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In this paper, a neuro-fuzzy model is introduced. The model describes a fuzzy relational "IF-THEN" reasoning scheme using an adaptive structure based on fuzzy relations. Two training schemes for the learning of the parameters based respectively on the backpropagation algorithm and pseudo-inverse matrix technique are illustrated. The model qualities are investigated by a series of simulation examples: function approximation, classification and rule extraction. These preliminary and promising results show that the model has a good performance and that it could be used for complex systems in real world applications.
In this article, a novel attention-based reinforced interval type-2 fuzzy clustering neural network (ARIT2FCN) is developed to improve the generalization performance of fuzzy clustering-based neural networks (FCNNs). Commonly, fuzzy rules in FCNNs are generated through the clustering-based rule generator. However, the generated fuzzy rules may not be able to fully describe the given data, because the clustering-based rule generator does not simultaneously consider the intracluster homogeneity and intercluster heterogeneity for both of data characteristics and label information when defining membership functions (MFs) of fuzzy rules. This negatively affects fuzzy rules to accurately quantify the interclass heterogeneity and intraclass homogeneity and degrades the performance of FCNNs. The ARIT2FCN is proposed with the aid of the attention-based clustering mechanism and the successive learning method. The attention-based clustering mechanism is designed to define MFs by simultaneously considering data characteristics and label information. The successive learning method is adopted to construct the desired fuzzy rules that can capture the interclass heterogeneity and intraclass homogeneity. Moreover, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L<inline-formula><tex-math notation="LaTeX">$_{2}$</tex-math></inline-formula></i> norm regularization is used to alleviate the overfitting effect. The performance of ARIT2FCN is evaluated on machine learning datasets with 16 comparative methods. In addition, two real-world problems are adopted to validate the effectiveness of ARIT2FCN. Experimental results demonstrate that the ARIT2FCN outperforms the comparative methods, and the statistical tests also support the superiority of ARIT2FCN.
In this paper, we develop a method for recognizing face images by combining wavelet decomposition, Fisherface method, and fuzzy integral. The proposed approach is comprised of four main stages. The first stage uses the wavelet decomposition that helps extract intrinsic features of face images. As a result of this decomposition, we obtain four subimages (namely approximation, horizontal, vertical, and diagonal detailed images). The second stage of the approach concerns the application of the Fisherface method to these four decompositions. The choice of the Fisherface method in this setting is motivated by its insensitivity to large variation in light direction, face pose, and facial expression. The two last phases are concerned with the aggregation of the individual classifiers by means of the fuzzy integral. Both Sugeno and Choquet type of fuzzy integral are considered as the aggregation method. In the experiments we use n-fold cross-validation to assure high consistency of the produced classification outcomes. The experimental results obtained for the Chungbuk National University (CNU) and Yale University face databases reveal that the approach presented in this paper yields better classification performance in comparison to the results obtained by other classifiers.
Software measures (metrics) are indicators describing complexity of software products and processes. By their very nature, software measures give rise to a number of complex and highly dimensional data (patterns) that attempt to provide some useful insights into the very nature of the software systems. Such findings help to investigate and quantify the key properties of the systems such as their reliability, maintainability, readability, etc. In this study, self-organizing maps (SOMs) are considered as a vehicle for analysis of multidimensional data. From the functional point of view, SOMs are neural networks that map highly dimensional data into low dimensional (usually two-dimensional) space in such a way that the topology of the data is preserved. The construction of a map is realized through a process of unsupervised learning. Owing to the visualization capabilities arising in the two-dimensional space, one can visualize a structure in the original data and identify potential clusters as well as their size (compactness) and mutual distribution in the map. In this study, analysis of software data concerning JAVA classes is being carried out.