A general class of fuzzy morphological associative memories

• Grant number: 06/06818-1
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: March 01, 2007
• End date: February 29, 2008
• Field of knowledge: Physical Sciences and Mathematics - Computer Science
• Principal Investigator: Peter Sussner
• Grantee: Marcos Eduardo Ribeiro Do Valle Mesquita
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

Neural associative memories are designed to store input-output pairs of patterns and are capable of recalling the desired output pattern upon presentation of an inclomplete or corrupted version of a certain input pattern. In this project, we propose to develop a new class of fuzzy morphological associative memories (FMAMs). The models of this class are called morphological because their neurons perform elementary morphological operations and they are referred to as fuzzy because they are defined in the fuzzy domain. This new class of associative memories should include as special cases implicative fuzzy associative memories (IFAMs) and various other models of fuzzy associative memories. In order to achive our goal, we suggest to begin by discussing and classifying the different approaches to fuzzy mathematical morphology. Based on these results, we will develop our new class of FMAMs. We will investigate models of morphological neurons and develop learning rules for FMAMs. This first part of the project corresponds to the first six months of the scholarship. The second part, corresponding to the remaining months, will be dedicated to the properties and applications of FMAMs, in particular of IFAMs. More precisely, we will introduce theorems that completely characterize the storage and recall phases of auto- and heteroassociative FMAMs. Furthermore, we will investigate applications of FMAMs in the areas of classification, control, and prediction of time series. (AU)

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)

VALLE, MARCOS EDUARDO; SUSSNER, PETER. Storage and recall capabilities of fuzzy morphological associative memories with adjunction-based learning. NEURAL NETWORKS, v. 24, n. 1, p. 75-90, JAN 2011. (06/06818-1)

SUSSNER, PETER; VALLE, MARCOS EDUARDO. Classification of fuzzy mathematical morphologies based on concepts of inclusion measure and duality. Journal of Mathematical Imaging and Vision, v. 32, n. 2, p. 139-159, OCT 2008. (06/06818-1)