General Type-2 Fuzzy Systems Research Articles

A New Hybrid Approach for Clustering, Classification, and Prediction of World Development Indicators Combining General Type-2 Fuzzy Systems and Neural Networks

A New Hybrid Approach for Clustering, Classification, and Prediction of World Development Indicators Combining General Type-2 Fuzzy Systems and Neural Networks

Interval Type-3 Fuzzy Inference System Design for Medical Classification Using Genetic Algorithms

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.

Enhancing Dynamic Parameter Adaptation in the Bird Swarm Algorithm Using General Type-2 Fuzzy Analysis and Mathematical Functions

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.

Shadowed Type-2 Fuzzy Sets in Dynamic Parameter Adaption in Cuckoo Search and Flower Pollination Algorithms for Optimal Design of Fuzzy Fault-Tolerant Controllers

In recent, various metaheuristic algorithms have shown significant results in control engineering problems; moreover, fuzzy sets (FSs) and theories were frequently used for dynamic parameter adaption in metaheuristic algorithms. The primary reason for this is that fuzzy inference system (FISs) can be designed using human knowledge, allowing for intelligent dynamic adaptations of metaheuristic parameters. To accomplish these tasks, we proposed shadowed type-2 fuzzy inference systems (ST2FISs) for two metaheuristic algorithms, namely cuckoo search (CS) and flower pollination (FP). Furthermore, with the advent of shadowed type-2 fuzzy logic, the abilities of uncertainty handling offer an appealing improved performance for dynamic parameter adaptation in metaheuristic methods; moreover, the use of ST2FISs has been shown in recent works to provide better results than type-1 fuzzy inference systems (T1FISs). As a result, ST2FISs are proposed for adjusting the Lèvy flight (P) and switching probability (P′) parameters in the original cuckoo search (CS) and flower pollination (FP) algorithms, respectively. Our approach investigated trapezoidal types of membership functions (MFs), such as ST2FSs. The proposed method was used to optimize the precursors and implications of a two-tank non-interacting conical frustum tank level (TTNCFTL) process using an interval type-2 fuzzy controller (IT2FLC). To ensure that the implementation is efficient compared with the original CS and FP algorithms, simulation results were obtained without and then with uncertainty in the main actuator (CV1) and system component (leak) at the bottom of frustum tank two of the TTNCFLT process. In addition, the statistical z-test and non-parametric Friedman test are performed to analyze and deliver the findings for the best metaheuristic algorithm. The reported findings highlight the benefits of employing this approach over traditional general type-2 fuzzy inference systems since we get superior performance in the majority of cases while using minimal computational resources.

An improved type-reduction algorithm for general type-2 fuzzy sets

General type-2 fuzzy systems (GT2 FLSs) provide a more flexible way of overcoming an uncertain lack of uniformity in different applications. Centroid type reduction is one of the major component of GT2 FLSs, it is currently one of the key factors restricting GT2 FLSs efficiency. This paper proposes a novel and efficient method for centroid type reduction. The method is based on α-plane representation, where a general type-2 fuzzy set is decomposing into a series of α planes. The centroid for each plane is the calculated, layer by layer, from the top down, until the α=0 plane is reached. In each α plane, a centroid type reduction calculation is performed using an improved enhanced opposite direction searching algorithm (IEODS). Finally, the centroids obtained for each plane are aggregated to obtain a type-1 fuzzy set, which form the centroid of general type-2 fuzzy set. Experiments show that this method results in less calculation time and fewer iterations than other α-plane representation-based reduction methods. By providing more efficient type reduction, the method improves the applicability of general type-2 fuzzy systems in more complex environments and embedded platforms, thereby enhancing their scope for future development.

Differential Evolution with Shadowed and General Type-2 Fuzzy Systems for Dynamic Parameter Adaptation in Optimal Design of Fuzzy Controllers

This work is mainly focused on improving the differential evolution algorithm with the utilization of shadowed and general type 2 fuzzy systems to dynamically adapt one of the parameters of the evolutionary method. Previously, we have worked with both kinds of fuzzy systems in different types of benchmark problems and it has been found that the use of fuzzy logic in combination with the differential evolution algorithm gives good results. In some of the studies, it is clearly shown that, when compared to other algorithms, our methodology turns out to be statistically better. In this case, the mutation parameter is dynamically moved during the evolution process by using shadowed and general type-2 fuzzy systems. The main contribution of this work is the ability to determine, through experimentation in a benchmark control problem, which of the two kinds of the used fuzzy systems has better results when combined with the differential evolution algorithm. This is because there are no similar works to our proposal in which shadowed and general type 2 fuzzy systems are used and compared. Moreover, to validate the performance of both fuzzy systems, a noise level is used in the controller, which simulates the disturbances that may exist in the real world and is thus able to validate statistically if there are significant differences between shadowed and general type 2 fuzzy systems.

A Novel Fractional-Order Multiple-Model Type-3 Fuzzy Control for Nonlinear Systems with Unmodeled Dynamics

In this paper, a novel control approach is proposed for a class of uncertain nonlinear system with unmodeled dynamics. Each output of the system is modeled by several first-order dynamic fractional-order fuzzy systems. The best dynamic model is selected at a period of time and the control signal is designed based on this model. The dynamic fractional-order models are based on the special case of general type-2 fuzzy systems which are called interval type-3 fuzzy logic systems (IT3FLSs). The adaptation laws for the consequent parameters of IT3FLSs are derived through stability analysis of the fractional-order systems based on the linear matrix inequality approach. The effectiveness of the proposed scheme is verified by normal simulation on the hyperchaotic Lorenz system with unmodeled dynamics, real-time simulation on the chaotic model of the brushless DC motors using Arduino boards and experimental examination on a heat transfer system with fully unknown dynamics.

An Efficient High-Order α-Plane Aggregation in General Type-2 Fuzzy Systems Using Newton–Cotes Rules

Nowadays, general type-2 fuzzy systems are an attractive alternative for non-linear control problems because they provide good robustness in real-world environments, where there exist many noise sources. This kind of fuzzy systems can have better performance in comparison to type-1 fuzzy systems as they offer uncertainty handling capabilities. However, one of the main problems in implementing general type-2 fuzzy systems is their elevated computational cost. The computational cost of a general type-2 fuzzy system depends on the representation that is used, for example, the α-planes representation consists on a discretization of general type-2 fuzzy systems into several horizontal slices called α-planes, then solving every α-plane as an interval type-2 fuzzy system and after that the integration of the results to approximate a general type-2 fuzzy system. The main contribution of this work is the proposed computational cost reduction of the α-planes representation by optimizing the α-planes integration process based on the composite Newton–Cotes rules. In this way, the number of α-planes required for a good approximation is reduced, and the computational cost is also reduced by introducing new equations for the α-planes aggregation. Finally, a systematic comparative analysis of the improvement offered by the proposed method with respect to the conventional approach is presented.

Comparative study of interval Type-2 and general Type-2 fuzzy systems in medical diagnosis

Nowadays, computer science has the ability of assisting experts in different application areas. Recently there has been increasing attention in the health area, and there exist different approaches based on artificial intelligence that have been proposed in the diagnosis of several kinds of diseases. In particular, fuzzy systems have been successfully used as Diagnosis Systems, in this way helping doctors to realize a faster and more accurate diagnosis. However, with the emergence of Type-2 Fuzzy Systems, there have been important improvements in handling the uncertainty with respect to traditional Fuzzy Systems (now called Type-1 Fuzzy Systems) in different kinds of problems. In the present paper, a new approach to Fuzzy Diagnosis based on Type-2 Fuzzy Systems is proposed and compared with respect to Type-1 Fuzzy Systems on a set of diagnosis problems, in order to evaluate the relevance of the uncertainty handling in this kind of problems. On the other hand, the paper is also aiming at observing the accuracy behavior in Fuzzy Diagnosis Systems by changing the uncertainty level in the models. Finally, a comparison of Interval Type-2 Fuzzy Systems with respect to General Type-2 Fuzzy Systems for a set of diagnosis problems is presented.

An approach for non-singleton generalized Type-2 fuzzy classifiers

In recent years, successful applications of singleton fuzzy inference systems have been made in a plethora of different kinds of problems, for example in the areas of control, digital image processing, time series prediction, fault detection and classification. However, there exists another relatively less explored approach, which is the use of non-singleton fuzzy inference systems. This approach offers an interesting way for handling uncertainty in complex problems by considering inputs with uncertainty, while the conventional Fuzzy Systems have their inputs with crisp values (singleton systems). Non-singleton systems have as inputs Type-1 membership functions, and this difference increases the complexity of the fuzzification, but provides the systems with additional non-linearities and robustness. The main limitations of using a non-singleton fuzzy inference system is that it requires an additional computational overhead and are usually more difficult to apply in some problems. Based on these limitations, we propose in this work an approach for efficiently processing non-singleton fuzzy systems. To verify the advantages of the proposed approach we consider the case of general type-2 fuzzy systems with non-singleton inputs and their application in the classification area. The main contribution of the paper is the implementation of non-singleton General Type-2 Fuzzy Inference Systems for the classification task, aiming at analyzing its potential advantage in classification problems. In the present paper we propose that the use of non-singleton inputs in Type-2 Fuzzy Classifiers can improve the classification rate and based on the realized experiments we can observe that General Type-2 Fuzzy Classifiers, but with non-singleton fuzzification, obtain better results in comparison with respect to their singleton counterparts.

Developing an online general type-2 fuzzy classifier using evolving type-1 rules

General type-2 fuzzy systems have been shown to handle more levels of uncertainty present in the majority of real-world applications. Nevertheless, the rapid growth of information generation does not allow utilizing general type-2 models for their complex learning process. This paper introduces a novel online general type-2 fuzzy classifier (called oGT2FC). It aims to reduce the computations needed to get the type-2 fuzzy sets. As in most online and evolving fuzzy schemes, the initial rule-base in oGT2FC is empty, and then the fuzzy rules are generated in completely online manner; without storing the samples. To specify the type-2 fuzzy sets, oGT2FC employs some experts' opinions, drawn from training data, to generate automatically some diverse type-1 fuzzy rule-bases. These type-1 rule-bases are updated/evolved by incoming new samples and are used to construct the general type-2 model. By defining a type-2 fuzzy set as the union of vertical slices, oGT2FC performs the type reduction in a fast and efficient manner. The efficiency of the proposed oGT2FC is assessed experimentally, using synthetic and real-world data streams, via comparing with other type-2 and type-1 evolving fuzzy classifiers as well as some state-of-the-art incremental algorithms. In addition, oGT2FC is compared against some fuzzy classifiers in its ability to model uncertainty.

Comparing the Performance Potentials of Interval and General Type-2 Rule-Based Fuzzy Systems in Terms of Sculpting the State Space

This paper provides application-independent perspectives on why improved performance usually occurs as one goes from an interval type-2 (IT2) fuzzy system to a general type-2 (GT2) fuzzy system. This is achieved by using the horizontal-slice representation of a GT2 fuzzy set and GT2 fuzzy system and by examining first- and second-order rule partitions as well as novelty partitions for the horizontal slices. It demonstrates that, for triangle and trapezoid secondary membership functions, the numbers of first- and second-order rule partitions are exactly the same for IT2 and GT2 fuzzy systems, but that a maximum amount of change always occurs in every second-order rule partition of a GT2 fuzzy system. This does not always occur in such partitions of an IT2 fuzzy system. Furthermore, when type reduction (TR) is used in a GT2 fuzzy system, the total number of novelty partitions is directly proportional to the number of horizontal slices; consequently, there are many more such partitions in a GT2 fuzzy system that uses TR than occur in an IT2 fuzzy system that also uses TR. It is the author's conjecture that it is the maximum changes that occur in every second-order rule partition, as well as the greater number of novelty partitions when TR is used, that provide a GT2 fuzzy system with the potential to outperform an IT2 fuzzy system.

Optimization of type-1, interval type-2 and general type-2 fuzzy inference systems using a hierarchical genetic algorithm for modular granular neural networks

In this paper, a new method for fuzzy inference system optimization is presented. The proposed method performs type-1, interval type-2 and general type-2 fuzzy inference systems design using a hierarchical genetic algorithm as optimization method. This method is an improvement of a fuzzy system optimization approach presented in previous works where only the optimization of type-1 and interval type-2 fuzzy inference systems was performed using a human recognition application. The human recognition is performed using three biometric measures namely iris, ear, and voice, where the main idea is to perform the combination of responses in the modular neural networks using an optimized fuzzy inference system to improve the final results without and with noisy conditions. The main contribution of the proposed method is an optimization able to select type of fuzzy logic, granulation of each fuzzy variable and fuzzy rules selection to design optimal fuzzy inference systems applied in combining modular neural networks responses. The results obtained show the effectiveness of the proposed method to design structures of fuzzy inference systems. Statistical comparisons are performed with previous results, where better results can be observed using the proposed method. The design of optimal structures of fuzzy inference systems include among other parameters; type of fuzzy logic (type-1, interval and general type-2 fuzzy logic), type of inference model (Mamdani model or Sugeno model), and consequents of the fuzzy if–then rules.

High order [formula omitted]-planes integration: A new approach to computational cost reduction of General Type-2 Fuzzy Systems

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.

A Novel Type-2 Fuzzy Logic for Improved Risk Analysis of Proton Exchange Membrane Fuel Cells in Marine Power Systems Application

A marine energy system, which is fundamentally not paired with electric grids, should work for an extended period with high reliability. To put it in another way, by employing electrical utilities on a ship, the electrical power demand has been increasing in recent years. Besides, fuel cells in marine power generation may reduce the loss of energy and weight in long cables and provide a platform such that each piece of marine equipment is supplied with its own isolated wire connection. Hence, fuel cells can be promising power generation equipment in the marine industry. Besides, failure modes and effects analysis (FMEA) is widely accepted throughout the industry as a valuable tool for identifying, ranking, and mitigating risks. The FMEA process can help to design safe hydrogen fueling stations. In this paper, a robust FMEA has been developed to identify the potentially hazardous conditions of the marine propulsion system by considering a general type-2 fuzzy logic set. The general type-2 fuzzy system is decomposed of several interval type-2 fuzzy logic systems to reduce the inherent highly computational burden of the general type-2 fuzzy systems. Linguistic rules are directly incorporated into the fuzzy system. Finally, the results demonstrate the success and effectiveness of the proposed approach in computing the risk priority number as compared to state-of-the-art methods.

A New Method for Parameterization of General Type-2 Fuzzy Sets

ABSTRACTIn this paper a new method for the parameterization of general type-2 fuzzy membership functions. The proposed method describes the methodology, equations and pseudo-code for building a set of general type-2 membership functions, which are a combination of two Gaussian-type primary membership functions (Gaussian with uncertain mean, and Gaussian with uncertain standard deviation), with multiple combinations of secondary membership functions (Gaussian, double Gaussian, general bell and trapezoidal). In addition, several application cases are used to illustrate the advantages of the proposed parameterization of general type-2 fuzzy sets; where the membership functions are designed using the parameterization approach and the general type-2 inference system is approximated using the α-planes theory. Simulation results illustrate that the parameterization offers an efficient way to represent these fuzzy sets. The main idea of the approach is to facilitate the use of general type-2 fuzzy systems in real world applications. The main contribution is a proposed new form of parameterizing general type-2 fuzzy sets that simplifies the efficient design of this type of sets.

Edge Detection Method Based on General Type-2 Fuzzy Logic Applied to Color Images

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.

A new load frequency control strategy for micro-grids with considering electrical vehicles

Owing to the intermittent nature of the renewable energies employed in smart grids, large frequency fluctuations occur when the load frequency control (LFC) capacity is not enough to compensate for the imbalance of generation and demand. This problem may become intensified when the system is working in an island operation mode. Meanwhile, electric vehicles (EVs) are growing in popularity, being used as dispersed energy storage units instead of small batteries in the systems. Accordingly, the vehicle-to-grid (V2G) power control can be applied to compensate for the inadequate LFC capacity and thereby to improve the frequency stability of smart grids, especially in the island operation mode. On the other hand, large scale and complex power systems encounter many different uncertainties. In order to handle these uncertainties, this study proposes a combination of the general type-2 fuzzy logic sets (GT2FLS) and the Modified Harmony Search Algorithm (MHSA) technique, as a novel heuristic algorithm, to adaptively tune the proportional-integral (PI) controller for LFC in islanded MicroGrids (MGs). Although implementing general type-2 fuzzy systems is generally computationally cumbersome, by using a recently introduced plane representation, GT2FLS can be regarded as a combination of several interval type-2 fuzzy logic systems (IT2FLS), each with its own corresponding α level and linguistic rules can directly be incorporated into the controller. This paper further presents a new modified optimization algorithm to tune the scaling factors and the membership functions of general type-2 fuzzy PI (GT2FPI) controller and thereby to minimize the frequency deviations of the MG system against load disturbances more effectively. To evaluate the efficiency of the proposed controller, the obtained results are compared with those of the proportional integral derivative (PID), Fuzzy-PID (FPID), and Interval Type II fuzzy based PI (IT2FPI) controllers, which are the most recent methods applied in this respect. Simulation results demonstrate the perfection and efficacy of proposed controller.

Speed control of electrical vehicles: a time‐varying proportional–integral controller‐based type‐2 fuzzy logic

The control of electrical vehicles (EVs) should be designed robustly and adaptively to improve the system on both dynamic and steady-state performances, because EV systems are basically time variant (e.g. the operation parameters of EV and the road condition are always varying) that make the operation of controlling an EV difficult. In this study, general type-2 fuzzy logic sets and the modified harmony search algorithm techniques for adaptive tuning of the most popular existing proportional–integral (PI) controller is integrated in order to address these uncertainties. Although it is computationally expensive to carry out general type-2 fuzzy systems, it can be examined as a composition of several interval type-2 fuzzy logic systems with a corresponding level of α for each by using a new plan which is presented, general type-2 fuzzy set. The controller uses the linguistic rules directly. The achieved results are compared with optimal fuzzy-PI controller and optimal interval type-2 fuzzy-PI controller results which are the most recent researches into in the present issue to evaluate the proficiency of the proposed controller. The simulation results demonstrate the successfulness and effectiveness of the proposed controller.

Direct adaptive general type‐2 fuzzy control for a class of uncertain non‐linear systems

In this study, a stable direct adaptive general type-2 fuzzy logic controller (DAG2FLC) is introduced for a class of non-linear systems. The proposed controller uses advantages of general type-2 fuzzy logic systems (GT2FLSs) in handling dynamic uncertainties to approximate unknown non-linear actions. Implementing general type-2 fuzzy systems is computationally costly; however, by using a recently introduced α-plane representation, a GT2FLS can be seen as composition of several interval type-2 fuzzy logic systems with a corresponding level of α for each. Linguistic rules are directly incorporated into the DAG2FLC controller and a H ∞ compensator is added to attenuate external disturbance and fuzzy approximation error. Also general type-2 fuzzy adaptation laws are derived using Lyapunov approach, and the stability of the closed-loop system has been proven by mathematical analysis. In order to evaluate the performance of the proposed controller, the results are compared with those obtained by direct adaptive type-1 fuzzy logic controller and a direct adaptive interval type-2 fuzzy logic controller, which are the latest researches in the problem in hand. The proposed controller is applied to a chaotic Gyro system as a case study. Simulation reveals the effectiveness of the proposed controller in presence of dynamic uncertainties and external disturbances.