Design Of Fuzzy System Research Articles

Recommendations on designing practical interval type-2 fuzzy systems

Interval type-2 (IT2) fuzzy systems have become increasingly popular in the last 20 years. They have demonstrated superior performance in many applications. However, the operation of an IT2 fuzzy system is more complex than that of its type-1 counterpart. There are many questions to be answered in designing an IT2 fuzzy system: Should singleton or non-singleton fuzzifier be used? How many membership functions (MFs) should be used for each input? Should Gaussian or piecewise linear MFs be used? Should Mamdani or Takagi–Sugeno–Kang (TSK) inference be used? Should minimum or product t-norm be used? Should type-reduction be used or not? How to optimize the IT2 fuzzy system? These questions may look overwhelming and confusing to IT2 beginners. In this paper we recommend some representative starting choices for an IT2 fuzzy system design, which hopefully will make IT2 fuzzy systems more accessible to IT2 fuzzy system designers.

Type-2 fuzzy cerebellar model articulation control system design for MIMO uncertain nonlinear systems

This paper aims to propose a more efficient neural network and applies it as an adaptive controller for the multi-input multi-output (MIMO) uncertain nonlinear systems. First, a more efficient fuzzy neural network named as fuzzy cerebellar model articulation controller (CMAC) is introduced, then an adaptive controller is proposed using a novel interval type-2 fuzzy CMAC (T2FCMAC). The T2FCMAC realizes an interval type-2 fuzzy logic system based on the structure of the CMAC. Due to the better ability of handling uncertainties provided by type-2 fuzzy sets, it can solve some complicated problems with outstanding effectiveness than type-1 fuzzy sets. In addition, an intelligent control system is proposed; this control system is comprised of a T2FCMAC and an auxiliary compensation controller. The T2FCMAC is utilized to approximate a perfect controller and the parameters of T2FCMAC are on-line tuned by the derived adaptive laws based on a Lyapunov function. The auxiliary compensation controller is designed to suppress the influence of residual approximation error between the perfect controller and the T2FCMAC. Finally, two MIMO uncertain nonlinear systems, a Chua’s chaotic circuit and a mass-spring-damper mechanical system, are performed to verify the effectiveness of the proposed control scheme. The simulation results confirm that the proposed intelligent adaptive control system can achieve favorable tracking performance with desired robustness.

A Constrained Representation Theorem for Well-Shaped Interval Type-2 Fuzzy Sets, and the Corresponding Constrained Uncertainty Measures

The representation theorem for interval type-2 fuzzy sets (IT2 FSs), proposed by Mendel and John, states that an IT2 FS is a combination of all its embedded type-1 (T1) FSs, which can be nonconvex and/or subnormal. These nonconvex and/or subnormal embedded T1 FSs are included in developing many theoretical results for IT2 FSs, including uncertainty measures, the linguistic weighted averages (LWAs), the ordered LWAs (OLWAs), the linguistic weighted power means (LWPMs), etc. However, convex and normal T1 FSs are used in most fuzzy logic applications, particularly computing with words. In this paper, we propose a constrained representation theorem (CRT) for well-shaped IT2 FSs using only its convex and normal embedded T1 FSs, and show that IT2 FSs generated from three word encoding approaches and four computing with words engines (LWAs, OLWAs, LWPMs, and perceptual reasoning) are all well-shaped IT2 FSs. We also compute five constrained uncertainty measures (centroid, cardinality, fuzziness, variance, and skewness) for well-shaped IT2 FSs using the CRT. The CRT and the associated constrained uncertainty measures can be useful in computing with words, IT2 fuzzy logic system design using the principles of uncertainty, and measuring the similarity between two well-shaped IT2 FSs.

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English

Personalized Rehabilitation Recognition for Ubiquitous Healthcare Measurements.

The physical therapeutic application needs personalized rehabilitation recognition (PRR) for ubiquitous healthcare measurements (UHMs). This study employed the adaptive neuro-fuzzy inference system (ANFIS) to generate a PRR model for a self-development system of UHM. The subjects wore a sensor-enabled wristband during physiotherapy exercises to measure the scheduled motions of their limbs. In the model, the sampling data collected from the scheduled motions are labeled by an arbitrary number within a defined range. The sample datasets are referred as the design of an initial fuzzy inference system (FIS) with data preprocessing, feature visualizing, fuzzification, and fuzzy logic rules. The ANFIS then processes data training to adjust the FIS for optimization. The trained FIS then can infer the motion labels via defuzzification to recognize the features in the test data. The average recognition rate was higher than 90% for the testing motions if the subject followed the sampling schedule. With model implementation, the middle section of motion datasets in each second is recommended for recognition in the UHM system which also includes a mobile App to retrieve the personalized FIS in order to trace the exercise. This approach contributes a PRR model with trackable diagrams for the physicians to explore the rehabilitation motions in details.

Novel QoS optimization paradigm for IoT systems with fuzzy logic and visual information mining integration

The Internet of Things is a new round of information technology revolution after computers, the Internet and mobile communications. Internet of Things technology is an important means to improve the level of social information, which will have a profound impact on economic development and social life. IoT can stimulate the economy, increase employment, improve efficiency and make people’s lives and work more convenient. Since fuzzy control can make good use of expert fuzzy information and effectively deal with the complex process of modeling, fuzzy control has received extensive attention once it has been proposed. Fuzzy logic system has become a research hotspot in academic and application fields due to its wide application. Fuzzy system identification includes structure identification and parameter identification. Fuzzy cognitive graph is a kind of soft computing method. It has stronger semantics than neural network because of its intuitive expression ability and powerful reasoning ability. Due to the widespread popularity of visual data acquisition devices, people can use the device to capture a large number of videos and images and spread them over the network in daily learning, production, life, work and entertainment. Computer science and technology, information computing technology, automated detection technology and Internet of Things technology contribute to the research of visual information data. In this paper, we conduct research on the novel QoS optimization paradigm for the IoT systems based on fuzzy logic and visual information mining integration. The experimental results show that the proposed optimization scheme has higher robustness.

Fuzzy Sets in Data Analysis: From Statistical Foundations to Machine Learning

Basic ideas and formal concepts from fuzzy sets and fuzzy logic have been used successfully in various branches of science and engineering. This paper elaborates on the use of fuzzy sets in the broad field of data analysis and statistical sciences, including modern manifestations such as data mining and machine learning. In the fuzzy logic community, this branch of research has recently gained in importance, especially due to the emergence of data science as a new scientific discipline, and the increasing relevance of machine learning as a key methodology of modern artificial intelligence. This development has been accompanied by an internal shift from largely knowledge-based to strongly data-driven fuzzy modeling and systems design. Reflecting on the historical dimension and evolution of the area, we discuss the role of fuzzy logic in data analysis and related fields, highlight existing contributions of fuzzy sets in these fields, and outline interesting directions for future work.

Evolutionary Fuzzy Systems for Explainable Artificial Intelligence: Why, When, What for, and Where to?

Evolutionary fuzzy systems are one of the greatest advances within the area of computational intelligence. They consist of evolutionary algorithms applied to the design of fuzzy systems. Thanks to this hybridization, superb abilities are provided to fuzzy modeling in many different data science scenarios. This contribution is intended to comprise a position paper developing a comprehensive analysis of the evolutionary fuzzy systems research field. To this end, the 4 W questions are posed and addressed with the aim of understanding the current context of this topic and its significance. Specifically, it will be pointed out why evolutionary fuzzy systems are important from an explainable point of view, when they began, what they are used for, and where the attention of researchers should be directed to in the near future in this area. They must play an important role for the emerging area of eXplainable Artificial Intelligence (XAI) learning from data.

Comparative Study in Fuzzy Controller Optimization Using Bee Colony, Differential Evolution, and Harmony Search Algorithms

This paper presents a comparison among the bee colony optimization (BCO), differential evolution (DE), and harmony search (HS) algorithms. In addition, for each algorithm, a type-1 fuzzy logic system (T1FLS) for the dynamic modification of the main parameters is presented. The dynamic adjustment in the main parameters for each algorithm with the implementation of fuzzy systems aims at enhancing the performance of the corresponding algorithms. Each algorithm (modified and original versions) is analyzed and compared based on the optimal design of fuzzy systems for benchmark control problems, especially in fuzzy controller design. Simulation results provide evidence that the FDE algorithm outperforms the results of the FBCO and FHS algorithms in the optimization of fuzzy controllers. Statistically is demonstrated that the better errors are found with the implementation of the fuzzy systems to enhance each proposed algorithm.

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.

Diagnosis of Coronary Artery Disease via a Novel Fuzzy Expert System Optimized by Cuckoo Search

In this paper, we propose a novel fuzzy expert system for detection of Coronary Artery Disease, using cuckoo search algorithm. This system includes three phases: firstly, at the stage of fuzzy system design, a decision tree is used to extract if-then rules which provide the crisp rules required for Coronary Artery Disease detection. Secondly, the fuzzy system is formed by setting the intervals for fuzzy variables and extracted rules. Finally, Cuckoo Search algorithm is used to optimize fuzzy membership functions. The accuracy of our proposed system is evaluated using Cleveland Cardiac Patient Database. The detection rate is 93.48% employing optimized membership functions. Also, 85.76% accuracy is obtained for predicting the risk of coronary artery disease. The superiority of proposed system is obvious by comparing it to the previously methods; it is more accurate and is also easier to implement.

Observer Design of Discrete-Time Fuzzy Systems Based on an Alterable Weights Method

This paper proposes an improvement on observer design of discrete-time fuzzy systems based on an alterable weights method. Different from the recent result, a more effective ranking-based switching mechanism is developed by introducing a bank of alterable weights for the sake of making use of the size difference information of the normalized fuzzy weighting functions more freely than before. Therefore, a positive result can be provided in this paper, that is, less conservative conditions of designing feasible fuzzy observers can be obtained than those existing results, while the computational cost of designing feasible fuzzy observers is even less than the up-to-date one. Finally, two numerical examples are given to show the progressiveness of the proposed method.

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.

A novel method for fuzzy diagnostic system design.

Background: In recent years, liver disorders have been continuously increased. Proper performance of data mining techniques in decision-making and forecasting caused to use them commonly in designing of automatic medical diagnostic systems. The main aim of this paper is to introduce a classifier for diagnosis of liver disease that not only has high precision but also is understandable and has been created without expert knowledge. Methods: In regards to this purpose, fuzzy association rules have been extracted from dataset according to fuzzy membership functions which determined by fuzzy C-means clustering method; while each time, extracting fuzzy association rules, one of the five quality measures including confidence, coverage, reliability, comprehensibility and interestingness is used and five fuzzy rule-bases extracted based on them. Then, five fuzzy inference systems are designed on the basis of obtained rule-bases and evaluated in order to choose the best model in terms of diagnostic accuracy. Results: The proposed diagnostic method was examined using data set of Indian liver patients available at UCI repository. Results showed that among considered quality measures, interestingness, reliability and truth outperformed respectively, and yielded precision, sensitivity, specificity and accuracy of more than 90%. Conclusion: In this paper, a classification method was developed to predict liver disease which in addition to high classification accuracy, it has been created without expert knowledge and provided an understandable explanation of data. This method is convenient, user friendly, efficient and requires no expertise.

Design and application of Type-2 fuzzy logic system based on improved ant colony algorithm

In this paper, an improved ant colony optimization (IACO) with global pheromone update is proposed based on ant colony optimization (ACO), and it is used to design interval Type-2 TSK fuzzy logic system (FLS), including parameters adjustment and rules selection. The performance of the system can be improved by obtaining the optimal parameters and reducing the redundant rules. In order to verify the feasibility of the proposed method, the intelligent FLS is applied to predict the international petroleum price and the Zhongyuan environmental protection shares price. It is proved that the IACO can improve the efficiency of the original algorithm and accelerate the convergence speed. The simulations show that both IACO and ACO are feasible and have a high performance for the design of FLS. The simulation results compared with back-propagation design (BP algorithm) show that intelligent algorithms have an advantage over the classical algorithm, the simulation result compared with without rule-selection shows that reduced redundant rules can improve the performance, and the result compared with the Type-1 FLS shows that interval Type-2 TSK FLS has a better performance than the Type-1 TSK FLS.

Event-Triggered Fault Detector and Controller Coordinated Design of Fuzzy Systems

This paper attempts to propose a new solution to the event-triggered fault detection problem for discrete-time Takagi–Sugeno fuzzy systems in a network environment. First, for the original Takagi–Sugeno fuzzy system, our focus is on constructing a new based-network residual system, considering the event-triggering mechanism, interval time-varying delays, and packet dropouts. Under the established system, a less conservative basis-dependent stability condition is obtained by using the reciprocally convex technique, which ensures that the corresponding residual system is mean-square asymptotically stable with a given $\mathcal{H}_{\infty }$ performance. Second, the desired fuzzy-rule-dependent fault detector and the controller scheme are established using a variable substitution approach. Furthermore, these criteria can be transformed into convex optimization problems and then calculated by the standard optimization toolbox. Finally, the advantages of the proposed fault detector and controller coordinated design technique are illustrated by the simulation results.

Stability Analysis and Memory Control Design of Polynomial Fuzzy Systems with Time Delay via Polynomial Lyapunov-Krasovskii Functional

This paper investigates the problems of delay-dependent stability analysis and memory control design of polynomial fuzzy systems with time delay. Using polynomial Lyapunov-Krasovskii functional and slack polynomial matrix variables, delay dependent sufficient stability and stabilizability conditions are derived in terms of sum of squares (SOS) which can be numerically (partially symbolically) solved via the recently developed SOSTOOLS. The main advantage of the proposed design is the reduction of conservatism for three great reasons. The first one is that polynomial matrices are not only dependent on the system state vector but also on the state vector with time delay. The second one is that the design conditions are formulated in delay dependent SOS. It is well known that the delay-dependent conditions are less conservative than those independent of time delay. The third one is that only correlated terms are used in the design of SOS. The simulation and comparison are given to illustrate the lesser conservativeness of the proposed result.

Optimization of granulation for fuzzy controllers of autonomous mobile robots using the Firefly Algorithm

This paper describes a methodology based on optimal granularity allocation for fuzzy system design, and the main contribution is a method, based on the Firefly Algorithm, to generate and test information granules for fuzzy controllers of autonomous mobile robots. The Firefly Algorithm automatically generates and tests these granules which are defined by the parameter values of the membership functions, which are evaluated based on simulations of the robot plant and the final result is an ideal combination of information granules. The evaluation is made with a comparison of the actual trajectory generated by the fuzzy controller of the robot with respect to the desired path. To verify that the obtained results are significantly better, a statistical test is performed between the firefly and the genetic algorithms.

Adaptive TOPSIS fuzzy CMAC back-stepping control system design for nonlinear systems

This paper aims to propose a more efficient control algorithm for nonlinear systems. A novel adaptive Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) fuzzy cerebellar model articulation controller (FCMAC) back-stepping control system is developed. The proposed adaptive TOPSIS FCMAC (ATFCMAC) incorporates a multi-criteria decision analysis with a fuzzy CMAC structure to determine the optimal threshold values for selecting suitable firing nodes, improving the computational efficiency, reducing the number of firing rules, and achieving good performance for nonlinear systems. A back-stepping technique is employed for the control system design. The proposed control system comprises an ATFCMAC and a robust compensator; the ATFCMAC is used to approximate an ideal controller and the robust compensator is used to reduce the influence of residual approximation error between the ideal controller and the ATFCMAC. The parameters of the proposed ATFCMAC are tuned online using the adaptation laws that are derived from a Lyapunov stability theorem, so that the stability of the control system is guaranteed. The simulation and experimental results for a Duffing–Holmes chaotic system and a magnetic ball levitation system are used to verify the effectiveness of the proposed control scheme.

Non-fragile controller design of uncertain saturated polynomial fuzzy systems subjected to persistent bounded disturbance

This paper investigates the problem of designing a non-fragile polynomial fuzzy controller for a class of polynomial fuzzy models subjected to persistent bounded disturbances and system uncertainty. The proposed controller is considered to satisfy the input saturation constraint. Furthermore, the resilient controller is affected by linear fractional uncertainties. The overall structure of the controller is obtained by the polynomial parallel distributed compensation concept. The sufficient conditions guarantee an L1 performance of the perturbed system and exponential stability of the non-perturbed system is achieved in terms of sum-of-squares decomposition conditions. Subsequently, the sum-of-squares-based conditions lead to minimization of the L1 performance such that the above-mentioned hard constraints on the control input and robustness of the closed-loop system against the system and controller uncertainties will be guaranteed. The controller gain matrices will be achieved by numerically solving the sum-of-squares-based conditions with the third-party MATLAB toolbox ‘SOSTOOLS’. Finally, extensive studies and hardware-in-the-loop simulations on a ball-and-beam system are presented, which illustrate the proposed controller can accurately and smoothly track the set point frequency. Furthermore, the proposed control approach is more robust over prior-art controllers for all the simulation scenarios.