A fuzzy clustering method for coherent generator groups identification based on A-K

This paper presented a reduced-order method for swing mode eigenvalue calculating based on fuzzy coherency recognition. First, we recognize the coherent generator groups using the fuzzy clustering method. Then we aggregated the generators in a coherent group into a single equivalent generator that the dimension of the state equation reduced evidently. Using QR algorithm to the reduced-order state equation we calculated the eigenvalues of the inter-area mode. The eigenvalues of local mode calculated by using QR algorithm to the sub-state matrices corresponding to the coherent groups separately. Thus, all eigenvalues of swing mode can be calculated. We have given detailed results of both the coherent generator groups recognition and the eigenvalues calculating of the 10-machine New England power system. The results shows that the method for eigenvalue calculation is simple and practical.

Fuzzy comprehensive evaluation cannot reasonably differentiate the close membership values, e.g. 0.70 and 0.69. When the results have to be decided on the basis of maximum fuzzy membership value, some related information among similar objects may be neglected. At the same time, supervised fuzzy clustering analysis selects the threshold according to subjective experience. But different users may give different thresholds, and different thresholds may further get different clustering results. Integrating both fuzzy comprehensive evaluation and fuzzy clustering analysis in a unified way, this paper proposes a fuzzy comprehensive clustering method based on the maximum remainder algorithms and maximum characteristics algorithms. First, the principle of fuzzy comprehensive clustering is given. Based on the membership matrix of fuzzy comprehensive evaluation, fuzzy similar matrix is generated. Then a fuzzy equivalent matrix is produced from the fuzzy similar matrix. According to the fuzzy equivalent matrix, fuzzy clustering is implemented via the maximum remainder algorithms on the basis of fuzzy confidence level. And the grades of the resulting clusters are computed by using the maximum characteristics algorithms. Finally, a case study is given on land grading in Nanning city, the results of which show the proposed fuzzy comprehensive clustering method is able to overcome the disadvantages of either fuzzy comprehensive evaluation or fuzzy clustering analysis.

The purpose of this chapter is the consideration of modern methods of the cluster analysis, crisp methods and fuzzy methods, robust probabilistic and possibilistic clustering methods, their properties and application. The problem of cluster analysis is formulated, main criteria and metrics are considered and discussed. Classification of cluster analysis methods is presented, several crisp methods are considered, in particular, hard C-means method and Ward’s method. Fuzzy clustering methods are considered and analyzed: fuzzy C-means method and its generalization Gustavsson-Kessel’s method of cluster analysis which is used when metrics of distance differs from Euclidian. The methods of initial location of cluster centers are considered: peak and differential grouping and their properties analyzed. Adaptive robust clustering algorithms are presented and analyzed which are used when initial data is distorted by high level of noise, or by outliers. In the Sect. 1.7 robust probabilistic algorithms of fuzzy clustering are considered and investigated for batch processing mode and on-line mode which may be used for clustering in BD bases. Experimental investigations of the considered clustering methods are presented, including clustering of UNO countries by indicators of sustainable development.

In this paper, on the basis of coherent grouping, fuzzy clustering method is used to study the effect of failure on coherent grouping. First this article use fuzzy clustering method to get a coherent classification result, use fuzzy clustering formula as a starting point, explore what factors will change before and after the fault, and then use the BPA program developed by the Chinese Academy of Electric Power to experiment on the IEEE39 node. As a result, it is obtained that the fault has a greater influence on the mutual admittance between generators and thus affects the grouping result.

The main purpose of applying fuzzy clustering method to dividing customer group is to divide series or establish serial platform, satisfying customer demand and promoting the robustness of product platform. Aiming at the deficiencies of current customer group dividing method based on fuzzy clustering, in this paper, an improved customer group dividing method based on fuzzy transitive closure dynamic clustering method is presented and a method to find the same result elements is adopted to simplify the calculation process of the transitive closure of a fuzzy similar matrix. And then, based on customer group dividing result, a product platform model based on customer group dividing is established in order to improve products based on platform. Finally, an instance of A electronic company manufacturing speakers is given in order to verify the effectiveness of the method proposed.

In order to reflect different importance of each index in flood classification, fuzzy analytic hierarchy process was used to determine the weights of flood classification indexes with reason, set pair analysis was used to construct fuzzy similar matrix R, and then a fuzzy clustering method based on set pair analysis and optimal fuzzy equivalent matrix, named SPA-OFEM for short, was established. The applied results show classification results are reasonable and high precision, the optimal fuzzy equivalent matrix Q can improve matrix transitive degree of R and reduce distortion problem of transitive closure method, and clustering results of history flood samples can be obtained directly based on Q. SPA-OFEM is a simple and effective improved fuzzy clustering method; it can be widely applied in management of flood disaster.

The premise condition of comprehensive evaluation of embankment safety is selection of representative unit embankment, on the basis of dividing the unit levee the influencing factors and classification of the unit embankment are drafted.Based on the rough set-fuzzy clustering, the influence factors of the unit embankment are measured by quantitative and qualitative indexes.Construct to fuzzy similarity matrix of standard embankment then calculate fuzzy equivalent matrix of fuzzy similarity matrix by square method. By setting the threshold of the fuzzy equivalence matrix, the unit embankment is clustered, and the representative unit embankment is selected from the classification of the embankment.

A new method for Web users fuzzy clustering based on analysis of user interest characteristic is proposed in this article. The method first defines page fuzzy categories according to the links on the index page of the site, then computes fuzzy degree of cross page through aggregating on data of Web log. After that, by using fuzzy comprehensive evaluation method, the method constructs user interest vectors according to page viewing times and frequency of hits, and derives the fuzzy similarity matrix from the interest vectors for the Web users. Finally, it gets the clustering result through the fuzzy clustering method. The experimental results show the effectiveness of the method.

Cluster analysis is a crucial and powerful tool for exploring and discovering the underlying structures in data. Among other approaches, the fuzzy c-means algorithm is the most well-known fuzzy clustering method. Recently, Tran and Wagner proposed a fuzzy entropy clustering method as an alternative to the fuzzy c-means. While the fuzzy c-means controls the degree of fuzziness and the membership function through the weighting exponent, the fuzzy entropy clustering method controls those by adjusting the ?parameter. In this work, we present a modified form of Tran andWagner's method using a different definition of distance measure that is involved with the Euclidean distance and its higher-order terms. The proposed scheme adds more degrees of freedom in controlling the clustering results through two extra parameters, a1 and a2. We have explicitly derived the formulae for updating the fuzzy partition matrix and the cluster centers. A theoretical analysis on the resulting membership functions has also been carried out. Examples are given to demonstrate the clustering results of the presented scheme for different combinations of input parameters.

This paper presents an image segmentation method based on fuzzy clustering and level set methods. The MRI image is firstly segmented with the fuzzy clustering method, and then the resulting fuzzy memberships are used to generate a new constraint function which guides the level-set curves evolution. Thanks to the new constraint term, the presented method is able to adaptively determine the directions of the curves evolution without any manual intervention. The new method does not depend excessively on the gradient information as the Geodesic Active Contour method does; therefore it is less sensitive to the noise. The region information provided by the first step of the algorithm allows to improve the segmentation accuracy of the brain tissues. The experimental quantitative and qualitative analyses indicate the capability of the proposed method to segment the brain tissues with high accuracy comparing with the fuzzy clustering method.

Images and visual understandings are basis in everyday life and are very important tool for decision making. However, for improving the image appearance to a human viewer, or to convert an image to a format better suited to machine processing, enhancing methods should be used. There are wide varieties of techniques for this purpose including, contrast and histogram modification, de-noising, statistical methods, and clustering. Among these techniques, clustering especially fuzzy clustering methods are among the most efficient methods that classifies each data into more than one cluster. In the literature, many fuzzy clustering methods have been presented such as Fuzzy C-Mean (FCM) and Possibilistic C-Mean (PCM), which uses Type-1 fuzzy logic. However, Type-2 fuzzy logic can provide better performance, especially when many uncertainties are presented. In this paper, we applied Type-2 fuzzy clustering method for enhancing the images and proposed a new fuzzy Type-2 Possibilistic c-means clustering (PCM) method. The performance of the proposed method in having good results is evaluated by using 6 images.

A Novel Spatial Fuzzy Clustering using Delaunay Triangulation for Large Scale GIS Data (NSFCDT)

Unsupervised robust planar segmentation of terrestrial laser scanner point clouds based on fuzzy clustering methods

Market definition and segmentation using fuzzy clustering methods

Fuzzy clustering method based on perturbation