Type-2 Fuzzy Model Research Articles

A type-2 fuzzy review topic-based model for personalized recommendation

A type-2 fuzzy review topic-based model for personalized recommendation

Vision-Locomotion Coordination Control for a Powered Lower-Limb Prosthesis Using Fuzzy-Based Dynamic Movement Primitives

An amputee cannot directly use the perceptual visual information to control the movements and gait patterns of his worn prosthesis. In order to help an amputee walk and cross over obstacles smoothly, the paper proposes a vision-locomotion coordination control method for a powered lower-limb prosthesis (PLLP), in which a vision system is proposed to detect obstacles, and a complete vision-locomotion loop is then constructed. With deep learning techniques, the vision system can recognize common obstacles (e.g., garbage cans, bricks and boxes) and obtain the features of obstacles (e.g., distance from obstacles to the depth camera and height of obstacles). Through integrating the vision system into the locomotion control system, the PLLP can make obstacle avoidance decisions and use dynamic movement primitives with type-2 fuzzy models (T2FDMPs) to help amputees cross over obstacles simultaneously. Utilizing the type-2 fuzzy models, smooth trajectories for crossing over obstacles can be obtained. The experimental results show that the PLLP with visual information can switch an amputee’s gaits between level walking and obstacle avoidance adaptively, which demonstrates the effectiveness of the vision-locomotion coordination control system. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —The paper is motivated by the challenge of obstacle avoidance of prostheses. Traditional prostheses cannot achieve autonomous obstacle avoidance because they lack of environmental perception capability. In addition, most prostheses always utilize use the human-robot interaction between amputees and prostheses to recognize the environments. However, due to noise and individual differences, recognition results are not accurate enough. We found that the integration of vision can improve the accuracy and efficiency of environmental recognition. Therefore, it is necessary to construct a complete vision and locomotion closed-loop. In the paper, a vision-locomotion coordination control is proposed, and to make the PLLP cross over obstacles smoothly, a novel trajectory shaping with fuzzy-based dynamic movement primitives is developed. The coordination control is partitioned into the obstacle detection, trajectory shaping and joint control, which can help the PLLP fulfill several obstacle avoidance tasks.

Data Driven Type-2 Fuzzy Modeling and Control of Personalized Thermal Comfort

Since the room thermal comfort has high uncertainties, it is difficult but necessary to study the modeling and control of thermal comfort. This paper tries to solve the modeling and control problem for the room thermal comfort by utilizing the temperature and humidity data collected from the working or living room. Firstly, in order to discard the noisy data and to obtain the reasonable intervals for modeling the temperature and humidity, a statistic method based preprocessing strategy is presented. Secondly, the Gaussian interval type-2 fuzzy set models are constructed to depict the personalized temperature and humidity comfort by measuring the uncertainty degrees of the obtained intervals. Thirdly, a interval type-2 fuzzy method based control scheme is proposed to realize the personalized thermal comfort regulation. Finally, some experimental results are given. And, the results show that the proposed thermal comfort models and control scheme can not only recommend a reasonable temperature and humidity range, but also can realize the optimal thermal comfort control.

Event-triggered interval type-2 fuzzy control of networked systems with extended dissipative under Markovian switching

In this technical note, the problem of the extended dissipative control for interval type-2 fuzzy model with nonlinear network systems in the event-triggered framework is investigated. A novel dynamic event-triggered strategy is developed to ascertain the instants of activation. It has the advantage of reducing data transmission and optimising the utilisation of communication resources. On the basis of the proposed mechanism, the stochastic Lyapunov function including internal dynamic variables is constructed. Based on this function, coupled with the inequality scaling technique and the application of Dynkin's formula, we derive a sufficient condition for the system's stochastic asymptotic stability and extended dissipativity. The design of the dynamic event-triggered extended dissipative controller becomes challenging because the new sufficient condition is nonlinear for some matrix variables. However, utilising the Projection Lemma and the co-design approach, such a controller can be developed based on the obtained analysis result. The methodology is demonstrated through a rigorous numerical simulation case study.

Interval Type-2 Fuzzy-Model-Based Sampled-Data Control of an AUV Depth System with Input Saturation

This paper proposes a sampled-data fuzzy controller design technique for an autonomous underwater vehicle (AUV) depth system represented by an interval type-2 (IT-2) fuzzy model, considering input saturation. In the Takagi–Sugeno (T–S) fuzzy model of an AUV depth system, surge velocity is chosen as a premise variable. To address the associated uncertainty with this variable, we employ the IT-2 fuzzy modeling technique. Also, the controller proposed in this paper utilizes time-varying gains, ensuring superior exponential stability compared with traditional fixed gain approaches. Furthermore, a membership function-dependent (MFD) H∞ criterion is employed to enhance robustness for each subsystem individually. Taking into account the mentioned aspects, the controller design condition is derived in the form of linear matrix inequalities (LMIs). Finally, the effectiveness of the proposed method is validated through simulation examples.

Event-based predictive control for interval type-2 Takagi–Sugeno fuzzy systems under Kalman filter

In this article, the event-based predictive control problem for a class of interval type-2 Takagi–Sugeno fuzzy system is investigated. To reduce the influence of Gaussian noise, an improved Kalman filter is proposed, in which the system state is filtered or not depends on an event-triggered mechanism. Then, by designing the network predictive control scheme via interval type-2 fuzzy model, some sufficient conditions are derived, which guarantee the Schur stabilization of the concerned system subject to network delays. Finally, the correctness and effectiveness are verified by two simulation examples.

Interval Type 2 Adaptive Neuro-Fuzzy Inference System-Based Artificial Pacemaker Design and Stability Analysis.

This paper presents the design and simulation of an Interval type 2 fuzzy system (IT2FS) based, adaptive neuro-fuzzy inference system (ANFIS) pacemaker controller in MATLAB. After designing the type 1 fuzzy logic model, the stability of the designed system has been verified in the time-domain (unit step response). In previous works, the type 1 (IT1FS) model step response was analyzed. They are compared with the other proportional integral derivative (PID) and fuzzy models that only least-square-estimation and the backpropagation algorithms are used for tuning membership functions (MF) and generation of type 1 fis (fuzzy inference system) file. At current work, fuzzy C means (FCM) method shows better results than other methods have been used. The pacemaker controller determines the pacing rate and adjusts the heart rate of the patient for the reference input signal. The rise-time, overshoot and settling-time have been improved significantly.

Membership-function-dependent [formula omitted] bumpless transfer control for switched interval type-2 fuzzy systems with time-delay

This paper addresses the H∞ bumpless transfer control for switched nonlinear delayed systems with exogenous perturbations via the interval type-2 fuzzy model. We firstly establish a novel characterization of bumpless transfer performance, which provides a framework to the bumpless transfer control of switched nonlinear systems. By using the multiple Lyapunov-Krasovskii functionals and the state-dependent switching strategy, sufficient conditions for asymptotically stability with H∞ bumpless transfer performance are obtained. More incisively, different from the existing results where the H∞ bumpless transfer control design conditions do not involve the information of membership functions, we adopt the piecewise-linear-membership-function technique to remove this limitation. Correspondingly, novel membership-function-dependent H∞ bumpless transfer criteria are derived, under which the state-dependent switching law and H∞ bumpless transfer controllers are jointly designed. Finally, a tunnel diode circuit model is exploited to verify the applicability and validity of the developed method.

Dynamic event-triggered fuzzy control for nonlinear singular semi-Markovian jump systems via state decomposition approach

This paper addresses the dynamic event-triggered fuzzy control problem of nonlinear singular semi-Markovian jump systems. Firstly, the interval type-2 fuzzy model is utilized to approximate nonlinear singular semi-Markovian jump systems. Secondly, by employing the state decomposition approach, the interval type-2 fuzzy singular system is decomposed into a differential equation and an algebraic equation. Thirdly, a new periodic dynamic event-triggered scheme with the adaptive variable is proposed to further relieve the communication pressure while ensuring the system performance. The hidden semi-Markov model is used to describe the phenomenon that the modes of fuzzy controller and the modes of original system are asynchronously operational. By designing the asynchronous event-triggered fuzzy controller based on quantized decomposed state vectors and constructing suitable Lyapunov-Krasovskii functional, sufficient conditions are derived to guarantee that the closed-loop fuzzy singular system is stochastically admissible. Finally, two simulation examples are provided to verify the validity and advantages of obtained results.

A fast detection method for building wood measurement based on interval type-2 fuzzy model

Automatic measurement detection in the process of wood processing can effectively improve production efficiency and yield to promote upgrading the wood processing industry. Therefore, this article researches visual detection technology for wood surface measurements and proposes a construction wood measurement detection method based on interval type-2 fuzzy theory. This method overcomes the problem of increasing heterogeneity and similarity of homogeneous areas on the wood surface, which increases the difficulty of measurement detection. Firstly, the Gaussian model is improved by establishing a wood measurement image feature model that considers rate neighborhood relationships as the basic model. Then, the basic model is fuzzified to construct an interval type-2 fuzzy model (IT2FM) to characterize the uncertainty features of the modeling and achieve measurement detection of building wood. We conducted experiments using a wood measurement detection dataset to study the influence of the construction form of IT2FM on wood measurement detection and evaluated the results using kappa values. The detection accuracy of this method is improved by about 10% compared to traditional machine learning and deep learning methods, and it only takes about 3–5 s to run the program. The experimental results show that the proposed method can effectively suppress the noise generated by wood measurement detection and prevent missed detection. It can achieve high-quality measurement detection of wood dead knots, loose knots, and cracked parts.

Type-2 fuzzy chance-constrained linear fractional programming model for a water resource management system: A case study of Taiyuan city, China

Abstract Uncertainties arising from extreme climate events and human activities pose a challenge to the efficient allocation of water resources. In this study, a type-2 fuzzy chance-constrained linear fractional programming (T2F-CCLFP) is developed to support the water resource management system under uncertainty by incorporating type-2 fuzzy sets, chance-constrained programming, and fractional programming into a comprehensive multi-objective optimization framework. The model enables the trade-off between economic, social, and environmental sustainability and provides water supply solutions associated with different levels of fuzzy uncertainty and risk of violating constraints. The T2F-CCLFP model is applied to Taiyuan, Shanxi Province, China, to support its water resource management. Results reveal that: (i) the industrial structure is transitioning toward diverse industries from energy and heavy industry dominance; (ii) external water transfer will be the major water-supply sources for the city in the future, accounting for 55 and 50% of the total water supply in 2025 and 2030, respectively; (iii) the water-supply security of the city is enhanced by provoking the utilization of reclaimed water (the annual growth rate is 13.9%). The results are helpful for managers in adjusting the current industry structure, enhancing water supply security, and contributing to the sustainable development of socio-economic and water systems.

Nonsingular Fast Terminal Sliding Mode Controller for a Robotic System: A Fuzzy Approach

This study presents a combination of Type-2 fuzzy logic and nonsingular fast sliding mode technique to design a robust controller for a robotic system. The control law is composed of two signals. The first one called equivalent control law is dedicated to maintaining the system on the sliding surface and then converges to zero. Since the system is uncertain, a Type-2 fuzzy nominal model was constructed, deduced from linear local models, which allows a good approximation of the real robotic system. The second signal, whose objective is to force the system to attain the sliding surface, is deduced from stability analysis using Lyapunov theory. Several simulations were conducted to evaluate the efficiency of the proposed approach, showing good tracking performance for different reference signals despite the presence of uncertainties and external disturbances.

Fuzzy nonsingular fast terminal sliding mode controller for a robotic system

This study introduces an innovative control strategy utilizing a nonsingular fast sliding mode technique tailored for robotic systems. The core of this approach lies in the development of a type-2 fuzzy logic-based nominal model, meticulously designed to accurately approximate the dynamics of the real system while adeptly handling the variability in system parameters. This method marks a departure from conventional approaches by inferring the switch signal for type-2 adaptive fuzzy systems, a critical step in achieving superior tracking performance without the necessity for extensive knowledge of the system's upper bounds in uncertainties and external disturbances. The efficacy of the proposed control law is rigorously validated through a series of simulations, encompassing a variety of initial conditions and reference signals, thereby demonstrating its robust performance capabilities.

An Exponential Stabilization Analysis for Switched Interval Type-2 Fuzzy Sampled-Data Control Systems

This work is focused on designing the admissible edge-dependent average dwell time (AE-DADT) based fuzzy sampled-data control problem for a class of switched nonlinear systems. The upper and lower grade of membership functions is used to characterize uncertain parameter-dependent nonlinear systems in the interval type-2 fuzzy (IT2F) model. Unlike from the existing literature, a new fuzzy dependent refined looped-Lyapunov functional (LF) is introduced which involves the new exponent terms and state information such as <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\frac{e^{2\gamma _{v}(\varrho -\varrho _{\mathscr {k}})}-1}{2\gamma _{v}}, \ \frac{e^{2\gamma _{v}(\varrho _{\mathscr {k}+1}-\varrho)}-1}{2\gamma _{v}}, \ \mathscr {z}(\varrho _{\mathscr {k}})$</tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathscr {z}(\varrho _{\mathscr {k}+1})$</tex-math></inline-formula> with tuning parameters and few slack variables. The AE-DADT switching property has also been taken into account for nonlinear systems, and it contributes to getting more information about previous modes. Based on the proposed new refined looped-LFs, new sufficient conditions are derived in terms of linear matrix inequalities (LMI), which ensure the global uniform exponential stability (GUES) of the nominated switched IT2F systems. The feasibility of the obtained results is verified by the numerical example, and the tunnel diode circuit system model and Lorenz chaotic system are established to illustrate the feasibility and efficacy of the theoretical findings.

An Extended Type-2 Fuzzy Relational Database Model for Aggregate and Grouping Operations

This paper introduces an extended type-2 fuzzy relational database model (ET-2FRDB) for aggregate and grouping operations that can represent and query uncertain and imprecise information in the real world applications. In ET-2FRDB, each fuzzy relation is represented by a type-2 fuzzy set whose membership degree of each tuple is a fuzzy number on [0, 1], the fuzzy aggregate functions, the fuzzy relational algebraic, aggregate and grouping operations are defined as extensions of those in the classical relational database model thereby the membership degree of tuples associated by using the minimum and maximum of fuzzy numbers. Also, some properties of the fuzzy relational algebraic, aggregate and grouping operations in ET-2FRDB are formulated and proven.

Dissipativity-based event-triggered fuzzy control for unreliable networked systems via looped-functional

In this study, a dissipativity-based event-triggered fuzzy control design was proposed for unreliable networked systems. The controlled plant was characterized as an interval type-2 fuzzy model and a controller with unreliable data transmission was provided via an event-triggered mechanism. The resulting closed-loop system was established by coupling the controlled system to a controller. Bilateral information in a sampling interval was used to create a looped-functional, based on which the existence of the controller can be inferred. Finally, we ensured that the closed-loop system was strictly stochastically 〈Q,S,R〉−γ-dissipative. The effectiveness of the proposed control method was demonstrated experimentally.

A pentagonal type-2 fuzzy variable defuzzification model with application in humanitarian supply chains

Disasters can be caused by humans or natural hazards, and they impact the vulnerability of communities worldwide. This study considers disasters caused by humans, including the rescue operation taken post-accidents. The objective of the research is to minimise time and cost to save people’s lives in the early stages of rescue operations from the fuzzy logic perspective by proposing a novel pentagonal type-2 fuzzy variable (PT2FV) defuzzification method. The multi-objective multi-modal services at the crucial early hours of a disaster solve a solid transportation problem mathematically using a weighted sum method and neutrosophic compromise programming in Lingo solver software. The novelty of the research has been justified by the sensitivity analysis test on various levels of credibility at different intervals of PT2FV. The various credibility level intervals have also been discussed, and the best possible interval is suggested. The outcome suggests an effective plan for humanitarian relief in difficult areas using multiple modes of transit for delivery of reliefs, availing rescue team and saving of victims along with a notion of an efficient contingency planning.

Dissipative Tracking Control of Nonlinear Markov Jump Systems With Incomplete Transition Probabilities: A Multiple-Event-Triggered Approach

This paper deals with the problem of multiple-event-triggered dissipative tracking control for nonlinear Markov jump systems (MJSs) with incomplete transition probabilities. An interval type-2 (IT2) fuzzy model with partially known transition probability matrix (TPM) is used to capture the underlying nonlinearities, and a hidden Markov model (HMM) with an incomplete conditional probability matrix (CPM) is employed to describe the possible asynchronous phenomenon between the plant and the tracking controller. A multiple-event-triggered methodology involving two adaptive event-triggered schemes (AETS) for the actuator channel and the sensor channel is proposed. By using the Lyapunov and dissipativity theory, sufficient conditions for the desired tracking controller are established in terms of linear matrix inequalities (LMIs). Last, two examples, involving one numerical and one practical model named the Hénon system, are utilized to show the effectiveness of the proposed tracking control algorithm.

Interval type-2 generalizing fuzzy model for monitoring the states of complex systems using expert knowledge

A type-2 interval generalizing fuzzy model is proposed for monitoring complex systems’ states. A set-theoretic approach is proposed to generalize the results of type-2 fuzzy models with interval membership functions. The study of the correspondence of expert assessments to the output value of the generalizing fuzzy model over the observation interval is presented. Examples of the use of generalizing fuzzy model type-2 in the task of monitoring the conditions of an artesian well are given. It is shown that in order to improve the quality of decisions made, the expert needs to pay attention to the value of the interval output of the generalizing type-2 fuzzy model. Recommendations are presented to experts to improve decision-making regarding the estimation of the output interval of the generalizing model.

Uncertainty clustering internal validity assessment using Fréchet distance for unsupervised learning

Knowing the number of clusters a priori is one of the most challenging aspects of unsupervised learning. Clustering Internal Validity Indices (CIVIs) evaluate partitions in unsupervised algorithms based on metrics like compactness, separation, and density. However, specialized CIVIs for specific applications have been designed, and there is no general CIVI that works in all scenarios. The absence of CIVIs based on crisp uncertainty metrics is especially critical in decision-making processes that involve ambiguity, non-convex distributions, outliers, and overlapping data. To address this problem, we propose a novel Uncertainty Fréchet (UF) CIVI that assesses the certainty of a well-defined partition. UF leverages uncertainty fingerprints based on Type-2 fuzzy Gaussian Mixture Models (T2FGMM) and the Fréchet distance between clusters to introduce a metric that evaluates partition quality. We integrate UF into a merging methodology that combines similar clusters within a partition, allowing us to determine the number of clusters without the need to run the clustering algorithms iteratively as other CIVIs require. We undertake a comprehensive evaluation of our proposal on 5,250 convex, 36 non-convex synthetic datasets, and five benchmark real datasets. In addition, we apply UF in a real-world scenario that involves high uncertainty: Passive Acoustic Monitoring (PAM) of ecosystems, which aims to study ecological transformations through acoustic recordings. The results show that UF exhibits notable performance in synthetic and real-world scenarios, obtaining an Adjusted Mutual Information (AMI) score higher than 0.88 for normal, uniform, gamma, and triangular distribution datasets. In the PAM application, UF identifies the transformation of ecosystems through sound using clustering algorithms and UF, achieving an F1 score of 0.84. Therefore, results show that the UF index is a suitable tool for researchers and practitioners working with highly uncertain data.