Contribució a l'estudi de les uninormes en el marc de les equacions funcionals.

Les uninormes són uns operadors d'agregació que, per la seva definició, es poden considerar com a conjuncions o disjuncions, i que han estat aplicades a camps molt diversos. En aquest treball s'estudien algunes equacions funcionals que tenen com a incògnites les uninormes, o operadors definits a partir d'elles. Una d'elles és la distributivitat, que és resolta per les classes d'uninormes conegudes, solucionant, en particular, un problema obert en la teoria de l'anàlisi no-estàndard. També s'estudien les implicacions residuals i fortes definides a partir d'uninormes, trobant solució a la distributivitat d'aquestes implicacions sobre uninormes. Com a aplicació d'aquests estudis, es revisa i s'amplia la morfologia matemàtica borrosa basada en uninormes, que proporciona un marc inicial favorable per a un nou enfocament en l'anàlisi d'imatges, que haurà de ser estudiat en més profunditat.Las uninormas son unos operadores de agregación que, por su definición se pueden considerar como conjunciones o disjunciones y que han sido aplicados a campos muy diversos. En este trabajo se estudian algunas ecuaciones funcionales que tienen como incógnitas las uninormas, o operadores definidos a partir de ellas. Una de ellas es la distributividad, que se resuelve para las classes de uninormas conocidas, solucionando, en particular, un problema abierto en la teoría del análisis no estándar. También se estudian las implicaciones residuales y fuertes definidas a partir de uninormas, encontrando solución a la distributividad de estas implicaciones sobre uninormas. Como aplicación de estos estudios, se revisa y amplía la morfología matemática borrosa basada en uninormas, que proporciona un marco inicial favorable para un nuevo enfoque en el análisis de imágenes, que tendrá que ser estudiado en más profundidad.Uninorms are aggregation operators that, due to its definition, can be considered as conjunctions or disjunctions, and they have been applied to very different fields. In this work, some functional equations are studied, involving uninorms, or operators defined from them as unknowns. One of them is the distributivity equation, that is solved for all the known classes of uninorms, finding solution, in particular, to one open problem in the non-standard analysis theory. Residual implications, as well as strong ones defined from uninorms are studied, obtaining solution to the distributivity equation of this implications over uninorms. As an application of all these studies, the fuzzy mathematical morphology based on uninorms is revised and deeply studied, getting a new framework in image processing, that it will have to be studied in more detail

Stability Analysis and Stabilization of Fuzzy State Space Models

Die Dissertation von <A HREF=" http://www.shaker.de/Online-Gesamtkatalog/Details.asp ?ISBN=3-8322-5552-4 ">Kunping Zhu Stability Analysis and Stabilization of Fuzzy State Space Models (ISBN-10: 3-8322-5552-4, ISBN-13: 978-3-8322-5552-7)wurde parallel im Shaker Verlag veröffentlicht Abstract: Fuzzy control has achieved numerous successful industrial applications. However, stability analysis for fuzzy control systems remains a difficult problem, and most of the critical comments on fuzzy control are due to the lack of a general method for its stability analysis. Although significant research efforts have been made in the literature, appropriate tools for this issue have yet to be found. This thesis focuses on the problem of stability of fuzzy control systems. Both linguistic fuzzy models and T-S fuzzy models are discussed. The main work of this thesis can be summarized as follows: (1). A necessary and sufficient condition for the global stability of linguistic fuzzy models is given by means of congruence of fuzzy relational matrices. (2). A hyperellipsoid-based approach is proposed for stability analysis and control synthesis of a class of T-S (affine) fuzzy models with support-bounded fuzzy sets in the rule base. (3). Approaches of BMI-based fuzzy controller designs are proposed for the stabilization of T-S fuzzy models. (4). For the general T-S type fuzzy systems with norm-bounded uncertainties and time-varying delays, sufficient robust stabilization conditions are presented by employing the PDC-based fuzzy state feedback controllers. On stability analysis of T-S fuzzy models, most reported results based on the method of common quadratic Lyapunov functions require that each subsystem of the fuzzy models be stable in order to guarantee the stability of the overall systems. This restriction is overcome in our results by means of employing the structural information in the fuzzy rules

Neurofuzzy approach for nonlinear dynamical systems modeling

Orientadores: Fernando Antonio Campos Gomide, Pyramo Pires Costa JuniorTese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de ComputaçãoResumo: Este trabalho propõe um procedimento sistemático para obtenção de modelos de sistemas dinâmicos não-lineares complexos utilizando redes neurais nebulosas. As redes neurais nebulosas aplicadas em modelagem são capazes de extrair conhecimento de dados entrada/saída e representar este conhecimento na forma de regras nebulosas do tipo se-então, gerando modelos lingüísticos convenientes para compreensão humana. Duas novas classes de redes neurais nebulosas são propostas a partir de generalizações dos neurônios lógicos AND e OR. Estas generalizações, denominadas unineurons e nullneurons, implementam, além da plasticidade sináptica, outra importante característica dos neurônios biológicos, a plasticidade neuronal. Desta forma, os neurônios propostos neste trabalho são capazes de modificar parâmetros internos em resposta à alterações, permitindo que unineurons e nullneurons variem individualmente de um neurônio AND para um neurônio OR (e vice-e-versa), dependendo da necessidade do problema. Conseqüentemente, uma rede neural nebulosa composta por unineurons e nullneurons é mais geral do que as redes neurais nebulosas similares sugeridas na literatura. Além da introdução de redes neurais com unineurons e nullneurons, um novo algoritmo de treinamento para obtenção de modelos nebulosos de sistemas dinâmicos é proposto utilizando aprendizado participativo. Neste algoritmo, uma nova informação fornecida à rede por meio de um dado entrada/saída é comparada com o conhecimento que já se tem a respeito do sistema. A nova informação só tem influência na atualização do conhecimento se não entrar em conflito com o conhecimento adquirido anteriormente. Como conseqüência, redes neurais nebulosas que utilizam este novo algoritmo de treinamento são mais robustas a dados de treinamento com valores que correspondem a comportamentos anômalos ou mesmo a erros durante a obtenção destes dados. As abordagens propostas foram utilizadas para desenvolver modelos para previsão de séries temporais e modelagem térmica de transformadores de potência. Os resultados experimentais mostram que os modelos aqui propostos são mais robustos e apresentam os melhores desempenhos, tanto em termos de precisão quanto em termos de custos computacionais, quando comparados com abordagens alternativas sugeridas na literaturaAbstract: This work suggests a systematic procedure to develop models of complex nonlinear dynamical systems using neural fuzzy networks. The neural fuzzy networks are able to extract knowledge from input/output data and to encode it explicitly in the form of if-then rules. Therefore, linguistic models are obtained in a form suitable for human understanding. Two new classes of fuzzy neurons are introduced to generalize AND and OR logic neurons. These generalized login neurons, called unineurons and nullneurons, provide a mechanism to implement synaptic plasticity and an important characteristic of biological neurons, the neuronal plasticity. Unineurons and nullneurons achieve synaptic and neuronal plasticity modifying their internal parameters in response to external changes. Thus, unineurons and nullneurons may individually vary from a AND neuron to a OR neuron (and vice-versa), depending upon the necessity of the modeling task. Neural fuzzy networks constructed with unineurons and nullneurons are more general than similar fuzzy neural approaches suggested in literature. Training algorithms for neural fuzzy networks with unineurons and nullneurons are also studied. In particular, a new training algorithm based on the participatory learning is introduced to develop fuzzy models of dynamical systems. In the participatory learning algorithm, a new information brought to the network through an input/output data is first compared with the knowledge that the network already has about the model. The new information influences the update of the knowledge only if it does not conflict with the current knowledge. As a result, neural fuzzy networks trained with participatory learning show greater robustness to training data with anomalous values than their counterparts. The neural fuzzy network and training algorithms suggested herein are used to develop time series forecast models and thermal models of power transformers. Experimental results show that the models proposed here are more robust and perform best in terms of accuracy and computational costs when compared against alternative approaches suggested in the literatureDoutoradoAutomaçãoDoutor em Engenharia Elétric

Uninetworks In Time Series Forecasting

This paper presents an approach for time series forecasting using a new class of fuzzy neural networks called uninetworks. Uninetworks are constructed using a recent generalization of the classic and and or logic neurons. These generalized logic neurons, called unineurons, provide a mechanism to implement general nonlinear processing and introduce important characteristics of biological neurons such as neuronal AND synaptic plasticity. Unineurons achieve synaptic and neuronal plasticity modifying their internal parameters in response to external changes. Thus, unineurons may individually vary from an and neuron to an or neuron (and vice-versa), depending upon the necessity of the modeling task. Besides, the proposed neural fuzzy networks are able to extract knowledge from input/output data and to encode it explicitly in the form of if-then rules. Therefore, linguistic models are obtained in a form suitable for human understanding. Experimental results show that the models proposed here are more general and perform best in terms of accuracy and computational costs when compared against alternative approaches suggested in the literature. ©2009 IEEE.Minist. Commun. Inf. Technol. AzerbaijanInfield, D.G., Hill, D.C., Optimal smoothing for trend removal in short term electricity demand forecasting (1998) IEEE Trans. on Power Systems, 13 (3), pp. 1115-1120. , AugPapalexopoulos, A.D., Hesterberg, T.C., A regression-based approach to short-term load forecasting (1990) IEEE Trans. on Power Systems, 5 (4), pp. 1535-1550. , NovRahman, S., Hazim, O., A generalized knowledge-based short term load-forecasting technique (1993) IEEE Trans. on Power Systems, 8 (2), pp. 508-514. , MayHuang, S.J., Shih, K.R., Short-term load forecasting via ARMA model identification including non-Gaussian process considerations (2003) IEEE Trans. Power Systems, 18 (2), pp. 673-679. , MayBox, G.E.P., Jenkins, G.M., Time Series Analysis-Forecasting and Control (1976) Holden-Day, , San Francisco, CA-USAIrisarri, G.D., Widergren, S.E., Yehsakul, P.D., On-line load forecasting for energy control center application (1982) IEEE Trans. on Power Apparatus and Systems, 101 (1), pp. 71-78. , JanHaykin, S., Neural Networks: A Comprehensive Foundation (1998) Prentice Hall, , NJ-USA, ed. 2Pedrycz, W., Rocha, A., Fuzzy set based models of neuron and knowledge-based networks (1993) IEEE Trans. on Fuzzy Systems, 1 (4), pp. 254-266Rutkowski, L., Cpalka, K., Design and learning of adjustable quasitriangular norms with applications to neuro-fuzzy systems (2005) IEEE Trans. on Neural Networks, 13 (1), pp. 140-151M. Hell, P. Costa Jr., F. Gomide, Nullneurons-based hybrid neurofuzzy network, In Proceedings of Annual Meeting of the North American Fuzzy Information Processing Society, NAFIPS 07, pp. 331-336, San Diego-CA, USA, June 2007Hell, M., Costa Jr., P., Gomide, F., Hybrid neurofuzzy computing with nullneurons (2008) Proceedings of IEEE World Congress on Computational Intelligence - WCCI, , Hong Kong, China, JuneYager, R., Rybalov, A., Uninorm aggregation operators (1996) Fuzzy Sets and Systems, 80 (1), pp. 111-120Calvo, T., De Baets, B., Fodor, J., The functional equations of Frank and Alsina for uninorms and nullnorms (2001) Fuzzy Sets Systems, 120, pp. 385-394Pedrycz, W., Logic-based neurocomputing with unineurons (2006) IEEE Trans. on Fuzzy Systems, 14 (6), pp. 860-873Kandel, E.R., Schwartz, J.H., Jessel, T.M., Principles of Neural Science (2000) McGraw-Hill, , NY-USA, 4th. edFodor, J.C., On fuzzy implication operators (1991) Fuzzy Sets and Systems, 42, pp. 293-300J. C. Fodor, R. R. Yager, and R. 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A Fast Learning Algorithm For Uninorm-based Fuzzy Neural Networks

This paper suggests a fast learning algorithm for weighted uninorm-based neural networks. Fuzzy neural networks are models capable to approximate functions with high accuracy and to generate transparent models through extraction of linguistic information from the resulting topology. A fuzzy neural network model based on weighted uninorms has been developed recently. It was shown that this model approximates any continuous real function on a compact subset. In this paper we introduce a fast learning algorithm for this class of fuzzy neural networks based on ideas from extreme learning machine. The algorithm is detailed and computational experiments reported to illustrate the accuracy and time efficiency of the learning approach. The results show that neural fuzzy model is accurate and learning speed is as good as or faster than alternative neural network models. © 2012 IEEE.Minist. Commun. Inf. Technol. Republic AzerbaijanPedrycz, W., Fuzzy Neural Networks and Neurocomputations (1993) Fuzzy Sets and Systems, 56 (1), pp. 1-28. , MAY 25Caminhas, W., Tavares, H., Gomide, F., Pedrycz, W., Fuzzy sets based neural networks: Structure, learning and applications (1999) Journal of Advanced Computational Intelligence, 3 (3), pp. 151-157Gomide, F., Pedrycz, W., (2007) Fuzzy Systems Engineering: Toward Human-Centric Computing, , NJ, USA: Wiley InterscienceBallini, R., Gomide, F., Learning in recurrent, hybrid neurofuzzy networks (2002) IEEE International Conference on Fuzzy Systems, pp. 785-791Hell, M., Costa, P., Gomide, F., Participatory learning in power transformers thermal modeling (2008) IEEE Transactions on Power Delivery, 23 (4), pp. 2058-2067. , OctGobi, A.E., Pedrycz, D., Logic minimization as an efficient means of fuzzy structure discovery (2008) IEEE Transactions on Fuzzy Systems, 16 (3), pp. 553-566. , JUNPedrycz, W., Logic-based fuzzy neurocomputing with unineurons (2006) IEEE Transactions on Fuzzy Systems, 14 (6), pp. 860-873. , DECPedrycz, W., Hirota, K., Uninorm-based logic neurons as adaptive and interpretable processing constructs (2007) Soft Computing, 11 (1), pp. 41-52. , JANHell, M., Gomide, F., Ballini, R., Costa, P., Uninetworks in time series forecasting (2009) NAFIPS 2009. Annual Meeting of the North American Fuzzy Information Processing Society, 2009, pp. 1-6. , juneLemos, A., Caminhas, W., Gomide, F., New uninorm-based neuron model and fuzzy neural networks (2010) 2010 Annual Meeting of the North American Fuzzy Information Processing Society (NAFIPS), pp. 1-6Lemos, A., Kreinovich, V., Caminhas, W., Gomide, F., Universal approximation with uninorm-based fuzzy neural networks (2011) 2011 Annual Meeting of the North American Fuzzy Information Processing Society (NAFIPS), pp. 1-6. , marchYager, R., Rybalov, A., Uninorm aggregation operators (1996) Fuzzy Sets and Systems, 80 (1), pp. 111-120. , MAY 27Calvo, T., Baets, B.D., Fodor, J., The functional equations of frank and alsina for uninorms and nullnorms (2001) Fuzzy Sets and Systems, 120 (3), pp. 385-394Herrera, F., Lozano, M., Verdegay, J.L., Tackling real-coded genetic algorithms: Operators and tools for behavioural analysis (1998) Artif. Intell. Rev., 12 (4), pp. 265-319Huang, G.-B., Zhu, Q.-Y., Siew, C.-K., Extreme learning machine: A new learning scheme of feedforward neural networks (2004) 2004 IEEE International Joint Conference on Neural Networks (IJCNN), 2, pp. 985-990. , july vol.2Huang, G.-B., Chen, L., Siew, C.-K., Universal approximation using incremental constructive feedforward networks with random hidden nodes (2006) Neural Networks, IEEE Transactions on, 17 (4), pp. 879-892. , julyYager, R., Uninorms in fuzzy systems modeling (2001) Fuzzy Sets and Systems, 122 (1), pp. 167-175. , AUG 16Huang, G.-B., Siew, C.-K., Extreme learning machine with randomly assigned rbf kernels (2005) International Journal of Information Technology, 11 (1), pp. 16-24Montesino-Pouzols, F., Lendasse, A., Evolving fuzzy optimally pruned extreme learning machine for regression problems (2010) Evolving Systems, 1 (1), pp. 43-58. , AugustBartlett, P., The sample complexity of pattern classification with neural networks: The size of the weights is more important than the size of the network (1998) IEEE Transactions on Information Theory, 44 (2), pp. 525-536. , marSerre, D., (2002) Matrices: Theory and Applications, , New York, US: Springer- VerlagBox, G.E.P., Jenkins, G., (1990) Time Series Analysis, Forecasting and Control, , Holden-Day, IncorporatedRiedmiller, M., Braun, H., A direct adaptive method for faster backpropagation learning: The rprop algorithm (1993) IEEE International Conference on Neural Networks, 1993, 1, pp. 586-591Jang, J., ANFIS - Adaptive-Network-Based Fuzzy Inference System (1993) IEEE Transactions on Systems Man and Cybernetics, 23 (3