Interval Type-2 Research Articles

Comparative Study of Type-1 and Interval Type-2 Fuzzy Logic Systems in Parameter Adaptation for the Fuzzy Discrete Mycorrhiza Optimization Algorithm

The Fuzzy Discrete Mycorrhiza Optimization (FDMOA) Algorithm is a new hybrid optimization method using the Discrete Mycorrhiza Optimization Algorithm (DMOA) in combination with type-1 or interval type-2 fuzzy logic system. In this new research, when using T1FLS, membership functions are defined by type-1 fuzzy sets, which allows for a more flexible and natural representation of uncertain and imprecise data. This approach has been successfully applied to several optimization problems, such as in feature selection, image segmentation, and data clustering. On the other hand, when DMOA is using IT2FLS, membership functions are represented by interval type-2 fuzzy sets, which allows for a more robust and accurate representation of uncertainty. This approach has been shown to handle higher levels of uncertainty and noise in the input data and has been successfully applied to various optimization problems, including control systems, pattern recognition, and decision-making. Both DMOA using T1FLS and DMOA using IT2FLS have shown better performance than the original DMOA algorithm in many applications. The combination of DMOA with fuzzy logic systems provides a powerful and flexible optimization framework that can be adapted to various problem domains. In addition, these techniques have the potential to more efficiently and effectively solve real-world problems.

Outlier-resistant observer-based control for interval type-2 T-S fuzzy systems under adaptive event-triggered protocols

This paper is concerned with the outlier-resistant observer-based control problem for a class of interval type-2 (IT2) Takagi–Sugeno (T-S) fuzzy systems under adaptive event-triggered protocol (AETP). To improve the efficiency of resource utilization, AETP is mainly through an adjustable threshold parameter to dynamically schedule the data transmission, which occurs in the sensor-to-controller channel. In order to resist the abnormal measurement values, an output saturation composition is constructed in the observer. With the aid of Lyapunov theory, sufficient conditions are obtained to ensure the desired performance. Furthermore, the desired controller is designed for a class of IT2 T-S fuzzy systems. The combination of orthogonal decomposition and linear matrix inequalities is implemented to deal with the nonlinear coupling terms in the gain solving process. Finally, a numerical example is employed to justify the practicality and effectiveness of the proposed control scheme.

Self-Organizing Interval Type-2 Fuzzy Neural Network Compensation Control Based on Real-Time Data Information Entropy and Its Application in n-DOF Manipulator.

In order to solve the high-precision motion control problem of the n-degree-of-freedom (n-DOF) manipulator driven by large amount of real-time data, a motion control algorithm based on self-organizing interval type-2 fuzzy neural network error compensation (SOT2-FNNEC) is proposed. The proposed control framework can effectively suppress various types of interference such as base jitter, signal interference, time delay, etc., during the movement of the manipulator. The fuzzy neural network structure and self-organization method are used to realize the online self-organization of fuzzy rules based on control data. The stability of the closed-loop control systems are proved by Lyapunov stability theory. Simulations show that the algorithm is superior to a self-organizing fuzzy error compensation network and conventional sliding mode variable structure control methods in control performance.

Probabilistic-constrained control of interval type-2 T–S fuzzy systems under the multi-node round-robin scheduling protocol

This work concentrates on the control design of interval type-2 (IT2) T–S fuzzy systems under probabilistic saturation constraints. The actual control signals are allowed to exceed some preset thresholds with a certain frequency. Meanwhile, the sensors are governed by the multi-node round-robin scheduling protocol, which permits more than one sensors to transmit their information at every moment. The main objective is to synthesize a fuzzy controller such that the closed-loop system is locally stochastically stable under probabilistic saturated constraints and the multi-node round-robin scheduling protocol. To this end, the probabilistic saturation constraints are characterized by a Bernoulli-distributed stochastic process, and the received state at the controller side is formulated based on an updating rule and a compensation strategy. By constructing new membership functions, a token-dependent control law is subsequently designed. The stability analysis is facilitated by a modified sector condition dealing with the saturation nonlinearities. With suitable selection of initial states, sufficient conditions are derived to achieve the local stochastic stability of the closed-loop IT2 T–S fuzzy system. A larger domain of stochastic stability can be obtained via a searching algorithm. Finally, the proposed method is illustrated via a simulation example.

Multiobjective Optimization Design of Interpretable Evolutionary Fuzzy Systems With Type Self-Organizing Learning of Fuzzy Sets

This paper proposes a new multiobjective optimization approach for designing a self-generated interpretable fuzzy logic system (FLS). The types of fuzzy sets can be constructed automatically by self-organizing method, so as to form a hybrid fuzzy system. Different from the existing evolutionary type-1 fuzzy system, which is full of type-1 fuzzy sets, and the evolutionary interval type-2 fuzzy system, which is full of interval type-2 fuzzy sets, there are both type-1 fuzzy sets and interval type-2 fuzzy sets in the hybrid fuzzy system. A new transparency-oriented objective function is defined, and the constraint of the footprint of uncertainty (FOU) of the interval type-2 (IT2) fuzzy set (FS) is considered for the first time. A new FS merging criterion focusing on the proximity of the cores of fuzzy sets is proposed, which is easy to calculate and maintains the characteristics of classical similarity measures. Combined with the new merging criterion, the online cluster and fuzzy set updating (OCFU) algorithm is employed to initialize the reference rule base and the type of fuzzy sets, as it is assumed that no training data are collected in advance. Based on the reference rule base, the advanced multiobjective front-guided continuous ant colony optimization (AMO-FCACO) algorithm is introduced to optimize all the free parameters of the FLS. With the operation mentioned above, the self-generated FLSs achieve a good balance between interpretability and performance. The effectiveness of the proposed method is verified by three nonlinear system tracking problems.

Optimization the reliability of emergency safety barriers based on the subjective safety analysis and evidential reasoning theory. Case study

PurposeThis study aims to improve the reliability of emergency safety barriers by using the subjective safety analysis based on evidential reasoning theory in order to develop on a framework for optimizing the reliability of emergency safety barriers.Design/methodology/approachThe emergency event tree analysis is combined with an interval type-2 fuzzy-set and analytic hierarchy process (AHP) method. In order to the quantitative data is not available, this study based on interval type2 fuzzy set theory, trapezoidal fuzzy numbers describe the expert's imprecise uncertainty about the fuzzy failure probability of emergency safety barriers related to the liquefied petroleum gas storage prevent. Fuzzy fault tree analysis and fuzzy ordered weighted average aggregation are used to address uncertainties in emergency safety barrier reliability assessment. In addition, a critical analysis and some corrective actions are suggested to identify weak points in emergency safety barriers. Therefore, a framework decisions are proposed to optimize and improve safety barrier reliability. Decision-making in this framework uses evidential reasoning theory to identify corrective actions that can optimize reliability based on subjective safety analysis.FindingsA real case study of a liquefied petroleum gas storage in Algeria is presented to demonstrate the effectiveness of the proposed methodology. The results show that the proposed methodology provides the possibility to evaluate the values of the fuzzy failure probability of emergency safety barriers. In addition, the fuzzy failure probabilities using the fuzzy type-2 AHP method are the most reliable and accurate. As a result, the improved fault tree analysis can estimate uncertain expert opinion weights, identify and evaluate failure probability values for critical basic event. Therefore, suggestions for corrective measures to reduce the failure probability of the fire-fighting system are provided. The obtained results show that of the ten proposed corrective actions, the corrective action “use of periodic maintenance tests” prioritizes reliability, optimization and improvement of safety procedures.Research limitations/implicationsThis study helps to determine the safest and most reliable corrective measures to improve the reliability of safety barriers. In addition, it also helps to protect people inside and outside the company from all kinds of major industrial accidents. Among the limitations of this study is that the cost of corrective actions is not taken into account.Originality/valueOur contribution is to propose an integrated approach that uses interval type-2 fuzzy sets and AHP method and emergency event tree analysis to handle uncertainty in the failure probability assessment of emergency safety barriers. In addition, the integration of fault tree analysis and fuzzy ordered averaging aggregation helps to improve the reliability of the fire-fighting system and optimize the corrective actions that can improve the safety practices in liquefied petroleum gas storage tanks.

Ball and Beam Control: Evaluating Type-1 and Interval Type-2 Fuzzy Techniques with Root Locus Optimization

This study evaluates the performance of three control systems, namely the root locus method, type-1 Mamdani fuzzy logic system (FLS), and interval type-2 Mamdani FLS, in noise-free and noisy ball and beam systems. The main contribution of this study is enabling improved design and implementation of control systems in real-world applications by offering a comprehensive understanding of each control system's performance. The methodology involves conducting four tests focusing on various input types, including a 0.8-meter step input and sine wave function, and assessing the presence of noise in the system. The performance of each control system is analyzed using parameters such as rise time, setting time, and percentage overshoot, with the interval type-2 Mamdani FLS further examined by varying footprint of uncertainty values. Results from noise-free tests reveal that the root locus method has shorter rise and setting times, but a higher percentage overshoot compared to the type-1 Mamdani FLS and type-2 Mamdani FLS. In noisy environments, the type-2 Mamdani FLS with varying Footprint of Uncertainty values outperforms the type-1 Mamdani FLS with reduced rise time, setting time, and percentage overshoot. The root locus method shows a significantly higher percentage overshoot in noisy conditions compared to the other two control systems. In conclusion, the type-2 Mamdani FLS control system demonstrates superior capability under changing conditions compared to the type-1 Mamdani FLS, with its performance varying based on footprint of uncertainty values. This study highlights the importance of selecting the appropriate control system depending on specific needs and environmental factors.

Event-Triggered Extended Dissipativity Fuzzy Filter Design for Nonlinear Markovian Switching Systems against Deception Attacks

This article is concerned with the adaptive-event-triggered filtering problem as it relates to a class of nonlinear discrete-time systems characterized by interval Type-2 fuzzy models. The system under investigation is susceptible to Markovian switching and deception attacks. It is proposed to implement an improved event-triggering mechanism to reduce the unnecessary signal transmissions on the communication channel and formulate the extended dissipativity specification to quantify the transient dynamics of filtering errors. By resorting to the linear matrix inequality approach and using the information on upper and lower membership functions, stochastic analysis establishes sufficient conditions for the existence of the desired filter, ensuring the mean-squared stability and extended dissipativity of the augmented filtering system. Further, an optimization-based algorithm (PSO) is proposed for computing filter gains at an optimal level of performance. The developed scheme was finally tested through experimental numerical illustrations based on a single-link robot arm and a lower limbs system.

Application of interval type-2 fuzzy logic and type-1 fuzzy logic-based approaches to social networks for spam detection with combined feature capabilities.

Social networks are large platforms that allow their users to interact with each other on the Internet. Today, the widespread use of social networks has made them vulnerable to malicious use through different methods such as fake accounts and spam. As a result, many social network users are exposed to the harmful effects of spam accounts created by malicious people. Although Twitter, one of the most popular social networking platforms, uses spam filters to protect its users from the harmful effects of spam, these filters are insufficient to detect spam accounts that exhibit new methods and behaviours. That's why on social networking platforms like Twitter, it has become a necessity to use robust and more dynamic methods to detect spam accounts. Fuzzy logic (FL) based approaches, as they are the models such that generate results by interpreting the data obtained based on heuristics viewpoint according to past experiences, they can provide robust and dynamic solutions in spam detection, as in many application areas. For this purpose, a data set was created by collecting data on the twitter platform for spam detection. In the study, fuzzy logic-based classification approaches are suggested for spam detection. In the first stage of the proposed method, a data set with extracted attributes was obtained by applying normalization and crowdsourcing approaches to the raw data obtained from Twitter. In the next stage, as a process of the data preprocessing step, six attributes in the binary form in the data set were subjected to a rating-based transformation and combined with the other real-valued attribute to create a database to be used in spam detection. Classification process inputs were obtained by applying the fisher-score method, one of the commonly used filter-based methods, to the data set obtained in the second stage. In the last stage, the data were classified based on FL based approaches according to the obtained inputs. As FL approaches, four different Mamdani and Sugeno fuzzy inference systems based on interval type-1 and Interval Type-2 were used. Finally, in the classification phase, four different machine learning (ML) approaches including support vector machine (SVM), Bayesian point machine (BPM), logistic regression (LR) and average perceptron (Avr Prc) methods were used to test the effectiveness of these approaches in detecting spam. Experimental results were obtained by applying different FL and ML based approaches on the data set created in the study. As a result of the experiments, the Interval Type-2 Mamdani fuzzy inference system (IT2M-FIS) provided the highest performance with an accuracy of 0.955, a recall of 0.967, an F-score 0.962 and an area under the curve (AUC) of 0.971. However, it has been observed that FL-based spam models have a higher performance than ML-based spam models in terms of metrics including accuracy, recall, F-score and AUC values.

Interval type-2 fuzzy controller-based power quality enhancement in HSES grid-Integrated scheme

In the case of hybrid sustainable energy power systems made up of Solar Photovoltaic, wind, and an integrated energy storing system connected to a grid network, this research suggests a better control technique for optimal Power Quality improvement. The Unified Power Quality Conditioner with Real and Reactive Power are built-in with the proposed Hybrid Sustainable Energy Systems, and they include Type-1 and Interval Type-2 Fuzzy-based controllers. The main objective is to simultaneously control voltages while minimizing power losses and Total Harmonic Distortion. The Unified Power Quality Conditioner is utilized to reduce Power Quality concerns such as sag, swell, real power, reactive power, and harmonic distortion related to voltage/current by utilizing a proposed controller. The innovative method is displayed in various ways, such as simultaneous PQ replenishment and RES power injections, RESP > 0, and RESP = 0. In addition, the recommended methodology outperforms earlier literature approaches, such as PID controllers. The system is built on the MATLAB Simulink platform, where various performance studies are conducted.

Fuzzy Hidden Markov Model Using Aggregation Operators

The Fuzzy Markov Model (FMM) is a fascinating domain for dealing with ambiguity in real-world scenarios. In type 2 fuzzy set (T2F), it has an uncertainty footprint, and the region circumscribed by the lower and upper interval membership functions is uncertain. In fuzzy sets, Triangular norms (t-norms) are a valuable tool for understanding the conjunction in fuzzy logic and, as a result, determining where fuzzy sets intersect. Norms and conforms in Triangular operations that generalize logical conjunction and disjunction. They also provide a natural explanation for the conjunction and disjunction in mathematical fuzzy logic semantics. Fuzzy Frank Triangular Norms have been used to verify this t-norm as there are many of them the aggregation qualities of Trapezoidal Interval Type-2 numbers (TpIT2FNs) because triangular norm meets the compatibility with Frank norms. Frank triangular norms provide more flexibility and robustness this requires more justification in the information fusion process than other triangular norms. Previous works on not concentrate on Frank’s norms. Other Aggregation works on norms that are not flexible to get the solution. Because of that, the Frank norms are used for the hidden Markov model. We've also used them in the Viterbi method with TpIT2FNs for Fuzzy Hidden Markov Model in the staff selection process.

Interval Type-2 Fuzzy Risk Evaluation and Prevention for Parallel Breast Cancer Treatment System

Breast cancer (BC) seriously threatens women’s health. The establishment of a risk evaluation model cancer is conducive to early screening and prevention of BC. In this article, a new method of the evaluation and the framework of prevention for BC are proposed by synthesizing interval type-2 fuzzy sets (IT2 FSs), two-level fuzzy comprehensive evaluation, and parallel control (Artificial societies, Computational experiments, and Parallel execution, ACP). At the same time, 12 risk factors were selected as indicators to evaluate the risk level of BC, and then, according to the evaluation results, the correspondingly prevention strategies and intervention measures for different risk levels were discussed. Then, the prevention strategies are analyzed and selected in the computational experiment module of the artificial system, and the patient indexes are monitored in real time by the parallel mechanism between the actual and the artificial system, to feedback, adjust, and optimize the prevention scheme in time. This parallel BC prevention process can achieve dynamic closed-loop control effects. A new effective way for BC prevention was presented, which is of great significance for reducing its incidence rate and developing new medical means.

Evaluation of the effects of blockchain technology characteristics on SCOR model supply chain performance measurement attributes using an integrated fuzzy MCDM methodology

ABSTRACT This research aims to investigate and identify the effects of blockchain technology (BT) characteristics on SCOR supply chain (SC) performance measurement attributes. To achieve this, initially, the importance weights of blockchain characteristics (BC) in the context of the SC are determined by using the Interval Type-2 Fuzzy AHP. Furthermore, in order to rank Supply Chain Operation Reference (SCOR) model SC performance measurement attributes, the Interval Type-2 Fuzzy TOPSIS method is used. As for the conclusion, this research signifies that decentralised, security, and immutability are among the top three in terms of importance weights for SC while the consensus is ranked last and as for BC, SCOR model SC performance measurement attributes are ranked as reliability, asset management efficiency, responsiveness, cost, and agility. This study and its outcomes may serve organisations that are striving to boost their SC performance by applying BT.

Uncertain project network analysis with fuzzy–PERT and Interval Type–2 fuzzy activity durations

Project network analysis is often subject to different uncertainties that can occur in real world scenarios. These uncertainties are not always measurable which makes its statistical estimation hard, so the use of third party information coming from experts is useful to provide an estimation of activity durations of the project. Projects usually have multiple experts who provide different estimates of their perceptions about activity durations which can be represented as Type-2 fuzzy sets in cases where experts do not agree on their estimates. Such disagreement/ambiguitites can be either expressed with Interval Type-2 fuzzy numbers or the proposed fuzzy-PERT set which is an extension of the classical PERT distribution to a fuzzy environment. To do so, a mathematical formulation of the fuzzy problem is presented, two solution methods are described and two illustrative examples are solved.

Adaptive Event-Triggered Interval Type-2 T-S Fuzzy Control for Lateral Dynamic Stabilization of AEVs With Intermittent Measurements and Actuator Failure

This article presents an adaptive event-triggered dynamic output feedback interval type-2 (IT-2) T-S fuzzy control method for autonomous electric vehicle systems. First, the IT-2 T-S fuzzy model is introduced to describe the nonlinear lateral dynamics of the vehicle systems. Second, a novel adaptive event-triggered strategy is designed to reduce the computational burden. Third, the phenomenon of intermittent measurements is depicted by the Bernoulli random distributed process, and the failure of the actuator is also included. According to the Lyapunov stability theory, an IT-2 T-S fuzzy dynamic output feedback controller (DOFC) is presented to ensure the random stability and performance of the vehicle systems. Finally, the effectiveness and real-time performance of the proposed control strategy are verified via numerical simulation and a hardware-in-the-loop (HIL) test platform.

Stochastic Data-Based Denial-of-Service Attack Strategy Design Against Remote State Estimation in Interval Type-2 T–S Fuzzy Systems

This article focuses on designing a novel stochastic data-based denial-of-service (DoS) attack strategy that can intercept measurements and reduce the quality of remote state estimation in interval type-2 (IT2) T–S fuzzy systems. The new proposed DoS attack strategy has two main characteristics. First different from most of the existing DoS models, it is data-based, which mainly attacks the packets playing important roles in the system performance. Therefore, compared with the existing indiscriminate DoS attack approaches, the data-based DoS attack is more intelligent and can cause larger disruptions. Second, the proposed attack strategy is random, which has better concealment than the periodic or consecutive DoS attack models. Then, by using a stochastic method, the relationship among attack effect, attack probability, and attack parameter are analyzed and shown in Theorem <xref ref-type="theorem" rid="theorem9" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</xref> . Furthermore, if the attacks are energy-constrained, the relation between the attack rate threshold and the upper bound of the attack parameter is expressed analytically, which is shown in Theorem <xref ref-type="theorem" rid="theorem12" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</xref> . Simulation results demonstrate that, compared with some existing DoS models, the proposed stochastic data-based DoS attack strategy brings about greater destructiveness to the estimation quality of the systems, which demonstrates the effectiveness of the proposed attack strategy from the attacker’s perspective.

New results on [formula omitted] control for interval type-2 fuzzy singularly perturbed systems with fading channel: The weighted try-once-discard protocol case

This article deals with the interval type-2 (IT2) fuzzy model-based H∞ control problem for networked singularly perturbed systems (SPSs) under fading channel. To prevent data collision, a weighted try-once-discard (WTOD) communication scheme is adopted to adjust the communication sequence of sensor nodes. Based on this transmission strategy, only one sensor with more considerable difference is allowed to be transmitted at each time instant. On the other hand, a time-varying stochastic process model is introduced to describe the behavior of the fading channels in unreliable networks. Based on fading state signal and known bounds, the imperfectly matched membership functions (MFs) are reconstructed in the controller. Accordingly, under the effect of fading channels and WTOD protocol, a new IT2 fuzzy controller is constructed for the networked IT2 fuzzy SPSs. Meanwhile, by constructing a singular perturbation parameter (SPP) dependent Lyapunov function, sufficient conditions are established to guarantee the mean square stability of networked IT2 fuzzy SPSs, and the numerical stiffness issue is avoided. Finally, the practicability of the proposed methods is proved through a tunnel diode circuit simulation.

More Than Accuracy: A Composite Learning Framework for Interval Type-2 Fuzzy Logic Systems

In this article, we propose a novel composite learning framework for interval type-2 (IT2) fuzzy logic systems (FLSs) to train regression models with a high accuracy performance and capable of representing uncertainty. In this context, we identify three challenges, first, the uncertainty handling capability, second, the construction of the composite loss, and third, a learning algorithm that overcomes the training complexity while taking into account the definitions of IT2-FLSs. This article presents a systematic solution to these problems by exploiting the type-reduced set of IT2-FLS via fusing quantile regression and deep learning (DL) with IT2-FLS. The uncertainty processing capability of IT2-FLS depends on employed center-of-sets calculation methods, while its representation capability is defined via the structure of its antecedent and consequent membership functions. Thus, we present various parametric IT2-FLSs and define the learnable parameters of all IT2-FLSs alongside their constraints to be satisfied during training. To construct the loss function, we define a multiobjective loss and then convert it into a constrained composite loss composed of the log-cosh loss for accuracy purposes and a tilted loss for uncertainty representation, which explicitly uses the type-reduced set. We also present a DL approach to train IT2-FLS via unconstrained optimizers. In this context, we present parameterization tricks for converting the constraint optimization problem of IT2-FLSs into an unconstrained one without violating the definitions of fuzzy sets. Finally, we provide comprehensive comparative results for hyperparameter sensitivity analysis and an inter/intramodel comparison on various benchmark datasets.

Advanced Control of Three-Phase PWM Rectifier Using Interval Type-2 Fuzzy Neural Network Optimized by Modified Golden Sine Algorithm

Three-phase Pulse-Width Modulated (PWM) rectifiers used between the power grid and the load in applications requiring DC voltage have features such as high efficiency, high power factor, and low harmonics. This paper proposes a hybrid control approach to improve the dynamic performance of three-phase PWM rectifiers under different operating conditions. Operating conditions are considered as step response, internal disturbance, and regenerative operation. First, Interval Type-2 Fuzzy Neural Network (IT2FNN) is designed and then antecedent and consequent parameters of IT2FNN are optimized with Modified Golden Sine Algorithm (GoldSA-II). The dynamic performance of the hybrid controller, named GoldSA-II-IT2FNN, is analyzed for all operating conditions in Matlab/Simulink environment. The simulation studies are realized to evaluate the performance of the proposed controller. In the simulations, settling times of proposed controller are observed as 27.2 ms, and 10.8 ms for step response, respectively. Moreover, recovery times are calculated as being 12 ms to 5.5 ms for internal disturbance, and 7.2 ms to 19 ms for regenerative operation, respectively. The obtained results demonstrate that the proposed controller not only provides better dynamic performance but also improves the stability of PWM rectifier.

Finite-time tolerant containment control for IT2 T–S fuzzy network multi-agent systems with actuator faults, packet dropouts and DoS attacks

This article studies finite-time tolerant containment control issue for uncertain nonlinear networked multi-agent systems (MASs) with actuator faults, denial-of-service (DoS) attacks and packet dropouts, under the framework of interval type-2 (IT2) Takagi–Sugeno (T–S) fuzzy method. Firstly, based on establishing the actuator fault models and introducing Bernoulli random distribution to represent the packet dropouts phenomenon, the IT2 T–S fuzzy network MASs under actuator faults and packet dropouts are constructed as switchable systems according to the attack situations on the communication channels. Secondly, the slack matrix with more information of lower and upper membership functions is introduced in the stability analysis to reduce conservatism. And on basis of Lyapunov stability theory and average dwell-time method, finite-time tolerant containment control protocol is proposed, which makes the follower’ states converge to the convex hull controlled by the leaders in finite time. Finally, the effectiveness of the control protocol designed in this article is verified by numerical simulation.