Estimation of Mappings between Lattices Using (Fuzzy) Neurocomputing for Pattern Recognition

• Grant number: 09/16284-2
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: May 01, 2010
• End date: February 28, 2014
• Field of knowledge: Physical Sciences and Mathematics - Computer Science - Computational 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

Abstract

Recently, the importance of computational intelligence methods based on lattice theory has been increasing since many classes of information granules such as fuzzy sets, intervals, interval-valued and intuitionistic fuzzy sets, etc., represent lattices. In particular, we developed the morphological perceptron with competitive learning (MP/CL) in order to solve classification problems in a lattice that corresponds to a product of chains that are endowed with an additional algebraic structure.In this project, our goal is to develop new (fuzzy) neurocomputing models for applications in classification and regression problems in more general lattices that are possibly equipped with an additional algebraic structure. To this end, we will resort to a decomposition theorem by Banon and Barrera, which states that any mapping between complete lattices can be written in terms of elementary morphological operators, in order to obtain an suitable mapping for a given supervised pattern recognition problem. Subsequently, we intend to express the morphological operators corresponding to the respective mapping in terms of certain convolutions that allow for the definition of weights of a morphological neural network. In this manner, we wish to achieve an adequate generalization performance of the resulting neuralnetwork.

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)

SUSSNER, PETER; ESMI, ESTEVAO L.; VILLAVERDE, IVAN; GRANA, MANUEL. The Kosko Subsethood Fuzzy Associative Memory (KS-FAM): Mathematical Background and Applications in Computer Vision. Journal of Mathematical Imaging and Vision, v. 42, n. 2-3, p. 134-149, FEB 2012. (09/16284-2)

ESMI, ESTEVAO; SUSSNER, PETER; BUSTINCE, HUMBERTO; FERNANDEZ, JAVIER. Theta-Fuzzy Associative Memories (Theta-FAMs). IEEE TRANSACTIONS ON FUZZY SYSTEMS, v. 23, n. 2, p. 313-326, APR 2015. (09/16284-2, 11/10014-3)

SUSSNER, PETER; NACHTEGAEL, MIKE; MELANGE, TOM; DESCHRIJVER, GLAD; ESMI, ESTEVAO; KERRE, ETIENNE. Interval-Valued and Intuitionistic Fuzzy Mathematical Morphologies as Special Cases of L-Fuzzy Mathematical Morphology. Journal of Mathematical Imaging and Vision, v. 43, n. 1, p. 50-71, MAY 2012. (09/16284-2)

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

LAUREANO, Estevão Esmi. 'Theta'-FAMs: fuzzy associative memories based on functions-'theta'. 2014. Doctoral Thesis - Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica Campinas, SP.