The Three Gorges is a region with a very high landslide distribution density and a concentrated population. In Three Gorges there are often landslide disasters, and the potential risk of landslides is tremendous. In this paper, focusing on Three Gorges, which has a complicated landform, spatial forecasting of landslides is studied by establishing 20 forecast factors (spectra, texture, vegetation coverage, water level of reservoir, slope structure, engineering rock group, elevation, slope, aspect, etc). China-Brazil Earth Resources Satellite (Cbers) images were adopted based on C4.5 decision tree to mine spatial forecast landslide criteria in Guojiaba Town (Zhigui County) in Three Gorges and based on this knowledge, perform intelligent spatial landslide forecasts for Guojiaba Town. All landslides lie in the dangerous and unstable regions, so the forecast result is good. The method proposed in the paper is compared with seven other methods: IsoData, K-Means, Mahalanobis Distance, Maximum Likelihood, Minimum Distance, Parallelepiped and Information Content Model. The experimental results show that the method proposed in this paper has a high forecast precision, noticeably higher than that of the other seven methods.

In this paper, we develop a comprehensive conceptual and algorithmic framework to cope with a problem of clustering homogeneous information granules. While there have been several approaches to coping with granular (viz. nonnumeric) data, the origin of granular data themselves considered there is somewhat unclear and, as a consequence, the results of clustering start lacking some full-fledged interpretation. In this paper, we offer a holistic view at clustering information granules and an evaluation of the results of clustering. We start with a process of forming information granules with the use of the principle of justifiable granularity (PJG). With this regard, we discuss a number of parameters used in this development of information granules as well as quantify the quality of the granules produced in this manner. In the sequel, Fuzzy C-Means is applied to cluster the derived information granules, which are represented in a parametric manner and associated with weights resulting from the usage of the PJG. The quality of clustering results is evaluated through the use of the reconstruction criterion (quantifying the concept of information granulation and degranulation). A suite of experiments using synthetic and publicly available datasets is reported to quantify the performance of the proposed approach and highlight its key features.

Big data with a large number of observations (samples) have posed genuine challenges for fuzzy clustering algorithms, and Fuzzy C-Means (FCM), in particular. In this study, we propose an original algorithm referred to as a hyperplane division method to split the entire data set into disjoint subsets. By disjoint subsets, we mean that the data subspaces (parts of the entire data space), each of which is supported or spanned by the data points in the corresponding subset, do not overlap each other. The disjoint subsets turned out to be beneficial to improving the quality of the clusters formed by the clustering algorithms. Moreover, considering that either a large number (say, thousands) or a small number (say, a few) of clusters may be pursued in the clustering task, we propose corresponding strategies (based on the hyperplane division method) to make clustering processes feasible, efficient, and effective. By validating the proposed strategies on both synthetic and publicly available data, we show their superiority (in terms of both efficiency and effectiveness) manifested in a visible way over the method of clustering the entire data and over some representative big data clustering methods.

In this paper, we propose a gradient-based method to approximate a fuzzy set through a trapezoidal fuzzy set (TFS). By adding some constraints in the formulated optimization problem, the major characteristics of the fuzzy set such as the core, the major part of the support, and the shape of the membership function could be preserved; also the form of the optimized result as a TFS is guaranteed. We regard the optimized TFS as the ``skeleton'' (blueprint) of the original fuzzy set. Based on this skeleton, we further extend the TFS to a higher type, that is, an interval type-2 TFS (IT2 TFS), so that more information about the original fuzzy set could be captured but the number of the parameters used to describe the original fuzzy set is still maintained low (nine parameters are required for an IT2 TFS). The principle of justifiable granularity is used to ensure that the formed type-2 information granule exhibits a sound interpretation. Both synthetic fuzzy sets and those constructed by the fuzzy C-means algorithm applied to the publicly available data have been used to demonstrate the usefulness of the proposed approximation methods.