A review on type-2 fuzzy logic applications in clustering,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. At the moment, most of the applications in this review use interval type-2 fuzzy logic, which is easier to handle and less computational expensive than generalized type-2 fuzzy logic.     

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.     

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.     

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     

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.     

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.     

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.     

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 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.     

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.

     

模糊控制理论在继电保护领域的可行性研究及其实现

本文简单阐述了继电保护的发展现状,研究了模糊逻辑与模糊模式识别在电力系统继电保护领域重合闸环节中的应用,并且提出了基于模糊综合决策的自动重合闸控制过程及其实现步骤,以提高重合闸的成功率。     

Interval type-2 fuzzy logic and modular neural networks for face recognition applications

In this paper we present a method for response integration in multi-net neural systems using interval type-2 fuzzy logic and fuzzy integrals, with the purpose of improving the performance in the solution of problems with a great volume of information. The method can be generalized for pattern recognition and prediction problems, but in this work we show the implementation and tests of the method applied to the face recognition problem using modular neural networks. In the application we use two interval type-2 fuzzy inference systems (IT2-FIS); the first IT2-FIS was used for feature extraction in the training data, and the second one to estimate the relevance of the modules in the multi-net system. Fuzzy logic is shown to be a tool that can help improve the results of a neural system by facilitating the representation of human perceptions.     

On type-reduction of type-2 fuzzy sets: A review

As an undetachable module of type-2 (T2) fuzzy computations and reasoning, type-reduction methods play an important role in various fuzzy disciplines including fuzzy logic systems and fuzzy clustering. Importance of type-reduction techniques lies in the fact that they are the main tools for collecting the entire inherent vagueness of the data. Therefore, type-reduction methods form the output of type-2 fuzzy sets (T2 FSs) as the representative of the entire uncertainty in a given space. Hence, their accuracy, precision, and performance speed is of much interest. This paper, presents a comprehensive review on various type-reduction and defuzzification strategies for general and interval type-2 fuzzy sets and systems. It is tried to analyze the existing approaches from different point of views accompanied by extensive comparisons on different features of type-reduction methods to facilitate further research studies by the fuzzy community.     

二型模糊相似度及其应用

二型模糊集可以直接处理高度不确定性,并且具有很强的实际应用背景。基于二型模糊相似度的公理化定义,给出了新的二型模糊相似度计算公式。进一步,将二型模糊相似度与Yang-Shih方法相结合,用于二型模糊数据的聚类分析,聚类结果与Yang-Lin的结果进行了比较,实例表明新的相似度更合理。此外,基于二型模糊相似度,讨论了二型模糊信息系统的属性约简问题,给出了相应约简的分辨函数法,并通过实例说明了该方法的具体计算步骤。     

Dual-centers type-2 fuzzy clustering framework and its verification and validation indices

In this paper we present a clustering framework for type-2 fuzzy clustering which covers all steps of the clustering process including: clustering algorithm, parameters estimation, and validation and verification indices. The proposed clustering algorithm is developed based on dual-centers type-2 fuzzy clustering model. In this model the centers of clusters are defined by a pair of objects rather than a single object. The membership values of the objects to the clusters are defined by type-2 fuzzy numbers and there are not any type reduction or defuzzification steps in the proposed clustering algorithm. In addition, the relation among the size of the cluster bandwidth, distance between dual-centers and fuzzifier parameter are indicated and analyzed to facilitate the parameters estimation step. To determine the optimum number of clusters, we develop a new validation index which is compatible with the proposed model structure. A new compatible verification index is also defined to compare the results of the proposed model with existing type-1 fuzzy clustering model. Finally, the results of computational experiments are presented to show the efficiency of the proposed approach.     

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 Fuzzy Logic: A Historical View

Type-2 fuzzy logic offers an opportunity to model levels of uncertainty with which traditional fuzzy logic (type-1) struggles. This article provides a historical perspective of the development of type-2 fuzzy logic with a retrospective review of important developments in the field. We discuss key questions about the technology such as - when should type-2 systems be used? and why has it taken so long for this technology to emerge? The article concludes by highlighting areas where, we believe, type-2 fuzzy logic will have a significant role to play in the future     

Rotation, scale and translation invariant handwritten Devanagari numeral character recognition using general fuzzy neural network

In this paper a general fuzzy hyperline segment neural network is proposed [P.M. Patil, Pattern classification and clustering using fuzzy neural networks, Ph.D. Thesis, SRTMU, Nanded, India, January 2003]. It combines supervised and unsupervised learning in a single algorithm so that it can be used for pure classification, pure clustering and hybrid classification/clustering. The method is applied to handwritten Devanagari numeral character recognition and also to the Fisher Iris database. High recognition rates are achieved with less training and recall time per pattern. The algorithm is rotation, scale and translation invariant. The recognition rate with ring data features is found to be 99.5%.     

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.