Transformation between type-2 TSK fuzzy systems and an uncertain Gaussian mixture model

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

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.

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.

In this paper the identification and control of dynamic plants using type-2 TSK fuzzy neural system (FNS) is considered. The systems constructed on the base of type-1 fuzzy systems cannot directly handle the uncertainties associated with information or data in the knowledge base of the process. One possible way to alleviate the problem is to resort to the use of type-2 fuzzy systems. In this paper, a type-2 TSK fuzzy neural system (FNS), is proposed and its gradient learning algorithm is derived. Its performance for identification and control of time-varying plants is evaluated and compared with other approaches seen in the literature; the time-varying nature of the plants being handled as uncertainties in the plant coefficients which can be described by type-2 fuzzy sets.

Direct inverse control of cable-driven parallel system based on 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 mathematical equivalence between the conditional mean of a Epanechnikov mixture model (EMM) and the defuzzified output of a rule-centered generalized fuzzy model (RCGFM) is derived theoretically. Our results provide a new perspective for fuzzy systems, i.e., interpreting them from a probabilistic viewpoint. Thus, instead of directly estimating the parameters of the fuzzy rules in a rule-centered generalized fuzzy model, we can first estimate the parameters of the corresponding EMM using any popular density estimation algorithm like the expectation maximization (EM) algorithm. Our experimental results clearly indicate that a rule-centered generalized fuzzy model trained in such a new way has higher approximation accuracy and generalization ability than other models.

Unknown input based observer synthesis for an interval type-2 polynomial fuzzy system with time delays and uncertainties

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.

One of the main concerns in Wireless Sensor Networks is the efficient energy management of the nodes. Hierarchical techniques such as clustering have been developed in an effort to solve this problem. In this paper we present a smart evolution of a distributed clustering method that uses a turn-based scheduling cluster head selection process based on an interval Type-2 fuzzy system. The method we propose offers four main improvements. First, the setup process guided by the Base Station is adapted to tune the skip parameter during the network lifetime, which controls how many rounds the clusters are not updated. Second, the normalization of the fuzzy system input variables is carefully performed based on a statistical analysis to reduce the effect of fluctuations in edge values. Third, the value of the coefficient applied to the output of the inner Type-2 fuzzy system is updated to balance the number of cluster heads at early stages. Finally, only the strongest candidate nodes, those with the highest probability, are selected to become cluster heads. The proposed design and scheduling aim to achieve low-energy processing in the nodes. When our proposed techniques are applied, they give better results compared with other similar approaches.

Successful implementation of type-1 Fuzzy Systems (FS) in diverse application areas have been accomplished till date. Nonetheless type-1 FS are not able to handle significant amount of uncertainties present in dynamic real world applications. An improved performance against these uncertainties is achieved by type-2 FS. In this paper, a type-2 FS is proposed to remove variable gaussian noise from a number of images using multilevel two dimensional wavelet transform and multilevel soft threshold. We have displayed that the proposed type-2 FS achieve a good efficiency in removing the noise from the wavelet transformed images and also has a superior performance compared to type-1 FS.

E-learning platforms facilitate the interaction between students and instructors while mitigating temporal or spatial constraints. Nevertheless, such platforms require measuring the degree of students' engagement with the delivered course content and teaching style. Such information is highly valuable for evaluating the quality of the teaching and altering the teaching delivery style in massively crowded online learning platforms. When the number of learners is high, it is essential to attain overall engagement and feedback, yet doing so is highly challenging due to the high levels of uncertainties related to students and the learning context. To handle these uncertainties more robustly, we present a method based on type-2 fuzzy logic utilizing visual RGB-D features, including head pose direction and facial expressions captured from Kinect v2, a low-cost but robust 3D camera, to measure the engagement degree of students in both remote and on-site education. This system augments another self-learning type-2 fuzzy logic system that helps teachers with recommendations of how to adaptively vary their teaching methods to suit the level of students and enhance their instruction delivery. This proposed dynamic e-learning environment integrates both on-site and distance students as well as teachers who instruct both groups of students. The rules are learned from the students' and teachers' learning/teaching behaviors, and the system is continuously updated to give the teacher the ability to adapt the delivery approach to varied learners' engagement levels. The efficiency of the proposed system has been tested through various real-world experiments in the University of Essex iClassroom among a group of thirty students and six teachers. These experiments demonstrate the capabilities--compared to type-1 fuzzy systems and non-adaptive systems--of the proposed interval type-2 fuzzy logic-based system to handle the uncertainties and improve average learners' motivations to engage during learning.

One of the important problems of robotics is the navigation of mobile robots in uncertain environments that are densely cluttered with obstacles. The control of robots using the traditional control algorithms is not satisfactory as far as the navigational accuracy and the distance and time to reach the goal are concerned, when the robot is in a complicated surrounding. One of alternative and efficient ways of constructing a control system that explicitly deal with uncertainty is the use of fuzzy systems approach. The paper is devoted to navigation of mobile robot using type-2 fuzzy system. The design principle of navigation algorithm using type-2 fuzzy system is presented. The fuzzy knowledge base that describes the relation between the input- current angle and distance signals and output signals that determine the robot turn angle is developed. The control rules of navigation and inference engine operations have been described. The comparative simulation results of robot navigation system demonstrate the advantage of the fuzzy navigation algorithm.

This article proposes a type-2 fuzzy system that works on the different spatio-temporal features (obtained by analyzing stills captured from surveillance videos) and uses it to differentiate a pedestrian from a human, a human from non-human etc. Existing systems propose a solution based on factors that can be influenced by several other environmental factors, for example data captured at infrared spectrum are influenced by weather conditions. Moreover, existing systems often neglect the differences between a human and a pedestrian. In this proposed work we propose a method specifying differences between non-human, human, and pedestrian as a case of human showing locomotion features in temporal domain. To achieve this, we have considered a type-2 fuzzy system because rather than calculating the probability of a subject being a human(human being pedestrian) we assess the subset of features that determine the subject’s chances of being a human (human’s chances of being a pedestrian), thereby emphasizing the need for a type-2 fuzzy system. Here the crisp output set is assumed to be {Pedestrian, Human, and Non-Human}. The achieved results are motivating towards these precise classifications and the use of fuzzy systems for the same.