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Economic risk is a probability that measures the possible alterations, as well as the uncertainty, generated by multiple internal or external factors. Sometimes it could cause the impossibility of guaranteeing the level of compliance with organizational goals and objectives, which is why for their administration they are frequently divided into multiple categories according to their consequences and impact. Global indicators are dynamic and sometimes the correlation is uncertain because they depend largely on a combination of economic, social, and environmental factors. Thus, our proposal consists of a model for prediction and classification of multivariate risk factors such as birth rate and population growth, among others, using multiple neural networks and General Type-2 fuzzy systems. The contribution is the proposal to integrate multiple variables of several time series using both supervised and unsupervised neural networks, and a generalized Type-2 fuzzy integration. Results show the advantages of utilizing the method for the fuzzy integration of multiple time series attributes, with which the user can then prevent future threats from the global environment that impact the scheduled compliance process. [ABSTRACT FROM AUTHOR]

An essential aspect of healthcare is receiving an appropriate and opportune disease diagnosis. In recent years, there has been enormous progress in combining artificial intelligence to help professionals perform these tasks. The design of interval Type-3 fuzzy inference systems (IT3FIS) for medical classification is proposed in this work. This work proposed a genetic algorithm (GA) for the IT3FIS design where the fuzzy inputs correspond to attributes relational to a particular disease. This optimization allows us to find some main fuzzy inference systems (FIS) parameters, such as membership function (MF) parameters and the fuzzy if-then rules. As a comparison against the proposed method, the results achieved in this work are compared with Type-1 fuzzy inference systems (T1FIS), Interval Type-2 fuzzy inference systems (IT2FIS), and General Type-2 fuzzy inference systems (GT2FIS) using medical datasets such as Haberman's Survival, Cryotherapy, Immunotherapy, PIMA Indian Diabetes, Indian Liver, and Breast Cancer Coimbra dataset, which achieved 75.30, 87.13, 82.04, 77.76, 71.86, and 71.06, respectively. Also, cross-validation tests were performed. Instances established as design sets are used to design the fuzzy inference systems, the optimization technique seeks to reduce the classification error using this set, and finally, the testing set allows the validation of the real performance of the FIS. [ABSTRACT FROM AUTHOR]

In all organizations, many decision analysts acquire their skills through the experience of facing challenges to structure complex problems. Therefore, every day, the use of tools to integrate indicators through multi-attribute ordering, component-based separation, and clustering to reduce the criteria required for decision-making and the achievement of goals and objectives is more frequent. Thus, our proposal consists of a new hybrid-hierarchical model for the classification and prediction of country indicators such as inflation, unemployment, population growth, and labor force, among others, in a decision-making environment using unsupervised neural networks and type-3 fuzzy systems. The contribution is achieving a type-3 fuzzy aggregation method in which the hierarchy is first represented by neural networks and later a set of type-1, type-2, and type-3 systems to combine the results, which allows multiple indicators to be separated and then integrated in an appropriate fashion. We can point out as one of the advantages of utilizing the method that the user can evaluate a range of qualities in multiple variables through the classification and prediction of time series attributes and assess a range of qualities for decision-making with uncertainty, according to the results of the simulations carried out. [ABSTRACT FROM AUTHOR]

This paper presents an initial proposal for the utilization of mediative fuzzy logic in control problems. Mediative fuzzy logic (MFL) was originally proposed with the idea of modeling situations in which there exists contradictory knowledge among several experts in an application domain. In this situation, a mediative solution may be a better choice in this particular decision-making situation. In this paper, we are extending the concept of fuzzy control to the realm of MFL for situations in which we have two or more control experts, and the design of the fuzzy controller has to be based on their knowledge. In this situation, we are taking advantage of the symmetrical nature of membership functions in reducing the complexity of designing the fuzzy controllers. The goal of this study was to improve control results by combining the knowledge of several experts, which MFL is aimed at executing. The initial architecture of mediative fuzzy control for type-1 fuzzy logic is presented, and an illustrative example is used to better comprehend the proposed approach. Later, we extend type-1 MFL to the realms of type-2 and type-3 fuzzy logic, and we also provide a comparative study that exhibits that the type-3 version surpasses the type-2 and type-1 versions of mediative fuzzy control. The idea of utilizing type-2 and type-3 is to improve the capabilities of the fuzzy controller in handling uncertainty coming from noise in the control process. [ABSTRACT FROM AUTHOR]

In this paper, we describe a review concerning the Quantum Computing (QC) and Deep Learning (DL) areas and their applications in Computational Intelligence (CI). Quantum algorithms (QAs), engage the rules of quantum mechanics to solve problems using quantum information, where the quantum information is concerning the state of a quantum system, which can be manipulated using quantum information algorithms and other processing techniques. Nowadays, many QAs have been proposed, whose general conclusion is that using the effects of quantum mechanics results in a significant speedup (exponential, polynomial, super polynomial) over the traditional algorithms. This implies that some complex problems currently intractable with traditional algorithms can be solved with QA. On the other hand, DL algorithms offer what is known as machine learning techniques. DL is concerned with teaching a computer to filter inputs through layers to learn how to predict and classify information. Observations can be in the form of plain text, images, or sound. The inspiration for deep learning is the way that the human brain filters information. Therefore, in this research, we analyzed these two areas to observe the most relevant works and applications developed by the researchers in the world. [ABSTRACT FROM AUTHOR]

The pursuit of continuous improvement across diverse processes presents a pressing challenge. Precision in manufacturing, efficient delivery route planning, and accurate diagnostics are imperative, prompting the exploration of innovative solutions. Nature-inspired algorithms offer a pathway for enhancing these processes. In this study, we address this challenge by dynamically adapting parameters in the Bird Swarm Algorithm using General Type-2 Fuzzy Systems, encompassing a range of rules and membership functions. Two complex case studies validate the effectiveness of our approach. The first evaluates Congress of Evolutionary Competition 2017 functions, while the second tackles the intricacies of Congress of Evolutionary Competition 2019 functions. Our methodology achieves an 97% improvement for Congress of Evolutionary Competition 2017 functions and a significant 70% enhancement for Congress of Evolutionary Competition 2019 functions. Notably, our results are benchmarked against the original method. Crucially, rigorous statistical analysis underscores the significant advancements facilitated by our proposed method. The comparison demonstrates clear and statistically significant improvements over the original approach. This study proves the marked impact of integrating General Type-2 Fuzzy Systems into the Bird Swarm Algorithm, presenting a promising avenue for addressing intricate optimization challenges in diverse domains. [ABSTRACT FROM AUTHOR]

In this article, a plant monitoring approach based on a hybrid mixture of type-3 fuzzy logic (T3FL) and the fractal dimension (FD) is presented. The main reason for combining type-3 and the fractal dimension is to take advantage of both their capabilities in solving the problem of monitoring a plant. Basically, T3FL helps in handling the uncertainty in monitoring the variables of a nonlinear system, while the FD helps to capture the signal complexity by finding key or hidden patterns in the data. The FD is utilized to estimate data complexity of the process variables being monitored. We utilize the box counting algorithm to approximate the values of the FD. A set of T3FL rules is utilized to model monitoring knowledge. The proposed approach was tested with a plant studied in previous works, which was solved with type-1 and type-2 fuzzy logic, and now type-3 is able to surpass the performance of previous approaches for this problem. The main contribution is the T3FL and FD hybrid proposal for plant monitoring, which has not been presented before in the literature. Simulation results illustrate the potential advantage of utilizing the T3FL and FD combination in this area. [ABSTRACT FROM AUTHOR]

The integration of key indicators from the results of the analysis of time series represents a constant challenge within organizations; this could be mainly due to the need to establish the belonging of each indicator within a process, geographic region or category. This paper thus illustrates how both primary and secondary indicators are relevant for decision making, and why they need to be integrated by making new final fuzzy indicators. Thus, our proposal consists of a type-2 fuzzy integration of multivariate time series, such as OECD country risk classification, inflation, population and gross national income (GNI) by using multiple type-1 fuzzy inference systems to perform time series classification tasks. Our contribution consists of the proposal to integrate multiple nested type-1 fuzzy inference systems using a type-2 fuzzy integration. Simulation results show the advantages of using the proposed method for the fuzzy classification of multiple time series. This is done in order so the user can have tools that allow them to understand the environment and generate comparative analyses of multiple information sources, and finally use it during the process prior to decision making considering the main advantage of modeling the inherent uncertainty. [ABSTRACT FROM AUTHOR]

In this paper, the latest global COVID-19 pandemic prediction is addressed. Each country worldwide has faced this pandemic differently, reflected in its statistical number of confirmed and death cases. Predicting the number of confirmed and death cases could allow us to know the future number of cases and provide each country with the necessary information to make decisions based on the predictions. Recent works are focused only on confirmed COVID-19 cases or a specific country. In this work, the firefly algorithm designs an ensemble neural network architecture for each one of 26 countries. In this work, we propose the firefly algorithm for ensemble neural network optimization applied to COVID-19 time series prediction with type-2 fuzzy logic in a weighted average integration method. The proposed method finds the number of artificial neural networks needed to form an ensemble neural network and their architecture using a type-2 fuzzy inference system to combine the responses of individual artificial neural networks to perform a final prediction. The advantages of the type-2 fuzzy weighted average integration (FWA) method over the conventional average method and type-1 fuzzy weighted average integration are shown. [ABSTRACT FROM AUTHOR]

We describe in this paper an approach for predicting the COVID-19 time series in the world using a hybrid ensemble modular neural network, which combines nonlinear autoregressive neural networks. At the level of the modular neural network, which is formed with several modules (ensembles in this case), the modules are designed to be efficient predictors for each country. In this case, an integrator is used to combine the outputs of the modules, in this way achieving the goal of predicting a set of countries. At the level of the ensembles, forming a part of the modular network, these are constituted by a set of modules, which are nonlinear autoregressive neural networks that are designed to be efficient predictors under particular conditions for each country. In each ensemble, the results of the modules are combined with an aggregator to achieve a better and improved result for the ensemble. Publicly available datasets of coronavirus cases around the globe from the last months have been used in the analysis. Interesting conclusions have been obtained that could be helpful in deciding the best strategies in dealing with this virus for countries in their fight against the coronavirus pandemic. In addition, the proposed approach could be helpful in proposing strategies for similar countries. [ABSTRACT FROM AUTHOR]

The world has been greatly affected by the COVID-19 pandemic, causing people to remain isolated and decreasing the interaction between people. Accordingly, various measures have been taken to continue with a new normal way of life, which is why there is a need to implement the use of technologies and systems to decrease the spread of the virus. This research proposes a real-time system to identify the region of the face using preprocessing techniques and then classify the people who are using the mask, through a new convolutional neural network (CNN) model. The approach considers three different classes, assigning a different color to identify the corresponding class: green for persons using the mask correctly, yellow when used incorrectly, and red when people do not have a mask. This study validates that CNN models can be very effective in carrying out these types of tasks, identifying faces, and classifying them according to the class. The real-time system is developed using a Raspberry Pi 4, which can be used for the monitoring and alarm of humans who do not use the mask. This study mainly benefits society by decreasing the spread of the virus between people. The proposed model achieves 99.69% accuracy with the MaskedFace-Net dataset, which is very good when compared to other works in the current literature. [ABSTRACT FROM AUTHOR]

In this work, several types of intuitionistic fuzzy sets, inspired by Type-2 and Type-3 concepts, are introduced. In particular, the newly proposed interval Type-3 intuitionistic sets are very interesting as they extend the opportunities of both interval Type-3 fuzzy sets and intuitionistic sets when capturing specific forms of uncertainty. A comparative study of interval Type-3 with respect to intuitionistic fuzzy is presented. Based on this comparison, a novel concept of an interval Type-3 intuitionistic fuzzy set is put forward to enhance the capabilities of modeling uncertainty with respect to the individual Type-3 and intuitionistic concepts. Basically, the secondary and tertiary membership functions are added to the intuitionistic fuzzy sets to build an interval Type-3 intuitionistic fuzzy set. An illustrative example dealing with controlling the imaging system of televisions is provided to envision the potential applicability and advantages of interval Type-3 intuitionistic fuzzy sets in real problems. For this application, the intuitionistic Type-3 approach shows the potential to outperform previous approaches in controlling this system. [ABSTRACT FROM AUTHOR]

Fuzzy dynamic parameter adaptation has proven to be of great help when it is implemented in bio-inspired algorithms for optimization in different application areas, such as control, mathematical functions, classification, among others. One of the main contributions of this work is the proposed improvement of the Bird Swarm algorithm using a Fuzzy System approach, and we called this improvement the Fuzzy Bird Swarm Algorithm. Furthermore, we use a set of complex Benchmark Functions of the Congress on Evolutionary Computation Competition 2017 to compare the results between the original algorithm and the proposed improvement of the algorithm. The fuzzy system is utilized for the dynamic parameter adaptation of the C1 and C2 parameters of the Bird Swarm Algorithm. As a result, the Fuzzy Bird Swarm Algorithm has enhanced exploration and exploitation abilities that help in achieving better results than the Bird Swarm Algorithm. We additionally test the algorithm's performance in a real problem in the medical area, using the optimization of a neural network to obtain the risk of developing hypertension. This neural network uses information, such as age, gender, body mass index, systolic pressure, diastolic pressure, if the patient smokes and if the patient has parents with hypertension. Hypertension is one of the leading causes of heart problems, which in turn are also one of the top causes of death. Moreover, these days it causes more complications and deaths in people infected with COVID-19, the virus of the ongoing pandemic. Based on the results obtained through the 30 experiments carried out in three different study cases, and the results obtained from the statistical tests, it can be concluded that the proposed method provides better performance when compared with the original method. [ABSTRACT FROM AUTHOR]

Optimization is essential for applications since it can improve the results provided in different areas; for this task, it is beneficial to use soft computing techniques, such as bio-inspired algorithms. In addition, it has been shown that if dynamic parameter adaptation is applied to these algorithms, they can provide a better result. For this work, the main contribution is to carry out the dynamic parameter adaptation to the bird swarm algorithm using interval type-2 fuzzy systems to realize a new fuzzy bio-inspired algorithm. The design of the proposed fuzzy system consists of two inputs corresponding to the iterations and diversity. As outputs, it takes the values of C and S, which are parameters to be adjusted by the algorithm. Once the design and the experimentation are realized, they are divided into two study cases. The first consists of a set of complex functions of the Congress of Evolutionary Competition 2017. The second case study consists of optimizing the membership functions in a fuzzy system designed to provide the nocturnal blood pressure profile, which corresponds to a neuro-fuzzy hybrid model to obtain the risk of hypertension. Analyzing the 30 experiments performed in both case studies, we can observe that the results obtained are improved when compared with the original method and other proposed methodologies, achieving good results in the complex functions. In addition, the optimized fuzzy system will reach an average of 97% correct classification. Statistically, it can be concluded that there is significant evidence to affirm that the proposed method provides good results. [ABSTRACT FROM AUTHOR]

In this work, information on COVID-19 confirmed cases is utilized as a dataset to perform time series predictions. We propose the design of ensemble neural networks (ENNs) and type-3 fuzzy inference systems (FISs) for predicting COVID-19 data. The answers for each ENN module are combined using weights provided by the type-3 FIS, in which the ENN is also designed using the firefly algorithm (FA) optimization technique. The proposed method, called ENNT3FL-FA, is applied to the COVID-19 data for confirmed cases from 12 countries. The COVID-19 data have shown to be a complex time series due to unstable behavior in certain periods of time. For example, it is unknown when a new wave will exist and how it will affect each country due to the increase in cases due to many factors. The proposed method seeks mainly to find the number of modules of the ENN and the best possible parameters, such as lower scale and lower lag of the type-3 FIS. Each module of the ENN produces an individual prediction. Each prediction error is an input for the type-3 FIS; moreover, outputs provide a weight for each prediction, and then the final prediction can be calculated. The type-3 fuzzy weighted average (FWA) integration method is compared with the type-2 FWA to verify its ability to predict future confirmed cases by using two data periods. The achieved results show how the proposed method allows better results for the real prediction of 20 future days for most of the countries used in this study, especially when the number of data points increases. In countries such as Germany, India, Italy, Mexico, Poland, Spain, the United Kingdom, and the United States of America, on average, the proposed ENNT3FL-FA achieves a better performance for the prediction of future days for both data points. The proposed method proves to be more stable with complex time series to predict future information such as the one utilized in this study. Intelligence techniques and their combination in the proposed method are recommended for time series with many data points. [ABSTRACT FROM AUTHOR]

In this work, a comparison of optimization techniques based on swarm intelligence to design Convolutional Neural Networks is performed. The optimization techniques used in this comparison are Grey Wolf Optimizer (GWO) and Whale Optimization Algorithm (WOA). The algorithms design convolutional neural networks (CNNs) architectures applied to face recognition. These techniques were chosen due to their similarity in their processes to find optimal results, such as their searching of prey. The design of CNNs consists of the number of layers (convolutional and fully connected), number and size of the filters, neurons fully connected, batch size, epoch, and algorithm for the learning phase. The simulation results are compared, using a different number of images for the learning phase to know which technique has a better performance using a smaller number of images to CNN design. [ABSTRACT FROM AUTHOR]

This document is a retraction note for an article titled "Optimization using the firefly algorithm of ensemble neural networks with type-2 fuzzy integration for COVID-19 time series prediction." The publisher has retracted the article due to concerns about compromised editorial handling and peer review process, inappropriate references, and the article not being in scope of the journal or the guest-edited issue. The authors of the article disagree with the retraction. The original article can be found online. [Extracted from the article]

Diabetes has become a global health problem, where a proper diagnosis is vital for the life quality of patients. In this article, a genetic algorithm is put forward for designing type-2 fuzzy inference systems to perform Diabetes Classification. We aim at finding parameter values of Type-2 Trapezoidal membership functions and the type of model (Mamdani or Sugeno) with this optimization. To verify the effectiveness of the proposed approach, the PIMA Indian Diabetes dataset is used, and results are compared with type-1 fuzzy systems. Five attributes are used considered as the inputs of the fuzzy inference systems to obtain a Diabetes diagnosis. The instances are divided into design and testing sets, where the design set allows the genetic algorithm to minimize the error of classification, and finally, the real behavior of the fuzzy inference system is validated with the testing set. [ABSTRACT FROM AUTHOR]

This paper describes two alternatives for hybridizing general type-2 fuzzy logic with the Support Vector Machine (SVM), which is one of the best classification methods in the literature. The main idea of using type-2 fuzzy logic is providing SVM with the ability for uncertainty handling in real-world situations, which suffer from dynamic changes and multiple sources of uncertainty. Two approaches for general type-2 fuzzy hybrid classifiers are proposed, tested and compared based on benchmark data sets. In order to find the best hybrid combination of these methods a comparison has been realized with different experiments using diagnosis benchmark datasets by measuring the classifier accuracy. The first approach consists on using fuzzy rules as additional features to the SVM in order to increase the separability of the data. On the other hand, the second approach consists on defining the Sugeno coefficients for a general type-2 fuzzy classifier as elements of the optimal hyperplane obtained by the SVM method. The motivation for proposing these hybrid approaches is finding the best classifier combining the abilities of the original methods, which are robustness and uncertainty handling. The conclusion based on the experimental results is that the hybrid combination of both methods produces a classifier that is better than the original individual approaches. [ABSTRACT FROM AUTHOR]

In this paper dynamic parameter adjustment in particle swarm optimization (PSO) for modular neural network (MNN) design using granular computing and fuzzy logic (FL) is proposed. Nowadays, there are a plethora of optimization techniques, but their implementations require having knowledge about these techniques in order to establish their parameters, because the performance and final results of a particular technique depend on the optimal parameter values. For this reason, in this paper the fuzzy adjustment of parameters during the execution is proposed, and this proposal allows to adjust the parameters depending on current PSO behavior in each iteration. The proposed method performs modular neural network optimization applied to human recognition using benchmark ear, iris and face databases. Two fuzzy inference systems are proposed to perform this dynamic adjustment, comparisons against a PSO without this dynamic adjustment (simple PSO) are performed to verify if the proposed adjustment using a fuzzy system is better improving recognition rate and execution time. The PSO variants presented in this paper are aimed at performing MNNs optimization. This optimization consists on finding optimal parameters, such as: the number of modules (or sub granules), percentage of data for the training phase, learning algorithm, goal error, number of hidden layers and their number of neurons. [ABSTRACT FROM AUTHOR]

This paper presents an approach to optimize a Convolutional Neural Network using the Fuzzy Gravitational Search Algorithm. The optimized parameters are the number of images per block that are used in the training phase, the number of filters and the filter size of the convolutional layer. The reason for optimizing these parameters is because they have a great impact on performance of the Convolutional Neural Networks. The neural network model presented in this work can be applied for any image recognition or classification applications; nevertheless, in this paper, the experiments are performed in the ORL and Cropped Yale databases. The results are compared with other neural networks, such as modular and monolithic neural networks. In addition, the experiments were performed manually, and the results were obtained (when the neural network is not optimized), and comparison was made with the optimized results to validate the advantage of using the Fuzzy Gravitational Search Algorithm. [ABSTRACT FROM AUTHOR]

Nowadays, with the emergence of computer-aided systems, diagnosis problems are one of the most important application areas of artificial intelligence. The present paper is focused on a specific kind of computer-aided diagnosis system based on General Type-2 Fuzzy Logic. The main goal is the generation of General Type-2 Fuzzy Classifiers that can handle the data uncertainty. The concept of embedded Type-1 Fuzzy membership functions has been proposed to be used in the design of General Type-2 Fuzzy Classifiers. A methodology for generating the embedded Type-1 fuzzy membership functions is introduced, and the subsequent approach for developing the Footprint of Uncertainty of the General Type-2 Fuzzy Classifier is presented. On the other hand, the proposed approach performance is evaluated by the experimentation with different diagnosis benchmark problems. In addition, a statistical comparison with respect to another existing approach of General Type-2 Fuzzy classifiers is presented. [ABSTRACT FROM AUTHOR]

Computer aided systems have been frequently used in recent times and the evolution of artificial intelligence allows the inclusion of this kind of systems in most complex problems, for example in diagnosis problems. Some of the most powerful algorithms or methods that have been applied to diagnosis problems are: Artificial Neural Networks, Support Vector Machines, Decision Threes, Fuzzy Inference Systems and hybrids of these algorithms. The present paper explores the applications of a special approximation of the Type-2 Fuzzy Inference System, which is the Shadowed Type-2 Fuzzy Inference System, and the reason for using this approach (and not another one) is because it provides a good approximation to General Type-2 Fuzzy Inference Systems, but with a computational cost reduction. Shadowed Type-2 Fuzzy Inference Systems are inspired on the Shadows Sets that simplify the traditional Type-1 Membership Function using two optimal α -cuts, which in our case are applied in the secondary membership function of the General Type-2 Fuzzy Inference System (modeled by the α -planes representation) in order to model the system with only two α -planes. Experiments were realized with eleven benchmark datasets in order to evaluate the accuracy of the proposed system. The obtained results demonstrate the advantages of using this approach over the conventional General Type-2 Fuzzy Inference Systems, and this is because we obtain better performance in most of the cases and with less computational resources. [ABSTRACT FROM AUTHOR]

The advancement of new tools in the field of control systems is a contemporary development. This work introduces the utilization of Type-3 fuzzy logic, a relatively recent concept that has been applied across various disciplines. In our case, a Type-3 fuzzy system is designed to enhance the optimization of parameters within the harmony search algorithm, specifically tailored for a control problem. Through a series of experiments, the efficacy of this novel Type-3 fuzzy logic tool is put to the test. Previous studies have primarily explored Type-1 and Type-2 fuzzy logic. To assess the performance of this new Type-3 fuzzy logic tool, a comparative analysis of results is conducted using statistical testing. The introduction of Type-3 fuzzy logic in the control domain represents a novel and innovative approach. This approach extends beyond the conventional Type-1 and Type-2 fuzzy logic, showcasing the dynamic evolution in the field. Results obtained through experimentation are analyzed, and statistical tests are employed to determine whether the Type-3 fuzzy logic tool yields superior outcomes compared to its predecessors. By doing so, this study contributes to the growing body of research that explores the potential benefits of Type-3 fuzzy logic and its application in control systems, offering new perspectives and opportunities for further advancements in the field. We have to mention that the utilization of Type-3 fuzzy logic in enhancing metaheuristics is a relatively new trend, and in this work, this research has extended this to the realm of harmony search. In addition, the application of the optimal design of the ball-and-beam fuzzy controllers has not been previously carried out with the Type-3 fuzzy harmony search algorithm, which is the novelty of this study. [ABSTRACT FROM AUTHOR]

Highlights • The hybrid intelligent model was built using artificial neural networks and fuzzy logic. • This hybrid model was tested with the MIT-BIH arrhythmia database. • A type-1 fuzzy system (type-1 FIS) and an interval type-2 fuzzy system (IT2FIS) were designed. • The best classification rate results are obtained using IT2FIS instead of type-1 FIS in the basic units. • A type-1 FIS is used to find a global classification for the 2 basic units in the hybrid model. Abstract This paper describes an approach using computational intelligence methods to form a hybrid model as a classification method for 2-lead cardiac arrhythmias. The hybridization of methods can increase the performance in a system and take advantage of the benefits offered by such techniques in solving complex problems. The interpretation of electrocardiograms is a useful task for physicians, but when it comes to reviewing more than 24 h of information, it becomes a laborious task for them. For this reason, the design a computational model that helps in such a task is very useful for the timely medical diagnosis. The hybrid model is build using artificial neural networks and fuzzy logic. Training and testing of the hybrid model was with the Massachusetts Institute of Technology and Beth Israel Hospital (MIT-BIH) arrhythmia database. The heartbeats are preprocessed to improve results of classification. Ten different classes of normal and arrhythmia signals for building the hybrid model are considered. We used two electrode signals or leads included in the MIT-BIH arrhythmia database, MLII and V1, V2, or V3 as second electrode signal. The hybrid model is composed by two basic module units, as described below. A basic module unit to perform the classification for each signal lead is used. Each basic module unit is composed of three different classifiers based on the following models: fuzzy KNN algorithm, multilayer perceptron with gradient descent and momentum (MLP-GDM), and multilayer perceptron with scaled conjugate gradient backpropagation (MLP-SCG). The outputs from the classifiers are combined using a fuzzy system for integration of results. We designed two fuzzy systems, Mamdani type-1 fuzzy system (type-1 FIS) and an interval type-2 fuzzy system (IT2FIS). The reason is to perform a comparison between type-1 FIS and IT2FIS in the hybrid model. We have obtained best results in the classification rate using IT2FIS instead of type-1 FIS in the basic units. Finally, a type-1 FIS is used to determine the global classification for the 2 basic units in hybrid model. We obtained a good classification rate in each basic module unit, 92.90% and 92.70% of classification rate for basic modules unit 1 and unit 2 respectively. Finally, we obtained a 93.80% when used type-1 FIS and 94.20% of classification rate used IT2FIS combining both basic module units. In the results presented, we improve the global classification in proposed hybrid model combining neural networks and fuzzy logic used both signal lead included in MIT-BIH arrhythmia database. The proposed hybrid model maybe extended to use multi-lead arrhythmia classification using other databases that contain 12 leads to be able to make a complete medical diagnosis. [ABSTRACT FROM AUTHOR]

At present time, general type-2 fuzzy logic provides better uncertainty modeling when compared to interval type-2 fuzzy logic, and this has been shown with the improvement in the performance of fuzzy logic controllers and fuzzy edge detectors. However, higher computational cost represents a limitation for many applications and implementation platforms, and it is because of this that the computational cost reduction is the main goal of this paper. The aim of this work is to model a GT2 FLS based on shadowed type-2 fuzzy sets (ST2 FS) and apply this approach to control problems. The ST2 FS consists of approximating the secondary membership function by shadowed sets and is because of this, that we present an analytic approach to obtain the shadowed set for triangular and Gaussian membership functions for any parameters. Based on this, we achieve a representation of the ST2 FS as a parameterized function, facilitating its implementation. The results are compared against the performance when a generalized type-2 fuzzy inference system is approximated using α-planes for control applications. [ABSTRACT FROM AUTHOR]

In this paper, we present a new model based on modular neural networks (MNN) to classify a patient's blood pressure level (systolic and diastolic pressure and pulse). Tests are performed with the Levenberg-Marquardt (trainlm) and scaled conjugate gradient backpropagation (traincsg) training methods. The modular neural network architecture is formed by three modules. In the first module we consider the diastolic pressure data; in the second module we use details of the systolic pressure; in the third module, pulse data is used and the response integration is performed with the average method. The goal is to design the best MNN architecture for achieving an accurate classification. The results of the model show that MNN presents an excellent classification for blood pressure. The contribution of this work is related to helping the cardiologist in providing a good diagnosis and patient treatment and allows the analysis of the behavior of blood pressure in relation to the corresponding diagnosis, in order to prevent heart disease. [ABSTRACT FROM AUTHOR]

The computing with words is an approach that has unique characteristics and advantages to model cognitive processes, this article explains the relationship and difference between type-1 and type-2 fuzzy sets in the definition of linguistic values. Here, we perform a compressive review and justify because type-2 sets are more appropriate in modeling linguistic values, and a heuristic procedure by examples is carried out to define linguistic values on a continuous variable. A visual comparison of a rule-based system, when linguistic values use crips, type-1, and type-2 fuzzy sets in modeling a cognitive system. [ABSTRACT FROM AUTHOR]

In this paper, a hybrid model using modular neural networks and fuzzy logic was designed to provide the hypertension risk diagnosis of a person. This model considers age, risk factors and behavior of the blood pressure in a period of 24 h, using as a basis the Framingham Heart Study. Records of blood pressure are collected with the ambulatory blood pressure monitoring (ABPM), a device which takes readings for a period of time of 24 h. A modular neural network was designed, with three modules, of which the first and second modules correspond to the systolic and diastolic pressures and the last one to the heart rate. Each module is trained with the data obtained by the ABPM of different patients, this in order that the neural network learns the different behaviors that the blood pressure may have. Also, different architectures and learning methods are considered to obtain the best possible architecture. In addition, two fuzzy inference systems (FISs) for classification purpose are proposed, the first one for the heart rate level and the second one for the night profile of the patient. These were tested with different types of membership functions and then selecting the FIS that obtained the best results. Furthermore, a third FIS as a blood pressure classifier is also used. The different proposed methodologies were tested, in the case of the modular neural network to find the architecture that produces better results and in the fuzzy inference systems to find which membership functions were the ideal ones for the case study, in this way obtaining overall good results. For the case of the modular neural network, the learning accuracy in the first module is 98%, in the second module is 97.62% and the third module is 97.83% respectively. For the night profile, the fuzzy system is compared to a traditional system of production rules, and it is noted that the first one gives all correct outputs and the second one just gives 53% of the outputs, this is due to the uncertainty handling that fuzzy systems can provide, which the traditional system cannot because its rules are very strict. Hybrid intelligent systems for the solution of this kind of complex problems have excellent performance, due to the good learning in each module of the neural network and the classification uncertainty that is well managed by the fuzzy systems, obtaining with this a hybrid combination for achieving good results. [ABSTRACT FROM AUTHOR]

Nowadays, there are different representations of Generalized Type-2 Fuzzy Sets that consider a non-uniform distribution of the uncertainty, for example, the Geometric approach, the Z-Slices method and the α -planes approximation. Each representation has advantages and disadvantages, however, the present work is focused on the α -planes representation, and this representation consists on realizing a horizontal discretization, the solution of each horizontal slice, and then the integration of these planes. Each horizontal slice results in an Interval Type-2 Fuzzy System, so, the computational cost is proportional to the discretization level, which means, is proportional to the number of α -planes used for modeling the Generalized Type-2 FS. The aim of this work is reducing the computational cost of Generalized Type-2 FS by a new approach of α -planes representation. In this paper the Newton–Cotes quadrature for the α -planes integration is proposed, achieving in this way a high-level discrete integration compared with the conventional α -planes integration. The proposed approach aims at reducing the number of α -planes necessary to obtain a good approximation of Generalized Type-2 FS. In order to validate the proposed approach, a set of experiments was realized with a randomly generated Generalized Type-2 Fuzzy Sets, and they are realized with a different number of α -planes in order to compare the performance of the proposed approach with respect to the conventional approach. On the other hand, the proposed approach was also applied to a control problem, as an example of applications of the proposed approach to real-world problems. [ABSTRACT FROM AUTHOR]

A neuro fuzzy hybrid model (NFHM) is proposed as a new artificial intelligence method to classify blood pressure (BP). The NFHM uses techniques such as neural networks, fuzzy logic and evolutionary computation, and in the last case genetic algorithms (GAs) are used. The main goal is to model the behavior of blood pressure based on monitoring data of 24 h per patient and based on this to obtain the trend, which is classified using a fuzzy system based on rules provided by an expert, and these rules are optimized by a genetic algorithm to obtain the best possible number of rules for the classifier with the lowest classification error. Simulation results are presented to show the advantage of the proposed model. [ABSTRACT FROM AUTHOR]

The main goal of this paper is to improve the performance of the Fireworks Algorithm (FWA). To improve the performance of the FWA we propose three modifications: the first modification is to change the stopping criteria, this is to say, previously, the number of function evaluations was utilized as a stopping criteria, and we decided to change this to specify a particular number of iterations; the second and third modifications consist on introducing a dispersion metric (dispersion percent), and both modifications were made with the goal of achieving dynamic adaptation of the two parameters in the algorithm. The parameters that were controlled are the explosion amplitude and the number of sparks, and it is worth mentioning that the control of these parameters is based on a fuzzy logic approach. To measure the impact of these modifications, we perform experiments with 14 benchmark functions and a comparative study shows the advantage of the proposed approach. We decided to call the proposed algorithms Iterative Fireworks Algorithm (IFWA) and two variants of the Dispersion Percent Iterative Fuzzy Fireworks Algorithm (DPIFWA-I and DPIFWA-II, respectively). [ABSTRACT FROM AUTHOR]

Interval Type-2 fuzzy systems allow the possibility of considering uncertainty in models based on fuzzy systems, and enable an increase of robustness in solutions to applications, but also increase the complexity of the fuzzy system design. Several attempts have been previously proposed to reduce the computational cost of the type-reduction stage, as this process requires a lot of computing time because it is basically a numerical approximation based on sampling, and the computational cost is proportional to the number of samples, but also the error is inversely proportional to the number of samples. Several works have focused on reducing the computational cost of type-reduction by developing strategies to reduce the number of operations. The first type-reduction method was proposed by Karnik and Mendel (KM), and then was followed by its enhanced version called EKM. Then continuous versions were called CKM and CEKM, and there were variations of this and also other types of variations that eliminate the type-reduction process reducing the computational cost to a Type-1 defuzzification, such as the Nie-Tan versions and similar enhancements. In this work we analyzed and proposed a variant of CEKM by viewing this process as solving a root-finding problem, in this way taking advantage of existing numerical methods to solve the type-reduction problem, the main objective being eliminating the type-reduction process and also providing a continuous solution of the defuzzification. [ABSTRACT FROM AUTHOR]

A comparison of different T-norms and S-norms for interval type-2 fuzzy number weights is proposed in this work. The interval type-2 fuzzy number weights are used in a neural network with an interval backpropagation learning enhanced method for weight adjustment. Results of experiments and a comparative research between traditional neural networks and the neural network with interval type-2 fuzzy number weights with different T-norms and S-norms are presented to demonstrate the benefits of the proposed approach. In this research, the definitions of the lower and upper interval type-2 fuzzy numbers with random initial values are presented; this interval represents the footprint of uncertainty (FOU). The proposed work is based on recent works that have considered the adaptation of weights using type-2 fuzzy numbers. To confirm the efficiency of the proposed method, a case of data prediction is applied, in particular for the Mackey-Glass time series (for = 17). Noise of Gaussian type was applied to the testing data of the Mackey-Glass time series to demonstrate that the neural network using a interval type-2 fuzzy numbers method achieves a lower susceptibility to noise than other methods. [ABSTRACT FROM AUTHOR]

This paper presents a new general type-2 fuzzy logic method for edge detection applied to color format images. The proposed algorithm combines the methodology based on the image gradients and general type-2 fuzzy logic theory to provide a powerful edge detection method. General type-2 fuzzy inference systems are approximated using the α-planes approach. The edge detection method is tested on a database of color images with the idea of illustrating the advantage of applying the fuzzy edge detection approach on color images against grayscale format images, and also when the images are corrupted by noise. This paper compares the proposed method based on general type-2 fuzzy logic with other edge detection algorithms, such as ones based on type-1 and interval type-2 fuzzy systems. Simulation results show that edge detection based on a general type-2 fuzzy system outperforms the other methods because of its ability to handle the intrinsic uncertainty in this problem. [ABSTRACT FROM AUTHOR]

In this paper a new optimization method for modular neural network (MNN) design using granular computing and a firefly algorithm is proposed. This method is tested with human recognition based on benchmark ear and face databases to verify the effectiveness and the advantages of the proposed method. Nowadays, there are a great number of optimization techniques, but it is very important to find an appropriate one that allows for better results depending on the area of application. For this reason, a comparison of techniques is presented in this paper, where the results achieved for ear recognition and face recognition by the proposed method are compared against a hierarchical genetic algorithm in order to know which of these techniques provides better results when a modular granular neural network is optimized and applied to pattern recognition mainly for human recognition. The parameters of modular neural networks that are being optimized are: the number of modules (or sub granules), percentage of data for the training phase, learning algorithm, goal error, number of hidden layers and their number of neurons. Simulation results show that the proposed approach combining the firefly algorithm with granular computing provides very good results in optimal design of MNNs. [ABSTRACT FROM AUTHOR]

A grey wolf optimizer for modular neural network (MNN) with a granular approach is proposed. The proposed method performs optimal granulation of data and design of modular neural networks architectures to perform human recognition, and to prove its effectiveness benchmark databases of ear, iris, and face biometric measures are used to perform tests and comparisons against other works. The design of a modular granular neural network (MGNN) consists in finding optimal parameters of its architecture; these parameters are the number of subgranules, percentage of data for the training phase, learning algorithm, goal error, number of hidden layers, and their number of neurons. Nowadays, there is a great variety of approaches and new techniques within the evolutionary computing area, and these approaches and techniques have emerged to help find optimal solutions to problems or models and bioinspired algorithms are part of this area. In this work a grey wolf optimizer is proposed for the design of modular granular neural networks, and the results are compared against a genetic algorithm and a firefly algorithm in order to know which of these techniques provides better results when applied to human recognition. [ABSTRACT FROM AUTHOR]

Edge detectors have traditionally been an essential part of many computer vision systems. There are different methods that have been proposed for improving edge detection in real images. This paper proposes an edge detection method based on the Sobel technique and generalized type-2 fuzzy logic systems. To limit the complexity of handling generalized type-2 fuzzy logic, the theory of $$\alpha $$ -planes is used. Simulation results are obtained with the Sobel operator (without fuzzy logic), then with a type-1 fuzzy logic system (T1FLS), an interval type-2 fuzzy logic system (IT2FLS) and with a generalized type-2 fuzzy logic system (GT2FLS). The proposed generalized type-2 fuzzy edge detection method is tested with synthetic images with promising results. To illustrate the advantages of using generalized type-2 fuzzy logic in combination with the Sobel operator, the figure of merit of Pratt measure is applied to measure the accuracy of the edge detection process. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to present a hybrid learning method for interval A2-C1 type-1 non-singleton type-2 TSK fuzzy logic system that uses the recursive orthogonal least-squares algorithm to tune the type-1 consequent parameters, and the back-propagation algorithm to tune the interval type-2 antecedent parameters. Based on the combination of these two training algorithms the new hybrid learning method changes the interval type-2 fuzzy model parameters adaptively and minimizes the proposed error function as the new type-1 non-singleton input-output data pairs are processed. Its antecedent sets are interval type-2 fuzzy sets, its consequent sets are type-1 fuzzy sets, and its inputs are type-1 non-singleton fuzzy numbers with uncertain standard deviations. Comparison with the non-hybrid interval A2-C1 type-1 non-singleton type-2 Takagi-Sugeno-Kang fuzzy logic system that only uses the back-propagation algorithm for both antecedent and consequent parameter's adaptation demonstrates that the proposed hybrid algorithm is a well-performing nonlinear adaptation that enables the interval type-2 fuzzy model to optimally match the nonlinear behavior of the process. The application of the interval type-2 fuzzy logic as adaptable predictor using the proposed hybrid learning method was constructed for the modeling and prediction of the transfer bar surface temperature in an industrial hot strip mill facility. Experimental results demonstrated that this method improves the temperature prediction performance of the interval A2-C1 type-1 non-singleton type-2 Takagi-Sugeno-Kang fuzzy logic system. [ABSTRACT FROM AUTHOR]

Highlights: [•] A survey of nature-inspired optimization algorithms with fuzzy logic is presented. [•] A review is made of the optimization techniques in which fuzzy logic is used for parameter adaptation. [•] The review covers Particle Swarm Optimization, Gravitational Search Algorithm, and Ant Colony Optimization. [Copyright &y& Elsevier]

This paper describes an optimization of interval type-2 and type-1 fuzzy integrators in ensembles of ANFIS models with genetic algorithms (GAs), this with emphasis on its application to the prediction of chaotic time series, where the goal is to minimize the prediction error. The Mackey-Glass time series was considered to validate the proposed ensemble approach. The methods used for the integration of the ensembles of ANFIS are: type-1 and interval type-2 Mamdani fuzzy inference systems (FIS). Genetic Algorithms are used for optimization of the membership function parameters of the FIS in each integrator. In the experiments we changed the type of the membership functions for each type-1 and interval type-2 FIS, thereby increasing the complexity of the training, The output (Forecast) generated by each integrator is calculated with the RMSE (root mean square error) to minimize the prediction error, therefore we compared the performance obtained by each FIS. [ABSTRACT FROM AUTHOR]

Abstract: A new model of a modular neural network (MNN) using a granular approach and its optimization with hierarchical genetic algorithms is proposed in this paper. This model can be used in different areas of application, such as human recognition and time series prediction. In this paper, the proposed model is tested for human recognition based on the ear biometric measure. A benchmark database of the ear biometric measure is used to illustrate the advantages of the proposed model over existing approaches in the literature. The proposed method consists in the optimization of the design parameters of a modular neural network, such as number of modules, percentage of data for the training phase, goal error, learning algorithm, number of hidden layers and their respective number of neurons. This method also finds out the amount of and the specific data that can be used for the training phase based on the complexity of the problem. [Copyright &y& Elsevier]

Highlights: [•] A review of type-2 fuzzy logic applications in pattern recognition and classification problems is presented. [•] Type-2 fuzzy logic has gained popularity in a wide range of applications. [•] A representative review of the most successful applications of type-2 fuzzy logic in these fields is presented. [ABSTRACT FROM AUTHOR]

Abstract: In this paper a new method for dynamic parameter adaptation in particle swarm optimization (PSO) is proposed. PSO is a metaheuristic inspired in social behaviors, which is very useful in optimization problems. In this paper we propose an improvement to the convergence and diversity of the swarm in PSO using fuzzy logic. Simulation results show that the proposed approach improves the performance of PSO. First, benchmark mathematical functions are used to illustrate the feasibility of the proposed approach. Then a set of classification problems are used to show the potential applicability of the fuzzy parameter adaptation of PSO. [Copyright &y& Elsevier]