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Granular computing, as a new and rapidly growing paradigm of information processing, has attracted many researchers and practitioners. Granular computing is an umbrella term to cover any theories, methodologies, techniques, and tools that make use of information granules in complex problem solving. The aim of this paper is to review foundations and schools of research and to elaborate on current developments in granular computing research. We first review some basic notions of granular computing. Classification and descriptions of various schools of research in granular computing are given. We also present and identify some research directions in granular computing.
Neural networks (NNs) with least square error (LSE) estimation form a certain type of single hidden layer feed-forward NNs. In this class of networks, the input connections (weights) and the biases of hidden neurons are generated randomly and fixed after being generated. The output connections are estimated by the LSE method rather than the back-propagation method. The random generation of the input connection weights and the hidden biases results in the larger number of hidden neurons to assure the quality of classification performance. To reduce the number of neurons in the hidden layer while maintaining the classification performance, we apply a "divide and conquer" strategy in this article. In other words, we divide an overall input space into several subspaces by using information granulation technique (Fuzzy C-Means clustering algorithm) and determine the local decision boundaries among related subspaces. A decision boundary defined in the input space can be considered as being composed of several decision boundaries defined in subspaces that form the entire input space. For the decision boundaries defined in the subspaces, their nonlinearity becomes lower in comparison with the one being encountered when considering the entire input space. Through the weighted LSE estimation instead of using the LSE estimation method, the connections of several NNs can be estimated without interfering with each other. After estimating the weights, the decision boundaries defined in the related subspaces are merged to a single decision boundary by using fuzzy ensemble technique. Several machine learning datasets and one real world application dataset are used to evaluate and validate the proposed fuzzy ensemble classifier. Based on the experimental results, the proposed classifier shows better classification performance when compared with the performance of some selected classifiers.