Generating Type 2 Trapezoidal Fuzzy Membership Function Using Genetic Tuning

Fuzzy inference system (FIS) is a process of fuzzy logic reasoning to produce the output based on fuzzified inputs. The system starts with identifying input from data, applying the fuzziness to input using membership functions (MF), generating fuzzy rules for the fuzzy sets and obtaining the output. There are several types of input MFs which can be introduced in FIS, commonly chosen based on the type of real data, sensitivity of certain rule implied and computational limits. This paper focuses on the construction of interval type 2 (IT2) trapezoidal shape MF from fuzzy C Means (FCM) that is used for fuzzification process of mamdani FIS. In the process, upper MF (UMF) and lower MF (LMF) of the MF need to be identified to get the range of the footprint of uncertainty (FOU). This paper proposes Genetic tuning process, which is a part of genetic algorithm (GA), to adjust parameters in order to improve the behavior of existing system, especially to enhance the accuracy of the system model. This novel process is a hybrid approach which produces Genetic Fuzzy System (GFS) that helps to enhance fuzzy classification problems and performance. The approach provides a new method for the construction and tuning process of the IT2 MF, based on the FCM outcomes. The result is compared to Gaussian shape IT2 MF and trapezoid IT2 MF generated by the classic GA method. It is shown that the proposed approach is able to outperform the mentioned benchmarked approaches. The work implies a wider range of IT2 MF types, constructed based on FCM outcomes, and an optimum generation of the FOU so that it can be implemented in practical applications such as prediction, analytics and rule-based solutions.     

A novel brain image segmentation using intuitionistic fuzzy C means algorithm

A process of splitting the image into pixel bands is the image segmentation. As medical imaging contain uncertainties, there are difficulties in classification of images into homogeneous regions. There is a need for segmentation algorithm for removing the noise from the medical image segmentation. The very popular algorithm is Fuzzy C‐Means (FCM) algorithm used for image segmentation. Fuzzy sets, rough sets, and the combination of fuzzy and rough sets play a prominent role in formalizing uncertainty, vagueness, and incompleteness in diagnosis. But it will use intensity values only which will be highly sensitive to noise. In this article, an Intuitionistic FCM (IFCM) algorithm is presented for clustering. Intuitionistic fuzzy (IF) sets are generalized sets and their elements are characterized by a membership value as well as nonmembership value. This IFCM has an uncertainty parameter which is called hesitation degree and a new objective function is integrated in the standard FCM based on IF entropy. The IFCM will provide better performance than FCM for image segmentation.     

Fuzzy clustering-based image segmentation techniques used to segment magnetic resonance imaging/computed tomography scan brain tissues: Comparative analysis

Medical images are obtained with computer-aided diagnosis using electronic devices such as CT scanners and MRI machines. The captured computed tomography (CT)/magnetic resonance imaging (MRI) images typically have limited spatial resolution, low contrast, noise and nonuniform variability in intensity due to environmental effects. Therefore, the distinctions of the objects are blurred, distorted and the meanings of the objects are not quite precise. Fuzzy sets and fuzzy logic are best suited for addressing vagueness and ambiguity. Fuzzy clustering technique has been commonly used for segmentation of images throughout the last decade. This study presents a comparative study of 14 fuzzy-clustered image segmentation algorithms used in the CT scan and MRI brain image segments. This study used 17 data sets including 4 synthetic data sets, namely, Bensaid, Diamond, Square, and its noisy version, 5 real-world digital images, and 8 CT scan/MRI brain images to analyze the algorithms. Ground truth images are used for qualitative analysis. Apart from the qualitative analysis, the study also quantitatively evaluated the methods using three validity metrics, namely, partition coefficient, partition entropy, and Fukuyama-Sugeno. After a thorough and careful review of the results, it is observed that extension of the fuzzy C-means (EFCM) outperformed every other image segmentation algorithm, even in a noisy environment, followed by kernel-based FCM σ, the output of which is also very good after EFCM.     

Uncertain Knowledge Reasoning Based on the Fuzzy Multi Entity Bayesian Networks

With the rapid development of the semantic web and the ever-growing size of uncertain data, representing and reasoning uncertain information has become a great challenge for the semantic web application developers. In this paper, we present a novel reasoning framework based on the representation of fuzzy PR-OWL. Firstly, the paper gives an overview of the previous research work on uncertainty knowledge representation and reasoning, incorporates Ontology into the fuzzy Multi Entity Bayesian Networks theory, and introduces fuzzy PR-OWL, an Ontology language based on OWL2. Fuzzy PR-OWL describes fuzzy semantics and uncertain relations and gives grammatical definition and semantic interpretation. Secondly, the paper explains the integration of the Fuzzy Probability theory and the Belief Propagation algorithm. The influencing factors of fuzzy rules are added to the belief that is propagated between the nodes to create a reasoning framework based on fuzzy PR-OWL. After that, the reasoning process, including the SSFBN structure algorithm, data fuzzification, reasoning of fuzzy rules, and fuzzy belief propagation, is scheduled. Finally, compared with the classical algorithm from the aspect of accuracy and time complexity, our uncertain data representation and reasoning method has higher accuracy without significantly increasing time complexity, which proves the feasibility and validity of our solution to represent and reason uncertain information.     

An improved fuzzy clustering method for cellular manufacturing

Fuzzy c-means (FCM) has been successfully adapted to solve the manufacturing cell formation problem. However, when the problem becomes larger and especially if the data is ill structured, the FCM may result in clustering errors, infeasible solutions, and uneven distribution of parts/machines. In this paper, an improved fuzzy clustering algorithm is proposed to overcome the deficiencies of FCM. We tested the effects of algorithm parameters and compared its performance with the original and two popular FCM modifications. Our study shows that the proposed approach outperformed other alternatives. Most of the solutions it obtained are close to and in some cases better than the control solutions.     

Performance of Fuzzy ART neural network and hierarchical clustering for part-machine grouping based on operation sequences

The problem context for this study is one of identifying families of parts having a similar sequence of operations. This is a prerequisite for the implementation of cellular manufacturing, group technology, just-in-time manufacturing systems and for streamlining material flows in general. Given this problem context, this study develops an experimental procedure to compare the performance of a fuzzy ART neural network, a relatively recent neural network method, with the performance of traditional hierarchical clustering methods. For large, industry-type data sets, the fuzzy ART network, with the modifications proposed here, is capable of performance levels equal or superior to those of the widely used hierarchical clustering methods. However, like other ART networks, Fuzzy ART also results in category proliferation problems, an aspect that continues to require attention for ART networks. However, low execution times and superior solution quality make fuzzy ART a useful addition to the set of tools and techniques now available for group technology and design of cellular manufacturing systems.     

Information Theoretic Weighted Fuzzy Clustering Ensemble

In order to improve performance and robustness of clustering, it is proposed to generate and aggregate a number of primary clusters via clustering ensemble technique. Fuzzy clustering ensemble approaches attempt to improve the performance of fuzzy clustering tasks. However, in these approaches, cluster (or clustering) reliability has not paid much attention to. Ignoring cluster (or clustering) reliability makes these approaches weak in dealing with low-quality base clustering methods. In this paper, we have utilized cluster unreliability estimation and local weighting strategy to propose a new fuzzy clustering ensemble method which has introduced Reliability Based weighted co-association matrix Fuzzy C-Means (RBFCM), Reliability Based Graph Partitioning (RBGP) and Reliability Based Hyper Clustering (RBHC) as three new fuzzy clustering consensus functions. Our fuzzy clustering ensemble approach works based on fuzzy cluster unreliability estimation. Cluster unreliability is estimated according to an entropic criterion using the cluster labels in the entire ensemble. To do so, the new metric is defined to estimate the fuzzy cluster unreliability; then, the reliability value of any cluster is determined using a Reliability Driven Cluster Indicator (RDCI). The time complexities of RBHC and RBGP are linearly proportional with the number of data objects. Performance and robustness of the proposed method are experimentally evaluated for some benchmark datasets. The experimental results demonstrate efficiency and suitability of the proposed method.     

模糊聚类分析在模糊神经网络结构优化中的应用

研究了模糊聚类分析在多变量模糊神经网络的结构确定中的应用,在传统的模糊C－均值算法的基础上,给出了一个衡量聚类有效性的函数和确定模糊指数的启发式方法,并给出了应用该算法的具体的模糊神经网络模型。     

Fault Pattern Recognition based on Kernel Method and Fuzzy C-means

A method about fault identification is proposed to solve the relationship among fault features of large rotating machinery,which is extremely complicated and nonlinear. This paper studies the rotor test-rig and the clustering of data sets and fault pattern recognitions. The present method firstly maps the data from their original space to a high dimensional Kernel space which makes the highly nonlinear data in low-dimensional space become linearly separable in Kernel space. It highlights the differences among the features of the data set. Then fuzzy C-means( FCM) is conducted in the Kernel space. Each data is assigned to the nearest class by computing the distance to the clustering center. Finally,test set is used to judge the results. The convergence rate and clustering accuracy are better than traditional FCM. The study shows that the method is effective for the accuracy of pattern recognition on rotating machinery.     

模拟退火与模糊C-均值聚类相结合的图像分割算法

模糊C-均值(FCM)聚类算法是一种结合无监督聚类和模糊集合概念的图像分割技术,比较有效,但存在着受初始聚类中心和隶属度矩阵影响,可能收敛到局部极小的缺点.将模拟退火算法(SA)与模糊C-均值聚类算法相结合,在合理选择冷却进度表的基础上,依据模糊C-均值聚类算法建立模拟退火算法的目标函数,实现了基于模拟退火的模糊C-均值聚类图像分割算法.实验表明,该方法具有搜索全局最优解的能力,因而可得到很好的图像分割结果.     

量子蚁群模糊聚类算法在图像分割中的应用

针对模糊C-均值算法对初始值的依赖,容易陷入局部最优值的缺点,本文提出将量子蚁群算法与FCM聚类算法结合,首先利用量子蚁群算法的全局性和鲁棒性以及快速收敛的优点确定图像的初始聚类中心和聚类个数,再将所得结果作为FCM聚类算法的初始参数,然后用FCM聚类算法对医学图像进行分割。实验结果表明,该方法有效解决了FCM算法对初始参数的依赖,克服了FCM算法及蚁群算法容易陷入局部极值的的缺点,而且在分割速度和精度上得到了较大提高。     

基于FCM优化的平面阵列电容成像算法

为提高平面阵列电容成像系统的成像精度,提出了一种基于FCM数据优化的成像算法。根据平面阵列电极电容数据的特点,为减小电容测量误差对介电常数的影响,利用FCM算法对测量电容值的不断收敛以实现数据优化的作用,在减弱噪声的同时提高电容值数据的稳定性。在此基础上,对一种隔热材料胶层进行缺陷检测实验,使重建图像的相关系数得到了提高,减小了图像重建误差。实验结果表明:图像重建结果的优化算法可获得更加稳定、有效的电容数据,胶层缺陷图像重建精度具有较大提升。     

模糊关系方程的解的模糊遗传寻优算法

在一般遗传算法ＧＡ的基础上，基于模糊集理论中的模糊关系方程的解的寻优问题提出了模糊遗传算法ＦＧＡ，它能有效地找出模糊关系方程的解的寻优问题的近似最优解。还给出了一个重要的定理：模糊模式定理。     

基于模糊C均值聚类算法的金刚石砂轮磨粒边缘检测

基于模糊C均值(FCM)聚类算法将金刚石砂轮表面检测数据划分成金刚石和结合剂两个类别,以数据的质心初始化聚类中心,用迭代的方法分别求出相应的最优聚类中心和隶属度矩阵,通过选取合适的隶属度阈值以及两个聚类中心的欧氏距离阈值来区分金刚石和结合剂,确定磨粒边缘。为验证方法的可行性,对多组数据进行检测,并用模拟的砂轮表面形貌对此方法进行了评定,评定结果与设定值误差不超过2.0%。     

Fuzzy C-Means Algorithm Automatically Determining Optimal Number of Clusters

In clustering analysis, the key to deciding clustering quality is to determine the optimal number of clusters. At present, most clustering algorithms need to give the number of clusters in advance for clustering analysis of the samples. How to gain the correct optimal number of clusters has been an important topic of clustering validation study. By studying and analyzing the FCM algorithm in this study, an accurate and efficient algorithm used to confirm the optimal number of clusters is proposed for the defects of traditional FCM algorithm. For time and clustering accuracy problems of FCM algorithm and relevant algorithms automatically determining the optimal number of clusters, kernel function, AP algorithm and new evaluation indexes were applied to improve the confirmation of complexity and search the scope of traditional fuzzy C-means algorithm, and evaluation of clustering results. Besides, three groups of contrast experiments were designed with different datasets for verification. The results showed that the improved algorithm improves time efficiency and accuracy to certain degree.     

Performance of Fuzzy ART neural network for group technology cell formation

This study investigates the performance of Fuzzy ART neural network for grouping parts and machines, as part of the design of cellular manufacturing systems. Fuzzy ART is compared with ART1 neural network and a modification to ART1, along with direct clustering analysis (DCA) and rank order clustering (ROC2) algorithms. A series of replicated clustering experiments were performed, and the efficiency and consistency with which clusters were identified were examined, using large data sets of differing sizes and degrees of imperfection. The performance measures included the recovery ratio of bond energy and execution times, It is shown that Fuzzy ART neural network results in better and more consistent identification of block diagonal structures than ART1, a recent modification to ART1, as well as DCA and ROC2. The execution times were found to be more than those of ART1 and modified ART1, but they were still superior to traditional algorithms for large data sets.     

模糊神经网络在钛合金研究领域中的应用

模糊神经网络具有较强的非线性问题处理能力,可直接处理"不确定性"结构化知识,已成为材料科学研究领域中重要的使用技术。综述了模糊神经网络在钛合金材料化学成分设计与优化、材料成分与性能关系、微观组织定量研究等领域的应用情况,指出将该方法应用于钛合金材料研究领域,不仅可精确地描述材料成分-工艺-组织-性能之间高度复杂非线性关系,而且能够应用到材料加工的智能控制以及性能预测等领域。     

基于遗传模糊C-均值聚类算法的除湿机故障诊断

针对除湿机系统的故障诊断问题及其特点,以CFTZ21型除湿机为对象,应用模糊C-均值聚类（FCM）算法进行了研究;引入遗传算法对传统模糊C-均值聚类算法进行了改进,克服了传统算法的不足;结合实验采集到的数据样本,对改进后的遗传模糊C-均值聚类算法进行检验,结果达到预期效果,由此说明,将改进的FCM应用于除湿机故障诊断是可行的。     

Adaptive Fuzzy C-Means clustering in process monitoring

Quite often, quality control models fail because, e.g., the mean values are changing continuously. These kinds of changes, e.g., process drifts due to seasonal fluctuations, are common in an activated sludge waste-water treatment plant in Finland. Different Fuzzy C-Means (FCM) clustering algorithms were tested in order to cope with these kinds of seasonal effects. Firstly, a Principal Component Analysis (PCA) model was constructed in order to visualize the data set and reduce the dimensionality of the problem. Then, score values of the PCA were used in the FCM. The cluster centers represented the different process conditions (winter and summer seasons). Different algorithms were used to update the cluster centers or to give them some flexibility. The testing of different FCM algorithms was carried out by using a separate test set. The adaptive and the flexible FCM algorithms were compared to the basic non-adaptive FCM. For both cases, modifications are proposed and a simple strategy for updating the cluster centers is given.     

Linguistic Similarity Test Methods Based on Fuzzy Relations

Behaviormetrika - In this paper we present new methods for testing linguistic similarity using the concept of fuzzy relation. By applying a fuzzy clustering technique, we show that the problem of...