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Theta - fuzzy associative memory: fundamentals, extensions, and applications

Grant number: 14/10067-8
Support type:Scholarships in Brazil - Post-Doctorate
Effective date (Start): November 01, 2014
Effective date (End): January 31, 2016
Field of knowledge:Physical Sciences and Mathematics - Mathematics
Principal Investigator:Peter Sussner
Grantee:Estevão Esmi Laureano
Home Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

Associative memories (AMs) are mathematical models geared to storing desired input-outputpairs called fundamental memories. In addition, some error correction capability is also desiredfor an AM model. In this project we will investigate in detail a class of AMs called $\Theta$-fuzzy associative memories ($\Theta$-FAMs), that correspond to mappings between classes of fuzzy sets given by two-layer fuzzy neural networks. Under some conditions, a -FAM has optimal absolute storage capability and is able to achieve perfect recall for noisy input patterns that are sufficiently close to uncorrupted pattern cues. The $\Theta$-FAMs models were successfully applied in many classification problems including several benchmarks and some real world applications such as vision-based robot self-localization, classification of time series of vegetaion indixes and speaker recognition. In this project we will extend -FAMs models in two ways: topologically and conceptually. The first extension aims at providing further degrees of freedom and flexibility of architecture forregression problems. The second extension refers to the use of the $\Theta$-FAM approach as the $\Theta$-FAM mathematical model of inference for general classes of information granules based on lattice theory.

Scientific publications
(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
ESMI, ESTEVAO; SUSSNER, PETER; DIAS IGNACIO, GUSTAVO BARROSO; DE BARROS, LAECIO CARVALHO. A parametrized sum of fuzzy numbers with applications to fuzzy initial value problems. FUZZY SETS AND SYSTEMS, v. 331, p. 85-104, JAN 15 2018. Web of Science Citations: 4.

Please report errors in scientific publications list by writing to: cdi@fapesp.br.