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| Author(s): |
Francisco Javier Ropero Peláez
Total Authors: 1
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| Document type: | Doctoral Thesis |
| Press: | São Paulo. |
| Institution: | Universidade de São Paulo (USP). Escola Politécnica (EP/BC) |
| Defense date: | 2001-11-01 |
| Examining board members: |
Newton Maruyama;
Aluízio Fausto Ribeiro Araújo;
Luiz Pereira Calôba;
Ademar Ferreira;
Paulo Carlos Kaminski
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| Advisor: | Marcelo Godoy Simoes; Newton Maruyama |
| Abstract | |
This thesis develops a new Theory of Probability that allows to understand statistical events as vectors in an Euclidean space. The concepts of angle and projection allowed to develop a new Gram-Schmidt-type algorithm for finding a basis of orthogonal vectors from any other set of vectors. This basis can be reduced when the axes are the so called Principal Components. A new algorithm for extracting the Principal Components was developed. These mathematical foundations served for grounding Fuzzy Logic and Neural Networks in a different way. Regarding Fuzzy Logic, these equations represent a different method for analytically designing membership functions and for finding the compositional inference rules. In the Neural Network field these foundations allowed the easy understanding of a new neural network based on the neuro-physiology of thalamus that extracts the Principal Components for achieving an efficient compression of information. This artificial thalamus was implemented in Matlab. (AU) | |