Direct inverse control of cable-driven parallel system based on type-2 fuzzy systems

An interval type-2 fuzzy logic system (IT2FLS) can function well with uncertain data, with which a type-1 fuzzy logic system (T1FLS) is ineffective because its membership function rests upon crisp values. However, similar to T1FLSs, there are challenges associated with IT2FLSs in selecting parameters, which can significantly affect the accuracy of the classification results with their relatively high sensitivity. This paper discusses and proposes a hybrid model based on IT2FLS and particle swarm optimization (PSO) for prediction problems. The main objective of this paper is to find the optimal solution for the unknown fuzzy systems using labelled data for training the fuzzy system. The PSO technique was used to find the optimal parameters of the Gaussian membership functions which utilized for IT2FLSs. The authors tested two data sets for each of the two prediction problems, namely: burnt forest area prediction and wine quality prediction. The predictive results were compared with other predictive methods including random forest (RF), support vector machines (SVM), artificial neural network (ANN), adaptive neuro fuzzy inference system (ANFIS) and IT2FLS with parameters generated by using the fuzzy c-means algorithm (IT2FLS-FCM). Experiment results showed that the proposed method could significantly improve accuracy compared to several other predictive techniques.

A fuzzy type-2 fault detection methodology to minimize false alarm rate in induction motor monitoring applications

Fuzzy logic Systems (FLSs) are credited with providing very good performances which are able to handle the uncertainty and imprecision present in real-world environments and applications. Using type-2 FLSs can enable handling higher levels of uncertainty when compared to type-1 FLSs. The majority of the type-2 FLSs employ singleton type-2 FLSs which handle the encountered input uncertainty through fuzzy sets representing the linguistic labels in the antecedent fuzzy sets. However, singleton type-2 FLSs assume that the input signal is perfect and thus there is no provision for handling the uncertainties in the incoming input signals. Hence, there have been some efforts to investigate non-singleton type-2 FLS. However, the papers that employed non-singleton type-2 FLSs assumed that the fuzzy inputs are having a predefined shape (mostly Gaussian) which might not model the encountered uncertainty properly. In our previous works, we presented adaptive type-2 input based non-singleton type-2 FLS which employs dynamic inputs which are not assuming any specific shape. We have shown how the adaptive type-2 input based non-singleton type-2 FLS outperforms singleton (type-1 and type-2) FLSs. In this paper, we will compare the adaptive type-2 input based non-singleton type-2 FLS with other non-singleton (type-1 and type-2) FLSs which employ Gaussian fuzzy inputs. We will present real-world robot experiments showing how the adaptive type-2 input based non-singleton type-2 FLS outperforms the non-singleton FLSs which employ Gaussian fuzzy inputs when large amounts of uncertainty are encountered.

This article provides a high-level retrospective of type-2 fuzzy sets and fuzzy logic systems. It explains how type-2 fuzzy sets can be used to model membership function uncertainties, and how by doing this smoother performance can be obtained than by using type-1 fuzzy sets. It also summarizes the notation that should be used for type-2 fuzzy sets, describes four important mathematical representations for these fuzzy sets, explains the differences between type-1 and type-2 fuzzy logic systems and which of the four representations is most useful when designing an optimal type-2 fuzzy logic system, provides a very useful strategy for optimal designs of fuzzy logic systems – one that guarantees performance improvement as one goes from a type-1 fuzzy logic system to a type-2 fuzzy logic system design – , and describes four methods for simplifying the designs of type-2 fuzzy logic systems. Finally, it explains why type-2 fuzzy sets can capture two kinds of linguistic uncertainties simultaneously (the uncertainty of an individual and the uncertainties of a group about a word), whereas type-1 fuzzy sets cannot, and that such type-2 fuzzy set word models are what should be used to implement Zadeh’s Computing With Words paradigm.

This paper presents a rigorous mathematical development for the design of robust intelligent type-2 fuzzy control systems with regards to the disturbance rejection problem. The majority of the papers in the literature uses only type-1 fuzzy systems for the modeling of both plant ant controller. In the control structure presented in this paper, we use type-2 fuzzy systems, which are more generalized than their type-1 counterparts and particularly known for handling uncertainties. This work extends and generalizes the previous results for the design of robust intelligent control systems. The final robust criteria are given based on linear matrix inequalities (LMIs), and two examples are provided to demonstrate the developed methodologies. The simulation results also show the potential of type-2 fuzzy controllers in improving robustness compared to type-1. The mathematically-sound general framework proposed in this paper provides a systematic tool for the design of robust intelligent controllers, and hence it is expected to widen their applications.

Soccer video summarization and classification is becoming a very important topic due to the world wide importance and popularity of soccer games which drives the need to automatically classify video scenes thus enabling better sport analysis, refereeing, training, advertisement, etc. Machine learning has been applied to the task of sports video classification. However, for some specific image and video problems (like sports video scenes classification), the learning task becomes convoluted and difficult due to the dynamic nature of the video sequence and the associated uncertainties relating to changes in light conditions, background, camera angle, occlusions and indistinguishable scene features, etc. The majority of previous techniques (such as SVM, neural network, decision tree, etc.) applied to sports video classifications did not provide a consummate solution, and such models could not be easily understood by human users; meanwhile, they increased the complexity and time of computation and the associated costs of the involved standalone machines. Hence, there is a need to develop a system which is able to address these drawbacks and handle the high levels of uncertainty in video scenes classification and undertake the heavy video processing securely and efficiently on a cloud computing based instance. Hence, in this paper we present a cloud computing based multi classifier systems which aggregates three classifiers based on neural networks and two fuzzy logic classifiers based on type-1 fuzzy logic and type-2 fuzzy logic classification systems which were optimized by a Big-Bang Big crunch optimization to maximize the system performance. We will present several real world experiments which shows the proposed classification system operating in real-time to produce high classification accuracies for soccer videos which outperforms the standalone classification systems based on neural networks, type-1 and type-2 fuzzy logic systems.

In this paper, an interval extension of the Gaussian mixture model called uncertain Gaussian mixture model (UGMM) is proposed and its transformation into the additive type-2 TSK fuzzy systems is presented. The conditions under which a UGMM becomes a corresponding type-2 TSK fuzzy system are derived theoretically. Furthermore, the mathematical equivalence between the conditional mean of a UGMM and the defuzzified output of a type-2 TSK fuzzy system is proved. Our results provide a new perspective for type-2 TSK fuzzy systems, i.e., interpreting them from a probabilistic viewpoint. Thus, instead of directly estimating the parameters of the fuzzy rules in a type-2 TSK fuzzy system, we can first estimate the parameters of the corresponding UGMM using any popular density estimation algorithm like the expectation maximization (EM) algorithm. Our experimental results clearly indicate that a type-2 fuzzy system trained in such a new way has higher approximation accuracy and stronger robustness than current type-2 fuzzy systems.

Type-2 systems has been becoming the focus of research in the field of fuzzy logic in recent years. Comparing with type-1 systems, type-2 fuzzy systems are more complex and relatively more difficult to understand and implement. We developed an interactive graphical user interface (GUI) based toolbox, MFLS tool, for interval type-2 fuzzy logic system. This paper presents MFLS toolbox. Moreover, the versatility of the software is demonstrated via an prediction problem.

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.

A comparative study of type-2 fuzzy inference systems optimization as an integration method of Modular Neural Networks (MNNs) is presented [32]. The optimization method for type-2 fuzzy systems is based on the footprint of uncertainty (FOU) of the membership functions. We use different benchmark problems to test the optimization method for the fuzzy systems [34, 35]. First, we tested the methodology by manually incrementing the percentage in the FOU, later we apply a Genetic Algorithm to find the optimal type-2 fuzzy system. We show the comparative results obtained for the benchmark problems.

A hybrid approach composed by different types of fuzzy systems, such as the Type-1 Fuzzy Logic System (T1FLS), Interval Type-2 Fuzzy Logic System (IT2FLS) and Generalized Type-2 Fuzzy Logic System (GT2FLS) for the dynamic adaptation of the alpha and beta parameters of a Bee Colony Optimization (BCO) algorithm is presented. The objective of the work is to focus on the BCO technique to find the optimal distribution of the membership functions in the design of fuzzy controllers. We use BCO specifically for tuning membership functions of the fuzzy controller for trajectory stability in an autonomous mobile robot. We add two types of perturbations in the model for the Generalized Type-2 Fuzzy Logic System to better analyze its behavior under uncertainty and this shows better results when compared to the original BCO. We implemented various performance indices; ITAE, IAE, ISE, ITSE, RMSE and MSE to measure the performance of the controller. The experimental results show better performances using GT2FLS then by IT2FLS and T1FLS in the dynamic adaptation the parameters for the BCO algorithm.

Parallel Interval Type-2 Subsethood Neural Fuzzy Inference System

This paper studies the continuity of the input-output mappings of fuzzy logic systems (FLSs), including both type-1 (T1) and interval type-2 (IT2) FLSs. We show that a T1 FLS being an universal approximator is equivalent to saying that a T1 FLS has a continuous input-output mapping. We also derive the condition under which a T1 FLS is discontinuous. For IT2 FLSs, we consider six type-reduction and defuzzification methods (the Karnik-Mendel method, the uncertainty bound method, the Wu-Tan method, the Nie-Tan method, the Du-Ying method, and the Begian-Melek-Mendel method) and derive the conditions under which continuous and discontinuous input-output mappings can be obtained. Guidelines for designing continuous IT2 FLSs are also given. This paper is to date the most comprehensive study on the continuity of FLSs. Our results will be very useful in the selection of the parameters of the membership functions to achieve a desired continuity (e.g., for most traditional modeling and control applications) or discontinuity (e.g., for hybrid and switched systems modeling and control).

In this paper, a neural network approach for the identification and control of a separately excited direct (DC) motor (SEDCM) driving a centrifugal pump load is applied. In this application, two radial basis function neural networks (RBFNN) are used: The first is a RBFNN identifier trained offline to emulate the dynamic performance of the DC motor-load system. The second is a RBFNN controller, which is trained to make the motor speed follow a selected reference signal. Two RBFNN control schemes are proposed using direct inverse and internal model control schemes. The performance of the RBFNN identifier and controller is investigated in terms of step response, sharp changes in speed trajectory, and sudden load change, as well as changes in motor parameters. The performance of RBFNN in system identification and control has been compared with the performance of the well-known back-propagation neural network (BPNN). The simulation results show that both of the BPNN and RBFNN controllers exhibit excellent dynamic response, adapt well to changes in speed trajectory and load connected to the motor, and adapt to the variations of motor parameters. Furthermore, the simulation results show that the step response of RBFNN internal model and direct inverse controllers are identical.

in this paper, we use an interval type-2 fuzzy logic system integrated with sliding mode control for synchronization of two different chaotic systems in presence of system unmodeling and external disturbances. To reduce the chattering and improve the robustness of reaching phase of the sliding mode control (SMC) an interval type-2 fuzzy logic controller is used. In addition, an adaptive interval type-2 fuzzy approximator is proposed (as equivalent control part of SMC) to approximate the unknown parts of the uncertain chaotic systems. Using type-2 fuzzy systems makes more effective synchronization results in presence of system uncertainty and disturbances in comparison with type-1 fuzzy systems. The stability analysis for the proposed control scheme is provided and simulation results compare the performance of proposed interval type-2 fuzzy controller with type-1 fuzzy controllers to verify the effectiveness of the proposed method.