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Theta - Fuzzy Associative Memory: Fundamentals, Extensions, and Applications

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


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.

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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, . (14/10067-8)
SUSSNER, PETER; ESMI, ESTEVAO; BARROS, LAECIO C.; IEEE. Controlling the Width of the Sum of Interactive Fuzzy Numbers with Applications to Fuzzy Initial Value Problems. 2016 IEEE INTERNATIONAL CONFERENCE ON FUZZY SYSTEMS (FUZZ-IEEE), v. N/A, p. 8-pg., . (14/10067-8)

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