A review on the applications of type-2 fuzzy logic in classification and pattern recognition

In this paper a review of type-2 fuzzy logic applications in pattern recognition, classification and clustering problems is presented. Recently, type-2 fuzzy logic has gained popularity in a wide range of applications due to its ability to handle higher degrees of uncertainty. In particular, there have been recent applications of type-2 fuzzy logic in the fields of pattern recognition, classification and clustering, where it has helped improving results over type-1 fuzzy logic. In this paper a concise and representative review of the most successful applications of type-2 fuzzy logic in these fields is presented.     

Application of interval type-2 fuzzy neural networks in non-linear identification and time series prediction

Neural networks (NNs), type-1 fuzzy logic systems and interval type-2 fuzzy logic systems (IT2FLSs) have been shown to be important methods in real world applications, which range from pattern recognition, time series prediction, to intelligent control. Recent research shows that embedding an IT2FLS on an NN can be very effective for a wide number of non-linear complex systems, especially when handling imperfect or incomplete information. In this paper we are presenting several models of interval type-2 fuzzy neural networks (IT2FNNs) that use a set of rules and interval type-2 membership functions for that purpose. Simulation results of non-linear function identification using the IT2FNN for one and three variables and for the Mackey–Glass chaotic time series prediction are presented to illustrate that the proposed models have potential for real world applications.     

增强型区间二型FCM算法

不确定性存在于图像处理、模式识别等众多领域的实际应用中, 模糊?? 均值聚类(FCM) 算法虽广泛应用于这些领域, 但其处理不确定性的能力较差. 引入区间二型模糊理论能有效提升算法处理不确定性的能力, 但相应地造成算法复杂度增加, 制约了区间二型FCM算法的推广应用. 鉴于此, 提出增强型区间二型FCM算法, 通过优化初始聚类中心和降型运算, 极大地减少了区间二型FCM算法的运算量, 并提升算法的收敛速度. 通过对随机和实际数据的实验比较验证了改进算法的有效性.

     

Experimental study of intelligent controllers under uncertainty using type-1 and type-2 fuzzy logic

Uncertainty is an inherent part in control systems used in real world applications. The use of new methods for handling incomplete information is of fundamental importance. Type-1 fuzzy sets used in conventional fuzzy systems cannot fully handle the uncertainties present in control systems. Type-2 fuzzy sets that are used in type-2 fuzzy systems can handle such uncertainties in a better way because they provide us with more parameters and more design degrees of freedom. This paper deals with the design of control systems using type-2 fuzzy logic for minimizing the effects of uncertainty produced by the instrumentation elements, environmental noise, etc. The experimental results are divided in two classes, in the first class, simulations of a feedback control system for a non-linear plant using type-1 and type-2 fuzzy logic controllers are presented; a comparative analysis of the systems’ response in both cases was performed, with and without the presence of uncertainty. For the second class, a non-linear identification problem for time-series prediction is presented. Based on the experimental results the conclusion is that the best results are obtained using type-2 fuzzy systems.     

Type-2 FLCs: A New Generation of Fuzzy Controllers

Type-1 fuzzy logic controllers (FLCs) have been applied to date with great success to many different applications. However, for dynamic unstructured environments and many real-world applications, there is a need to cope with large amounts of uncertainties. The traditional type-1 FLC using crisp type-1 fuzzy sets cannot directly handle such uncertainties. A type-2 FLC using type-2 fuzzy sets can handle such uncertainties to produce a better performance. Hence, type-2 FLCs will have the potential to overcome the limitations of type-1 FLCs and produce a new generation of fuzzy controllers with improved performance for many applications, which require handling high levels of uncertainty. This paper introduces briefly the interval type-2 FLC and its benefits. We also present briefly the type-2 FLC application to three challenging domains: industrial control, mobile robots control and ambient intelligent environments control     

Type-2 fuzzy logic-based classifier fusion for support vector machines

As a machine-learning tool, support vector machines (SVMs) have been gaining popularity due to their promising performance. However, the generalization abilities of SVMs often rely on whether the selected kernel functions are suitable for real classification data. To lessen the sensitivity of different kernels in SVMs classification and improve SVMs generalization ability, this paper proposes a fuzzy fusion model to combine multiple SVMs classifiers. To better handle uncertainties existing in real classification data and in the membership functions (MFs) in the traditional type-1 fuzzy logic system (FLS), we apply interval type-2 fuzzy sets to construct a type-2 SVMs fusion FLS. This type-2 fusion architecture takes considerations of the classification results from individual SVMs classifiers and generates the combined classification decision as the output. Besides the distances of data examples to SVMs hyperplanes, the type-2 fuzzy SVMs fusion system also considers the accuracy information of individual SVMs. Our experiments show that the type-2 based SVM fusion classifiers outperform individual SVM classifiers in most cases. The experiments also show that the type-2 fuzzy logic-based SVMs fusion model is better than the type-1 based SVM fusion model in general.     

Uncertain Fuzzy Clustering: Interval Type-2 Fuzzy Approach to C-Means

In many pattern recognition applications, it may be impossible in most cases to obtain perfect knowledge or information for a given pattern set. Uncertain information can create imperfect expressions for pattern sets in various pattern recognition algorithms. Therefore, various types of uncertainty may be taken into account when performing several pattern recognition methods. When one performs clustering with fuzzy sets, fuzzy membership values express assignment availability of patterns for clusters. However, when one assigns fuzzy memberships to a pattern set, imperfect information for a pattern set involves uncertainty which exist in the various parameters that are used in fuzzy membership assignment. When one encounters fuzzy clustering, fuzzy membership design includes various uncertainties (e.g., distance measure, fuzzifier, prototypes, etc.). In this paper, we focus on the uncertainty associated with the fuzzifier parameter m that controls the amount of fuzziness of the final C-partition in the fuzzy C-means (FCM) algorithm. To design and manage uncertainty for fuzzifier m, we extend a pattern set to interval type-2 fuzzy sets using two fuzzifiers m₁ and m₂ which creates a footprint of uncertainty (FOU) for the fuzzifier m. Then, we incorporate this interval type-2 fuzzy set into FCM to observe the effect of managing uncertainty from the two fuzzifiers. We also provide some solutions to type-reduction and defuzzification (i.e., cluster center updating and hard-partitioning) in FCM. Several experimental results are given to show the validity of our method     

On neurobiological, neuro-fuzzy, machine learning, and statisticalpattern recognition techniques

In this paper, we propose two new neuro-fuzzy schemes, one for classification and one for clustering problems. The classification scheme is based on Simpson's fuzzy min-max method (1992, 1993) and relaxes some assumptions he makes. This enables our scheme to handle mutually nonexclusive classes. The neuro-fuzzy clustering scheme is a multiresolution algorithm that is modeled after the mechanics of human pattern recognition. We also present data from an exhaustive comparison of these techniques with neural, statistical, machine learning, and other traditional approaches to pattern recognition applications. The data sets used for comparisons include those from the machine learning repository at the University of California, Irvine. We find that our proposed schemes compare quite well with the existing techniques, and in addition offer the advantages of one-pass learning and online adaptation.     

A simple design method for interval type-2 fuzzy pid controllers

In this study, a design method for single Input interval type-2 fuzzy PID controller has been developed. The most important feature of the proposed type-2 fuzzy controller is its simple structure consisting of a single input variable. The presented simple structure gives an opportunity to the designer to form the type-2 fuzzy controller output in closed form formulation for the first time in literature. This formulation cannot be achieved with present type-2 fuzzy PID controller structures which have employed the Karnik-Mendel type reduction. The closed form solution is derived in terms of the tuning parameters which are chosen as the heights of lower membership functions of the antecedent interval type-2 fuzzy sets. Elaborations are done on the derived closed form output and a simple strategy is presented for a single input type-2 fuzzy PID controller design. The presented interval type-2 fuzzy controller structure still keeps the most preferred features of the PID controller such as simplicity and easy design. We will illustrate how the extra degrees of freedom provided by the antecedent interval type-2 fuzzy sets can be used to enhance the control performance on linear and nonlinear benchmark systems by simulations. Moreover, the type-2 fuzzy controller structure has been implemented on experimental pH neutralization. The simulation and experimental results will illustrate that the proposed type-2 fuzzy controller produces superior control performance and can handle nonlinear dynamics, parameter uncertainties, noise and disturbances better in comparison with the standard PID controllers. Hence, the results and analyses of this study will give the control engineers an opportunity to draw a bridge and connect the type-2 fuzzy logic and control theory.     

Optimal design of adaptive type-2 neuro-fuzzy systems: A review

Type-2 fuzzy logic systems have extensively been applied to various engineering problems, e.g. identification, prediction, control, pattern recognition, etc. in the past two decades, and the results were promising especially in the presence of significant uncertainties in the system. In the design of type-2 fuzzy logic systems, the early applications were realized in a way that both the antecedent and consequent parameters were chosen by the designer with perhaps some inputs from some experts. Since 2000s, a huge number of papers have been published which are based on the adaptation of the parameters of type-2 fuzzy logic systems using the training data either online or offline. Consequently, the major challenge was to design these systems in an optimal way in terms of their optimal structure and their corresponding optimal parameter update rules. In this review, the state of the art of the three major classes of optimization methods are investigated: derivative-based (computational approaches), derivative-free (heuristic methods) and hybrid methods which are the fusion of both the derivative-free and derivative-based methods.     

Type-2 fuzzy neural networks with fuzzy clustering and differential evolution optimization

In many real-world problems involving pattern recognition, system identification and modeling, control, decision making, and forecasting of time-series, available data are quite often of uncertain nature. An interesting alternative is to employ type-2 fuzzy sets, which augment fuzzy models with expressive power to develop models, which efficiently capture the factor of uncertainty. The three-dimensional membership functions of type-2 fuzzy sets offer additional degrees of freedom that make it possible to directly and more effectively account for model’s uncertainties. Type-2 fuzzy logic systems developed with the aid of evolutionary optimization forms a useful modeling tool subsequently resulting in a collection of efficient “If-Then” rules.The type-2 fuzzy neural networks take advantage of capabilities of fuzzy clustering by generating type-2 fuzzy rule base, resulting in a small number of rules and then optimizing membership functions of type-2 fuzzy sets present in the antecedent and consequent parts of the rules. The clustering itself is realized with the aid of differential evolution.Several examples, including a benchmark problem of identification of nonlinear system, are considered. The reported comparative analysis of experimental results is used to quantify the performance of the developed networks.     

Type-2 fuzzy hidden Markov models and their application to speech recognition

This paper presents an extension of hidden Markov models (HMMs) based on the type-2 (T2) fuzzy set (FS) referred to as type-2 fuzzy HMMs (T2 FHMMs). Membership functions (MFs) of T2 FSs are three-dimensional, and this new third dimension offers additional degrees of freedom to evaluate the HMMs fuzziness. Therefore, T2 FHMMs are able to handle both random and fuzzy uncertainties existing universally in the sequential data. We derive the T2 fuzzy forward-backward algorithm and Viterbi algorithm using T2 FS operations. In order to investigate the effectiveness of T2 FHMMs, we apply them to phoneme classification and recognition on the TIMIT speech database. Experimental results show that T2 FHMMs can effectively handle noise and dialect uncertainties in speech signals besides a better classification performance than the classical HMMs.     

Type-2 fuzzy modeling for desulphurization of steel process

This paper presents a new type-2 fuzzy logic system model for desulphurization process of a real steel industry in Canada. The type-2 fuzzy logic system permits us to model rule uncertainties where every membership value of an element has a second order membership value of its own. In this paper, we propose an indirect method to create second order membership grades that are amplitudes of type-2 secondary membership functions, where the primary memberships are extracted by implementation of fuzzy clustering approach. In this research, Gaussian Mixture Model (GMM) is used for the creation of second order membership grades. Furthermore, a reduction scheme is implemented which results in type-1 membership grades. In turn, this leads to a reduction of the complexity of the system. Two methods are used for the estimation of the membership functions: indirect and direct methods. In the indirect method, the system uses an interpolation scheme for the estimation of the most appropriate membership functions. In the direct method, the system is tuned by an inference algorithm for the optimization of the main parametric system. In this case, the parameters are: Schweizer and Sklar t-norm and s-norm, combination of FATI and FITA inference approaches, and Yager defuzzification. Finally, the system model is applied to the desulphurization process of a real steel industry in Canada. It is shown that the proposed type-2 fuzzy logic system is superior in comparison to multiple regression and type-1 fuzzy logic systems in terms of robustness, and error reduction.     

改进模糊划分的FCM聚类算法的一般化研究

聚类分析是无监督模式识别中的一种重要方法,已广泛应用于数据挖掘、图像处理、计算机视觉、生物信息和文本分析中.在聚类算法中,模糊指数m对聚类结果有十分重要的影响.针对IFP-FCM算法模糊指数m被限定为2的问题,提出了一般化的改进模糊划分的FCM聚类算法GIFP-FCM.通过引入新的隶属度约束,解决了IFP-FCM算法模糊指数m的一般化问题;同时GIFP-FCM算法从Voronoi距离和竞争学习的角度对其鲁棒性和快速收敛性进行了合理解释;其次,通过引入模糊程度系数α,使得FCM算法和IFP-FCM算法分别表示为GIFP-FCM算法在α等于0和α趋于1时的特例.实验结果表明,GIFP-FCM算法较之于IFP-FCM和FCM算法具有更好的鲁棒性和参数适应性;在纹理图像分割中,GIFP-FCM也明显优于IFP-FCM和FCM算法.     

Type-1 and type-2 fuzzy inference systems as integration methods in modular neural networks for multimodal biometry and its optimization with genetic algorithms

We describe in this paper a comparative study between fuzzy inference systems as methods of integration in modular neural networks for multimodal biometry. These methods of integration are based on techniques of type-1 fuzzy logic and type-2 fuzzy logic. Also, the fuzzy systems are optimized with simple genetic algorithms with the goal of having optimized versions of both types of fuzzy systems. First, we considered the use of type-1 fuzzy logic and later the approach with type-2 fuzzy logic. The fuzzy systems were developed using genetic algorithms to handle fuzzy inference systems with different membership functions, like the triangular, trapezoidal and Gaussian; since these algorithms can generate fuzzy systems automatically. Then the response integration of the modular neural network was tested with the optimized fuzzy systems of integration. The comparative study of the type-1 and type-2 fuzzy inference systems was made to observe the behavior of the two different integration methods for modular neural networks for multimodal biometry.     

A hybrid approach for image recognition combining type-2 fuzzy logic, modular neural networks and the Sugeno integral

In this paper, a hybrid approach for image recognition combining type-2 fuzzy logic, modular neural networks and the Sugeno integral is described. Interval type-2 fuzzy inference systems are used to perform edge detection and to calculate fuzzy densities for the decision process. A type-2 fuzzy system is used for edge detection, which is a pre-processing applied to the training data for better use in the neural networks. Another type-2 fuzzy system calculates the fuzzy densities necessary for the Sugeno integral, which is used to integrate results of the neural network modules. In this case, fuzzy logic is shown to be a good methodology to improve the results of a neural system facilitating the representation of the human perception. A comparative study is also made to verify that the proposed approach is better than existing approaches and improves the performance over type-1 fuzzy logic.     

Optimization of interval type-2 fuzzy logic controllers using evolutionary algorithms

A method for designing optimal interval type-2 fuzzy logic controllers using evolutionary algorithms is presented in this paper. Interval type-2 fuzzy controllers can outperform conventional type-1 fuzzy controllers when the problem has a high degree of uncertainty. However, designing interval type-2 fuzzy controllers is more difficult because there are more parameters involved. In this paper, interval type-2 fuzzy systems are approximated with the average of two type-1 fuzzy systems, which has been shown to give good results in control if the type-1 fuzzy systems can be obtained appropriately. An evolutionary algorithm is applied to find the optimal interval type-2 fuzzy system as mentioned above. The human evolutionary model is applied for optimizing the interval type-2 fuzzy controller for a particular non-linear plant and results are compared against an optimal type-1 fuzzy controller. A comparative study of simulation results of the type-2 and type-1 fuzzy controllers, under different noise levels, is also presented. Simulation results show that interval type-2 fuzzy controllers obtained with the evolutionary algorithm outperform type-1 fuzzy controllers.     

Optimization of interval type-2 fuzzy systems for image edge detection

This paper presents the optimization of a fuzzy edge detector based on the traditional Sobel technique combined with interval type-2 fuzzy logic. The goal of using interval type-2 fuzzy logic in edge detection methods is to provide them with the ability to handle uncertainty in processing real world images. However, the optimal design of fuzzy systems is a difficult task and for this reason the use of meta-heuristic optimization techniques is also considered in this paper. For the optimization of the fuzzy inference systems, the Cuckoo Search (CS) and Genetic Algorithms (GAs) are applied. Simulation results show that using an optimal interval type-2 fuzzy system in conjunction with the Sobel technique provides a powerful edge detection method that outperforms its type-1 counterparts and the pure original Sobel technique.     

Dynamic parameter adaptation in particle swarm optimization using interval type-2 fuzzy logic

In this paper, we propose a new method for dynamic parameter adaptation in particle swarm optimization (PSO). PSO is an optimization method inspired in social behavior, which has been applied to different optimization problems obtaining good results. In this paper, we propose an improvement to the convergence and diversity of the swarm in PSO using interval type-2 fuzzy logic. Simulation results show that the proposed approach improves the performance of PSO. A comparison of the proposed method using type-2 fuzzy logic with the original PSO approach, and with PSO using type-1 fuzzy logic for dynamic parameter adaptation is presented.     

Type-2 hierarchical fuzzy system for high-dimensional data-based modeling with uncertainties

A type-2 hierarchical fuzzy system (T2HFS) is presented for the high-dimensional data-based modeling with uncertainties. Type-2 fuzzy logic system (T2FLS) is a powerful tool to handle uncertainties in complex processes. However, the operation of type-reduction has greatly increased the computational burden of T2FLSs. By integrating the T2FLS with hierarchical structure, a systematic design methodology of T2HFS is proposed to avoid the rule explosion and to simplify the computation complexity. The design methodology has included several procedures to establish the T2HFS. Firstly, the PCA-based method is developed to capture the prominent component from training data, and to determine the hierarchical structure of T2HFS. Furthermore, a novel clustering method is proposed to design the basic type-2 fuzzy logic unit (T2FLU) in uncertain environments. Finally, a hybrid-learning method is presented to fine-tune the parameters for the global optimization where the statistical and deterministic optimization methods are developed for the nominal and auxiliary performance, respectively. Simulation results have shown that the proposed T2HFS is very effective for the high-dimensional data-based modeling and control in uncertain environment.