Interval Type-2 Fuzzy System Research Articles

The integrated control strategy for interval Type-2 fuzzy logic power system stabilizer (IT2FLPSS) and compact digital fuzzy automatic voltage regulator (CDF-AVR) in electrical power system

The integrated control strategy for interval Type-2 fuzzy logic power system stabilizer (IT2FLPSS) and compact digital fuzzy automatic voltage regulator (CDF-AVR) in electrical power system

Finite-time stability and stabilization of interval type-2 fuzzy systems with time delay

Finite-time stability and stabilization of interval type-2 fuzzy systems with time delay

Optimal Design of Interval Type-2 Fuzzy Heart Rate Level Classification Systems Using the Bird Swarm Algorithm

In this paper, the optimal designs of type-1 and interval type-2 fuzzy systems for the classification of the heart rate level are presented. The contribution of this work is a proposed approach for achieving the optimal design of interval type-2 fuzzy systems for the classification of the heart rate in patients. The fuzzy rule base was designed based on the knowledge of experts. Optimization of the membership functions of the fuzzy systems is done in order to improve the classification rate and provide a more accurate diagnosis, and for this goal the Bird Swarm Algorithm was used. Two different type-1 fuzzy systems are designed and optimized, the first one with trapezoidal membership functions and the second with Gaussian membership functions. Once the best type-1 fuzzy systems have been obtained, these are considered as a basis for designing the interval type-2 fuzzy systems, where the footprint of uncertainty was optimized to find the optimal representation of uncertainty. After performing different tests with patients and comparing the classification rate of each fuzzy system, it is concluded that fuzzy systems with Gaussian membership functions provide a better classification than those designed with trapezoidal membership functions. Additionally, tests were performed with the Crow Search Algorithm to carry out a performance comparison, with Bird Swarm Algorithm being the one with the best results.

Event-based output tracking control for fuzzy networked control systems with network-induced delays

This paper investigates the problem of event-based output tracking control with network-induced time-varying delays for nonlinear networked control systems (NCSs) approximated by interval type-2 (IT2) fuzzy systems. The membership functions (MFs) with upper and lower bounds are utilized to capture the uncertainties in the nonlinear systems. A novel IT2 fuzzy controller is designed, where the premise variables and MFs are asynchronous and different from those of the fuzzy systems. It is shown that the proposed adaptive event-based control mechanism for IT2 fuzzy NCSs is effective to reduce the utilization of limited network resources. Finally, simulation examples are applied to show the advantages of the presented approach.

Event-Triggered Fault Detection Filter Design for Nonlinear Networked Systems

This paper investigates the problem of event-triggered fault detection (FD) filter design for nonlinear networked systems in the framework of interval type-2 fuzzy systems. In the system model, the parameter uncertainty is captured effectively by the membership functions (MFs) with upper and lower bounds. For reducing the utilization of limited communication bandwidth, an event-triggered communication mechanism is applied. A novel FD filter subject to event-triggered communication mechanism, data quantization, and communication delay is designed to generate a residual signal and detect system faults, where the premise variables are different from those of the system model. Consequently, the augmented FD system is with imperfectly matched MFs, which hampers the stability analysis and FD. To relax the stability analysis and achieve a better FD performance, the information of MFs and slack matrices are utilized in the stability analysis. Finally, two examples are employed to demonstrate the effectiveness of the proposed scheme.

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.

Dissipativity-based non-fragile sampled-data control design of interval type-2 fuzzy systems subject to random delays

This paper investigates the β-dissipativity-based reliable non-fragile sampled-data control problem for a class of interval type-2 (IT2) fuzzy systems. In particular, it is allowed to have randomly occurring time-varying delays in the controller design, which are modeled by Bernoulli distributed white noise sequences. Precisely, the IT2 fuzzy model and the non-fragile sampled-data controller are formulated by considering the mismatched membership functions. By constructing an appropriate Lyapunov–Krasovskii functional, a set of delay-dependent conditions is derived to guarantee that the closed-loop IT2 fuzzy system is strictly <Q,S,R>-β-dissipative. Moreover, the gain matrices of feedback reliable non-fragile sampled-data controller are derived in terms of linear matrix inequalities (LMIs), which can be solved by using existing LMI solvers. Two numerical examples are eventually given to illustrate the applicability and effectiveness of the proposed controller design technique.

Fuzzy numbers intuitionistic fuzzy descriptor systems

By using interval type-2 fuzzy systems and fuzzy numbers intuitionistic fuzzy sets, fuzzy numbers intuitionistic fuzzy descriptor systems are proposed in this paper. Their definition is given firstly, and the stability of this kind of systems is studied, the relations of interval type-2 fuzzy systems and T-S fuzzy descriptor systems and fuzzy numbers intuitionistic fuzzy descriptor systems are discussed. Fuzzy numbers intuitionistic fuzzy controller and the stability of fuzzy numbers intuitionistic fuzzy descriptor systems are deeply researched. Fuzzy numbers intuitionistic fuzzy descriptor systems can be better used to solve the problems of actual nonlinear control. Fuzzy numbers intuitionistic fuzzy descriptor systems will be a new research direction, and will become a universal method to solve practical problems. Finally, an example is given to illustrate effectiveness of the proposed method.

Explaining the Performance Potential of Rule-Based Fuzzy Systems as a &lt;italic&gt;Greater Sculpting of the State Space&lt;/italic&gt;

This paper provides some new and novel application-independent perspectives on why improved performance usually occurs as one goes from crisp, to type-1 (T1), and to interval type-2 (IT2) fuzzy systems, by introducing three kinds of partitions: (1) Uncertainty partitions that let us distinguish T1 fuzzy sets from crisp sets, and IT2 fuzzy sets from T1 fuzzy sets; (2) First-and second-order rule partitions that are direct results of uncertainty partitions, and are associated with the number of rules that fire in different regions of the state space, and, the changes in their mathematical formulae within those regions; and (3) Novelty partitions that can only occur in an IT2 fuzzy system that uses type-reduction. Rule and novelty partitions sculpt the state space into hyperrectangles within each of which resides a different nonlinear function. It is the author's conjecture that the greater sculpting of the state space by a T1 fuzzy system lets it outperform a crisp system, and the even greater sculpting of the state space by an IT2 fuzzy system lets it outperform a T1 fuzzy system. The latter can occur even when the T1 and IT2 fuzzy systems are described by the same number of parameters.

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.

Adaptive interval type-2 fuzzy dynamic surface control for uncertain nonlinear systems with unknown asymmetric dead-zone input

In this study, an adaptive dynamic surface control (DSC) scheme based on the interval type-2 fuzzy systems is proposed for uncertain nonlinear systems with unknown asymmetric dead-zone input and unknown control gains. The dead-zone nonlinearity is represented as a time-varying system with a bounded disturbance. The proposed approach invokes the interval type-2 fuzzy system to approximate the unknown nonlinear dynamics that appears in the virtual and actual control inputs. Also, it proposes adaptive terms to compensate the effect of the disturbance-like term in the dead-zone constraint. Then, the DSC scheme is designed based on the interval type-2 fuzzy system and the dead-zone model. Adaptive laws are derived to tune the consequent parameters of the interval type-2 fuzzy system and the dead-zone model. Stability analysis of the proposed scheme shows that all the signals of the closed-loop system are uniformly ultimately bounded and the tacking error can be made arbitrary small by proper selection of the design parameters. The proposed scheme avoids the “explosion of complexity” and “singularity” problems, simultaneously. Furthermore, it can compensate the effect of the dead-zone constraint without any need to its parameters. The simulation and comparison results are presented to demonstrate the effectiveness of the proposed control scheme.

State Feedback Control for Interval Type-2 Fuzzy Systems With Time-Varying Delay and Unreliable Communication Links

This study explores the stabilization problem of nonlinear systems subject to parameter uncertainties, time-varying delay, and data-packet dropouts. An interval type-2 Takagi-Sugenofuzzy model is employed to represent nonlinear systems subject to parameter uncertainties. The lower and upper membership functions of the system enable parameter uncertainties to be captured effectively. To enhance the flexibility of design, the proposed state feedback controller does not share the premise membership functions of the model. Unlike the majority of existing results, the present study simultaneously considers parameter uncertainties, time-varying delay, and data-packet dropouts in nonlinear control systems. A novel finite-sum inequality that includes well-known inequalities as special cases, is developed to derive new stability conditions in the form of linear matrix inequalities. Several examples of simulation are used to demonstrate the effectiveness of the proposed approach.

Retracted: Raw tumor MRI edge detection using interval Type 2 Fuzzy inference system and adaptive filter

Brain tumor edge detection system has been of great aid to the human physicians. This paper presents a comparison study of two of the most effective edge detection methods. The two methods are Interval type-2 fuzzy system and adaptive filter. The study is conducted using MATLAB. These edge detectors are tested on images added with 0.001 white Gaussian noise and salt and pepper noise. Main feature of the algorithm is that it has been designed by using the adaptive filter with IT2FLS which produces clearer and brighter edges as compared to conventional methods results found in the literature.

Type-2 Fuzzy Rule-Based Expert System for Diagnosis of Spinal Cord Disorders

The majority of people have experienced pain in their low back or neck in their lives. In this paper a type-2 fuzzy rule based expert system is presented for diagnosing the spinal cord disorders. The interval type-2 fuzzy logic system permits us to handle the high uncertainty of diagnosing the type of disorder and its severity. The spinal cord disorders are studied in five categories using historical data and clinical symptoms of the patients. The main novelty of this paper lies in presentation of the interval type-2 fuzzy hybrid rule-based system, which is a combination of the forward and backward chaining approaches in its inference engine and avoids unnecessary medical questions. Using of parametric operations for fuzzy calculations increases the robustness of the system and the compatibility of the diagnosis with a wide range of physicians’ diagnosis. The outputs of the system are comprised of type of disorder, location and severity as well as the necessity of taking a M.R. Image. A comparison of the performance of the developed system with the expert shows an acceptable accuracy of the system in diagnosing the disorders and determining the necessity of the M.R. Image.

Seismic control of buildings with active tuned mass damper through interval type-2 fuzzy logic controller including soil–structure interaction

This paper presents the application of interval type-2 fuzzy logic controller (IT2FLC) in ATMD for the response control of a building considering soil–structure interaction (SSI). One of the main constraints of the current fuzzy systems is their inability to consider uncertainty in fuzzy rules. Interval type-2 fuzzy systems have the ability to handle this deficiency. It also takes into account uncertainty in loading and structural behavior. To evaluate the influence of soil types on the behavior of structure, an 11-story shear building is used. This structure has been analyzed under the earthquake excitations recommended by the International Association of structural control (IASC) committee. The uncontrolled and controlled responses of structure with ATMD through IT2FLC are calculated with and without SSI effects. Numerical results indicate that SSI would significantly affect the structural response of the building. It is also found that when a structure is built on soft soil sites, the effectiveness of ATMD with IT2FLC in the case of suppressing the structural response is increased.

Interval Type-2 Mutual Subsethood Fuzzy Neural Inference System (IT2MSFuNIS)

This paper presents an interval type-2 mutual subsethood fuzzy neural inference system (IT2MSFuNIS). A mutual subsethood measure between two interval type-2 fuzzy sets (IT2 FS) has been derived and has been used in determining the similarity between the IT2 FS inputs and IT2 FS antecedents. The consequent weights are taken to be interval sets. The inputs to the system are fuzzified into IT2 FSs with Gaussian primary membership function having fixed center and uncertain variance. Aggregation of type-2 mutual subsethood based activation spreads is performed using product operator. The output is obtained using simplified type-reduction followed by defuzzification. The system learns using memetic procedure involving differential evolution for global search and gradient descent for local exploitation in solution space. The mathematical modeling and empirical studies of IT2MSFuNIS bring forth its efficacy in problems pertaining to function approximation, time-series prediction, control, and classification. Comparisons with other type-1 and type-2 neuro-fuzzy systems verify that IT2MSFuNIS compares excellently with other models with a performance better than most of them both in terms of total number of trainable parameters and result accuracy. Empirical studies indicate the intelligent decision making capability of the proposed model. The main contribution of this paper lies in the identification of mutual subsethood to find out the correlation between IT2 FSs and to find out its applicability in diverse application domains. The improved performance of the proposed method can be attributed to the better contrast handling capacity of mutual subsethood method and uncertainty handling capacity of IT2 FSs. The integration of mutual subsethood with interval type-2 fuzzy logic puts forth a novel model with various merits as demonstrated amply with the help of well-known problems reported in the literature.

Interval-valued fuzzy morphological associative memories: Some theoretical aspects and applications

Fuzzy morphological associative memories (FMAMs) are generalizations of many well-known fuzzy associative memory (FAM) models from the literature and have been employed to implement fuzzy rule-based systems. Inspired by the advent of type-2 fuzzy systems and in particular interval type-2 fuzzy systems, we present some theoretical foundations of interval-valued fuzzy morphological associative memories (IV-FMAMs), whose weight matrices can be constructed using representable interval-valued fuzzy operators, and we introduce a novel IV-FMAM approach towards interval type-2 fuzzy inference systems. The paper also includes some experimental results in non-linear function identification as well as time series prediction. These results are compared with the ones produced by some interval and general type-2 fuzzy models from the recent literature.

Novel event-triggered filter design for nonlinear networked control systems

This paper investigates the problem of event-triggered filter design for nonlinear networked control systems (NCSs) in the framework of interval type-2 (IT2) fuzzy systems. A novel IT2 fuzzy filter for ensuring asymptotic stability and H∞ performance of filtering error system is proposed, where the premise variables are different from those of the fuzzy model. Attention is focused on solving the problem of event-triggered filter design subject to parameter uncertainties, data quantization, and communication delay in a unified frame. It is shown that the proposed event-triggered filter design communication mechanism for IT2 fuzzy NCSs has the advantage of the existing event-triggered approaches to reduce the utilization of limited network resources and provides flexibility in balancing the tracking error and the utilization of network resources. Finally, simulation example is given to validate the advantages of the presented results.

A new type-2 fuzzy modelling and identification for electrophysiological signals: a comparison between PSO, BBO, FA and GA approaches

In this investigation a novel type-2 fuzzy model for electrophysiological signals is presented. It is based on interval type-2 fuzzy systems. This method can deal with the curve fitting and computational time problems of type-2 fuzzy systems. This approach will significantly reduce the number of type-2 fuzzy rules and simultaneously preserve the fitting quality. The proposed model comprises a parallel interconnection of two type-2 sub-fuzzy models. The first is the primary model, which represents an ordinary model with a low resolution for the electrophysiological signal under consideration, the second is a fuzzy sub-model called the error model, which represents uncertainty in the primary model. Identification is achieved by innovative metaheuristic optimisation algorithms. The method's effectiveness is evaluated through testing on synthetic and real ECG signals. In addition, a detailed comparative study with several benchmark methods will be given. Intensive computer experimentations confirm that the proposed method can significantly improve convergence and resolution.

Wave Forecasting using Meta-cognitive Interval Type-2 Fuzzy Inference System

Renewable energy is fast becoming a mainstay in today’s energy scenario. One of the important sources of renewable energy is the wave energy, in addition to wind, solar, tidal, etc. Wave prediction/forecasting is consequently essential in coastal and ocean engineering studies. However, it is difficult to predict wave parameters in long term and even in the short term due to its intermittent nature. This study aims to propose a solution to handle the issue using Interval type-2 fuzzy inference system, or IT2FIS. IT2FIS has been shown to be capable of handling uncertainty associated with the data. The proposed IT2FIS is a fuzzy neural network realizing Takagi-Sugeno-Kang inference mechanism employing meta-cognitive learning algorithm. The algorithm monitors knowledge in a sample to decide an appropriate learning strategy. Performance of the system is evaluated by studying significant wave heights obtained from buoys located in Singapore. The results compared with existing state-of-the art fuzzy inference system approaches clearly indicate the advantage of IT2FIS based wave prediction.