Uma contribuição ao estudo das categorias internas e de sua proliferação em redes ARTMAP

ART networks present some advantages: online learning; convergence in a few epochs of training; incremental learning, etc. Even though, some problems exist, such as: categories proliferation, sensitivity to the presentation order of training patterns, the choice of a good vigilance parameter, etc. Among the problems, the most important is the category proliferation that is probably the most critical. This problem makes the network create too many categories, consuming resources to store unnecessarily a large number of categories, impacting negatively or even making the processing time unfeasible, without contributing to the quality of the representation problem, i. e., in many cases, the excessive amount of categories generated by ART networks makes the quality of generation inferior to the one it could reach. Another factor that leads to the category proliferation of ART networks is the difficulty of approximating regions that have non-rectangular geometry, causing a generalization inferior to the one obtained by other methods of classification. From the observation of these problems, three methodologies were proposed, being two of them focused on using a most flexible geometry than the one used by traditional ART networks, which minimize the problem of categories proliferation. The third methodology minimizes the problem of the presentation order of training patterns. To validate these new approaches, many tests were performed, where these results demonstrate that these new methodologies can improve the quality of generalization for ART networks

Uma análise da aplicação do modelo de Rede Neural RePART em Comitês de classificadores

RePART (Reward/Punishment ART) is a neural model that constitutes a variation of the Fuzzy Artmap model. This network was proposed in order to minimize the inherent problems in the Artmap-based model, such as the proliferation of categories and misclassification. RePART makes use of additional mechanisms, such as an instance counting parameter, a reward/punishment process and a variable vigilance parameter. The instance counting parameter, for instance, aims to minimize the misclassification problem, which is a consequence of the sensitivity to the noises, frequently presents in Artmap-based models. On the other hand, the use of the variable vigilance parameter tries to smoouth out the category proliferation problem, which is inherent of Artmap-based models, decreasing the complexity of the net. RePART was originally proposed in order to minimize the aforementioned problems and it was shown to have better performance (higer accuracy and lower complexity) than Artmap-based models. This work proposes an investigation of the performance of the RePART model in classifier ensembles. Different sizes, learning strategies and structures will be used in this investigation. As a result of this investigation, it is aimed to define the main advantages and drawbacks of this model, when used as a component in classifier ensembles. This can provide a broader foundation for the use of RePART in other pattern recognition applications

On fuzzy ideals and fuzzy filters of fuzzy lattices

In the literature there are several proposals of fuzzi cation of lattices and ideals concepts. Chon in (Korean J. Math 17 (2009), No. 4, 361-374), using the notion of fuzzy order relation de ned by Zadeh, introduced a new notion of fuzzy lattice and studied the level sets of fuzzy lattices, but did not de ne a notion of fuzzy ideals for this type of fuzzy lattice. In this thesis, using the fuzzy lattices de ned by Chon, we de ne fuzzy homomorphism between fuzzy lattices, the operations of product, collapsed sum, lifting, opposite, interval and intuitionistic on bounded fuzzy lattices. They are conceived as extensions of their analogous operations on the classical theory by using this de nition of fuzzy lattices and introduce new results from these operators. In addition, we de ne ideals and lters of fuzzy lattices and concepts in the same way as in their characterization in terms of level and support sets. One of the results found here is the connection among ideals, supports and level sets. The reader will also nd the de nition of some kinds of ideals and lters as well as some results with respect to the intersection among their families. Moreover, we introduce a new notion of fuzzy ideals and fuzzy lters for fuzzy lattices de ned by Chon. We de ne types of fuzzy ideals and fuzzy lters that generalize usual types of ideals and lters of lattices, such as principal ideals, proper ideals, prime ideals and maximal ideals. The main idea is verifying that analogous properties in the classical theory on lattices are maintained in this new theory of fuzzy ideals. We also de ne, a fuzzy homomorphism h from fuzzy lattices L and M and prove some results involving fuzzy homomorphism and fuzzy ideals as if h is a fuzzy monomorphism and the fuzzy image of a fuzzy set ~h(I) is a fuzzy ideal, then I is a fuzzy ideal. Similarly, we prove for proper, prime and maximal fuzzy ideals. Finally, we prove that h is a fuzzy homomorphism from fuzzy lattices L into M if the inverse image of all principal fuzzy ideals of M is a fuzzy ideal of L. Lastly, we introduce the notion of -ideals and - lters of fuzzy lattices and characterize it by using its support and its level set. Moreover, we prove some similar properties in the classical theory of - ideals and - lters, such as, the class of -ideals and - lters are closed under intersection. We also de ne fuzzy -ideals of fuzzy lattices, some properties analogous to the classical theory are also proved and characterize a fuzzy -ideal on operation of product between bounded fuzzy lattices L and M and prove some results.