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| Author(s): |
Rodolfo Miyasaki
Total Authors: 1
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| Document type: | Master's Dissertation |
| Press: | Campinas, SP. |
| Institution: | Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica |
| Defense date: | 2007-06-25 |
| Examining board members: |
Peter Sussner;
Laécio Carvalho de Barros;
Fernando Antonio Campos Gomide
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| Advisor: | Peter Sussner |
| Abstract | |
Associative Memories (AMs) allow for the storage of pattern associations and the retrieval of the desired output patterns upon the presentation of a possibly noisy or imcomplete version of an input pattern. Fuzzy Associative Memories (FAMs) are models of AMs whose input and output patterns are fuzzy sets. FAMs have proven to be a powerful tool for implementing fuzzy rule-based systems. The fact that FAMs models are related to mathematical morphology (MM) has led to the development of fuzzy morphological associative memories (FMAMs), in particular fuzzy implicative fuzzy associative memories (IFAMs). The neurons of an FMAM perform one of the elementary operations of MM which as erosion, dilation, anti-erosion and anti-dilation. This thesis relates the existence of solutions in systems of fuzzy relational equations (FREs) to the perfect recall using IFAMs. We formulated the problem of choosing an appriopriate IFAM model for a given application as an optimization problem. More precisely, we determined the IFAM model given by a parameterized Yager t-norm which minimizes the error between the recalled patterns and the desired output patterns. A gray-scale image can be expressed as a fuzzy relation and, given a family of fuzzy sets, it can be compressed by means of FREs. Thus, the inverse problem arises of finding a reconstruction of the image original based on the compression. This master thesis determines the best approximation by means of a IFAMs (AU) | |
| FAPESP's process: | 05/03648-5 - An investigation of the relationship between implicative fuzzy associative memories and fuzzy relational with applications |
| Grantee: | Rodolfo Miyasaki |
| Support Opportunities: | Scholarships in Brazil - Master |