Fuzzy Vector Bundles for Classification via Neural Networks
In this paper we propose a method of classification based on standard feedforward neural networks. The novelty of the approach is that we calculate local approximations of Lie algebras which generate the leaves of a foliation, each leaf corresponds to a class. From these linear approximations we pass to the case where a point on a leaf is not known with precision but can be specified using fuzzy set theory. Integrating the approximating linear equations then provides us with ‘fuzzy leaves’ or fuzzy classes.
KeywordsFuzzy Number Fuzzy Classis Bias Vector Fuzzy Differential Equation Local Linear Approximation
Unable to display preview. Download preview PDF.
- C. Ehresmann. Les connexions infinitésimales dans un espace fibré. In Proceedings Colloque de Topologie, pages 29–55. Bruxelles, 1950.Google Scholar
- J.G. Hocking and G.S. Young. Topology. 1988.Google Scholar
- M. Mizamoto and K. Tanaka. Algebraic properties of fuzzy numbers. In Proceedings International Conference on Cybernetics and Society, pages 559–563. Washington DC, USA, 1976.Google Scholar
- D.W. Pearson. On linear fuzzy dynamical systems. In International Symposium on Soft Computing. Nîmes, France, 1997. to appear.Google Scholar
- D.W. Pearson. A property of linear fuzzy differential equations. Applied Mathematics Letters, 1997. to appear.Google Scholar
- D.W. Pearson. Some structural properties of fuzzy linear dynamical systems. In Proceedings International Symposium on Fuzzy Logic. Zurich, Switzerland, February 1997.Google Scholar
- D.W. Pearson and G. Dray. Construction of continuous classes using vertical vector fields. In Proceedings Engineering Systems Design and Analysis. Montpellier, France, July 1996.Google Scholar