolution of these prices in the US market.

We describe different hybrid approaches for controlling dynamical systems in electrochemical applications. The hybrid approaches combine soft computing techniques and mathematical models to achieve the goal of controlling the electrochemical process to follow a desired production plan. We develop several hybrid architectures that combine fuzzy logic, neural networks, and genetic algorithms, compare the performance of each of these combinations, and decide on the best one for our purpose. Electrochemical processes, like the ones used in battery charging, are very complex and for this reason very difficult to control. We achieved very good results using the fuzzy logic for control, neural networks for modelling the process, and genetic algorithms for tuning the hybrid intelligent system.

We describe a new method for the automated simulation of non-linear dynamical systems. This method is based on a hybrid fuzzy-genetic approach to achieve, in an efficient way, automated simulation of a particular dynamical system given its mathematical model. The use of genetic algorithms is to achieve automated parameter selection for the mathematical models. Our genetic algorithm uses a Lotka-Volterra approach to change the size of the population in each generation. The use of fuzzy logic simulates the process of expert behavior identification, by implementing the knowledge of identification by a set of fuzzy rules. We also use the concept of the fractal dimension of a time series to help make this identification more accurate. Experimental results for the case of robotic dynamic systems show the efficiency and accuracy of this new method for the simulation of complex non-linear dynamical systems.

We describe the application of a new method for automated simulation of nonlinear dynamical systems, using a fuzzy-genetic approach, to the problem of simulating companies as they compete for the market of their products. A particular company can be viewed as a dynamical system evolving in time and also competing with similar companies for the market of their products. Also, within an international trade agreement there are also competing companies from foreign countries, which complicates the problem even more. We can apply our new method for automated simulation (O. Castillo and P. Melin, 1998) to simulate the evolution of a company or a group of companies as they compete for a fixed market. As a result of these simulations, we can formulate specific mathematical conditions for a specific country to go bankrupt or specific conditions for another company to have success.

We describe a new method for automated simulation of nonlinear dynamical systems. This method is based on a hybrid fuzzy-fractal-genetic approach to achieve, in an efficient way, automated simulation of a particular dynamical system given its mathematical model. The use of genetic algorithms is to achieve automated parameter selection for the mathematical models. The use of fuzzy logic is to simulate the process of expert behavior identification, by implementing the knowledge of identification by a set of fuzzy rules. We also use the concept of the fractal dimension of a time series to help make this identification more accurate. Experimental results for the case of robotic dynamic systems show the efficiency and accuracy of this new method for the simulation of complex nonlinear dynamical systems.

Describes a method for adaptive model-based control of non-linear dynamic plants in the food industry using neural networks, fuzzy logic and fractal theory. The neuro-fuzzy-fractal method combines soft computing (SC) techniques with the concept of the fractal dimension for the domain of non-linear dynamic plant control. The new method for adaptive model-based control has been implemented as a computer program to show that our neuro-fuzzy-fractal approach is a good alternative for controlling non-linear dynamic plants. We illustrate our methodology with the case of controlling biochemical reactors in the food industry. For this case, we use mathematical models for the simulation of bacteria growth for several types of food.

We describe in this paper a new method for automated simulation of non-linear dynamical systems. This method is based on a hybrid fuzzy-fractal-genetic approach to achieve, in an efficient way, automated simulation of a particular dynamical system given its mathematical model. The use of genetic algorithms is to achieve automated parameter selection for the mathematical models. The use of fuzzy logic is to simulate the process of expert behavior identification, by implementing the knowledge of identification by a set of fuzzy rules. We also use the concept of the fractal dimension of a time series to help make this identification more accurate. Experimental results for the case of robotic dynamic systems show the efficiency and accuracy of this new method for the simulation of complex non-linear dynamical systems.

We describe the application of our new method for adaptive model based control (using a neuro-fuzzy-genetic approach) to the problem of controlling international trade dynamics. The problem of international trade between two or more countries is a very complex one because of the nonlinearities involved in the mathematical models (O. Castillo and P. Melin, 1998). We describe the methodology to develop an intelligent system for controlling international trade that can be used by the government of a specific country to maximize the profit from its international trade with other countries. Our method for adaptive model based control of nonlinear dynamical systems consists of using a fuzzy rule base for model selection, a genetic algorithm for identification and a neural network for control (O. Melin and P. Castillo, 1998). Accordingly, an intelligent control system based on our methodology has an architecture with three main modules: model selection, identification and control. For the case of international trade, we have developed the fuzzy rule base for selecting the appropriate mathematical models for the problem, the genetic algorithm for parameter identification, and the neural network for control.

We describe a new method for adaptive model-based control of robotic dynamic systems using a new hybrid neuro-fuzzy-fractal approach. Intelligent control of robotic systems is a difficult problem because the dynamics of these systems is highly nonlinear. Optimal control of many robotic systems also requires methods which make use of predictions of future behavior. We describe an intelligent system for controlling robot manipulators to illustrate our neuro-fuzzy-fractal hybrid approach for adaptive control. We use a new fuzzy inference system for reasoning with multiple differential equations for model selection based on the relevant selection parameters for the problem. We use neural networks for identification and control of robotic dynamic systems.

We describe a general method for adaptive model-based control of nonlinear dynamic systems using neural networks, fuzzy logic and fractal theory. The new neuro-fuzzy-fractal method combines soft computing techniques with the concept of the fractal dimension for the domain of nonlinear dynamic system control. The new method for adaptive model-based control has been implemented as a computer program to show that our neuro-fuzzy-fractal approach is a good alternative for controlling nonlinear dynamic systems. We illustrate our new methodology with the case of controlling aircraft dynamic systems. For this case, we use mathematical models for the simulation of aircraft dynamics during flight. The goal of constructing these models is to capture the dynamics of the aircraft, so as to have a way of controlling this dynamics to avoid dangerous behavior of the system.

The authors describe non-linear mathematical models that can be used to study the dynamics of international trade. Mathematical models of international trade (IT), between three or more countries, can show very complicated dynamics in time (with the possible occurrence of chaotic behavior). The simulation of these models is critical in understanding the behavior of the relevant financial and economical variables for the problem of IT. Also, performing the simulations for different parameter values of the models will enable the forecasting of future IT. The problem of simulation and forecasting of IT has been solved by using soft computing (SC) techniques. An intelligent system for automated simulation of IT, combining fuzzy logic techniques and genetic algorithms, has been developed for the simulation and behavior identification of the mathematical models. The intelligent system uses a specific genetic algorithm to generate the best set of parameter values for performing numerical simulation of the dynamical system (of IT) and a fuzzy rule base for behavior identification. The importance of simulation and forecasting of IT can be measured if one considers that one of the goals for a specific country is to find the optimum benefit from its international trade with other countries.

We describe in this paper a computer program for automated mathematical modelling and simulation of robotic dynamic systems using fuzzy logic techniques, genetic algorithms and fractal theory. The computer program combines soft computing (SC) techniques with mathematical methods and can be considered an intelligent system for the domain of modelling and simulation of robotic systems. This domain is quite complex because robotic systems can be viewed as nonlinear dynamical systems, and it is a well known fact that even very simple nonlinear dynamical systems can exhibit "chaotic" behavior. The computer program simulates the reasoning of a human expert in the process of developing mathematical models of robotic dynamic systems (RDS). The program contains the knowledge of the human experts expressed as fuzzy rules (in the knowledge base) for mathematical modelling and simulation (MMS) of robotic systems. The computer program uses efficiently SC techniques and fractal theory for MMS of RDS. Mathematical modelling and simulation of robotic systems is very important because it can help in the control of an actual system or in the design of a new system using the results of the simulations.

The authors describe paper non-linear mathematical models, from dynamical systems theory, that can be used to study the dynamics of international trade. Mathematical models of international trade (IT), between three or more countries, can show very complicated dynamics in time (with the possible occurrence of behavior known as chaos). The simulation of these models is critical in understanding the behavior of the relevant financial and economical variables for the problem of IT. Also, performing the simulations for different parameter values of the models will enable the prediction of future IT. The problem of modelling and simulation of IT has been solved in this paper by using artificial intelligence (AI) techniques. An intelligent system for automated modelling and simulation of IT has been developed to obtain the "best" mathematical model for a particular situation and then to obtain the "best" simulations for the model. The use of fuzzy logic techniques enables automated modelling of IT using as input real data (time series) for this problem and the use of expert systems technology enables the selection of the appropriate parameter values for the simulation, to obtain all the dynamic behaviors of the corresponding mathematical model. The importance of modelling, simulation and forecasting of IT can be measured if one considers that one of the goals for a specific country is to find the optimum benefit from its international trade with other countries.

We describe a new method for performing automated mathematical modelling for financial time series prediction using fuzzy logic techniques, dynamical systems and fractal theory. The main idea is that using fuzzy logic techniques we can simulate and automate the reasoning process of human experts in mathematical modelling for financial time series prediction. Our new method for automated modelling consists of three main parts: time series analysis, developing a set of admissible models, and selecting the "best" model. Our method for time series analysis consists of using the fractal dimension of a set of points as a measure of the geometrical complexity of the time series. Our method for developing a set of admissible dynamical systems models is based on the use of fuzzy logic techniques to simulate the decision process of the human experts in modelling financial problems. The selection of the "best" model for financial time series prediction (FTSP) is done using heuristics from the experts and statistical calculations. This new method can be implemented as a computer program and can be considered an intelligent system for automated mathematical modelling for FTSP.

Describes a computer program that can be considered as an intelligent system for the domain of financial time series prediction. The computer program is an implementation of a new algorithm for discovering mathematical models for financial time series prediction, combining artificial intelligence methodology with dynamical systems theory, fractal theory and statistical methods. Given a financial time series for an specific problem, the intelligent system develops mathematical models for the problem based on the geometry of the data, using three different approaches. First, the computer program develops regression models for the time series using traditional statistical methods, then it develops nonlinear mathematical models based on dynamical systems theory and chaos theory, and finally it develops fractal mathematical models based on the theory of fractal geometry. The intelligent system then analyzes all of the mathematical models obtained before making a selection of the model that gives the "best" prediction for the financial time series. This selection is done by the intelligent system using a combination of heuristics and calculations that are contained in the knowledge base. An intelligent system that can learn models from financial data would be very useful in practice in making the task of prediction easier and less time-consuming.