Fuzzy Associative Memories and Their Relationship to Mathematical Morphology

Sussner, Peter; Valle, Marcos Eduardo

doi:10.1002/9780470724163.ch33

Cited by 27 publications

(26 citation statements)

References 69 publications

(79 reference statements)

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“…Development of L-fuzzy MMs for other special cases of complete lattices L: Conventional, interval-valued, and intuitionistic fuzzy sets represent particular instances of information granules [8,90]. We suspect that there are other specific classes of information granules that form complete lattices and that are conducive to the application of morphological tools [81]. 3.…”

Section: Applications Of Interval-valued and Intuitionistic Fmmmentioning

confidence: 99%

“…3. Development of L-fuzzy -in particular interval-valued and intuitionistic fuzzy -extensions of existing morphological neural networks such as fuzzy morphological associative memories [76][77][78][79]81,85]: Training of these new models may be achieved by means of a generalization of the "fuzzy learning by adjunction" scheme [85]. This issue appears to be promising due to the large number of applications of interval-valued type-2 fuzzy sets in rulebased systems and approximate reasoning [26,83,84].…”

Section: Applications Of Interval-valued and Intuitionistic Fmmmentioning

confidence: 99%

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Interval-Valued and Intuitionistic Fuzzy Mathematical Morphologies as Special Cases of $\mathbb{L}$ -Fuzzy Mathematical Morphology

et al. 2011

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Mathematical morphology (MM) offers a wide range of tools for image processing and computer vision. MM was originally conceived for the processing of binary images and later extended to gray-scale morphology. Extensions of classical binary morphology to gray-scale morphology include approaches based on fuzzy set theory that give rise to fuzzy mathematical morphology (FMM). From a mathematical point of view, FMM relies on the fact that the class of all fuzzy sets over a certain universe forms a complete lattice. Recall that complete lattices provide for the most general framework in which MM can be conducted.The concept of L-fuzzy set generalizes not only the concept of fuzzy set but also the concepts of interval-valued fuzzy set and Atanassov's intuitionistic fuzzy set. In addition, the class of L-fuzzy sets forms a complete lattice whenever the underlying set L constitutes a complete lattice. Based on these observations, we develop a general approach towards L-fuzzy mathematical morphology in this paper. Our focus is in particular on the construction of connectives for interval-valued and intuitionistic fuzzy mathematical morphologies that arise as special, isomorphic cases of L-fuzzy MM. As an application of these ideas, we generate a combination of some well-known medical image reconstruction Grants or other notes.Peter Sussner and Estevão Esmi University of Campinas, Department of Applied Mathematics, Campinas, SP, 13083-859, Brazil Tel.: +55-19-3521 5959 Fax: +55-19-3289-5766 E-mail: sussner,ra050652@ime.unicamp.br Mike Nachtegael, Tom Mélange, Glad Deschrijver, and Etienne Kerre Ghent University, Department of Applied Mathematics and Computer Science, Krijgslaan 281 -S9, 9000 Ghent, Belgium Tel.: +32-9-264 4765 Fax: +32-9-264 4995 E-mail: Mike.Nachtegael,Tom.Melange,Glad.Deschrijver,Etienne.Kerre @UGent.be techniques in terms of interval-valued fuzzy image processing.

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Section: Applications Of Interval-valued and Intuitionistic Fmmmentioning

confidence: 99%

Section: Applications Of Interval-valued and Intuitionistic Fmmmentioning

confidence: 99%

Interval-Valued and Intuitionistic Fuzzy Mathematical Morphologies as Special Cases of $\mathbb{L}$ -Fuzzy Mathematical Morphology

et al. 2011

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“…Examples of FMAMs include Kosko's max-min and max-product FAMs [12], the generalized FAM of Chung and Lee [13], Junbo's FAM [14], the max-min FAM with threshold of Liu [15], the fuzzy logical bidirectional associative memory of Belohlávek [16], as well as implicative fuzzy associative memories [17]. All of these FAM models represent fully-connected fuzzy neural networks without hidden layers [18,19]. As mentioned before, -FAMs are equipped with a competitive hidden layer.…”

Section: Introductionmentioning

confidence: 99%

Tunable equivalence fuzzy associative memories

Esmi

Sussner

Sandri

2016

Fuzzy Sets and Systems

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“…No caso em que x ξ = y ξ , para todo ξ = 1, · · · , p, a memóriá e dita autoassociativa. Memórias associativas projetadas para o armazenamento e recordação de conjuntos fuzzy são chamadas memórias associativas fuzzy [5,8].…”

Section: Introductionunclassified

Memórias Associativas Recorrentes Exponenciais Fuzzy Generalizadas Aplicadas à Classificação de Padrões

Souza¹,

Valle²

2017

Proceeding Series of the Brazilian Society of Computational and Applied Mathematics

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Resumo. Memórias associativas são modelos matemáticos biologicamente inspirados para o armazenamento e recordação de um conjunto finito de itens. As memórias associativas recorrentes exponenciais fuzzy generalizadas (GRE-FAMs) podem ser efetivamente utilizadas para o armazenamento e recordação de uma família finita de conjuntos fuzzy. Neste trabalho, descrevemos como uma GRE-FAM pode ser aplicada em um problema de classificação de padrões. Experimentos computacionais mostraram que a acurácia obtida pelos classificadores definidos com base nas GRE-FAMsé competitiva comparada a outros classificadores da literatura.Palavras-chave. Memórias Associativas, Medidas de Similaridade, Classificação de Padrões.

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Fuzzy Associative Memories and Their Relationship to Mathematical Morphology

Cited by 27 publications

References 69 publications

Interval-Valued and Intuitionistic Fuzzy Mathematical Morphologies as Special Cases of $\mathbb{L}$ -Fuzzy Mathematical Morphology

Interval-Valued and Intuitionistic Fuzzy Mathematical Morphologies as Special Cases of $\mathbb{L}$ -Fuzzy Mathematical Morphology

Tunable equivalence fuzzy associative memories

Memórias Associativas Recorrentes Exponenciais Fuzzy Generalizadas Aplicadas à Classificação de Padrões

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