Please use this identifier to cite or link to this item: http://repositorio.unicamp.br/jspui/handle/REPOSIP/60512
Type: Artigo de periódico
Title: Interval-Valued and Intuitionistic Fuzzy Mathematical Morphologies as Special Cases of L-Fuzzy Mathematical Morphology
Author: Sussner, P
Nachtegael, M
Melange, T
Deschrijver, G
Esmi, E
Kerre, E
Abstract: 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 techniques in terms of interval-valued fuzzy image processing.
Subject: Mathematical morphology
Complete lattice
L-fuzzy sets
Interval-valued fuzzy sets
Atanassov's intuitionistic fuzzy sets
L-fuzzy mathematical morphology
L-fuzzy connectives
Inclusion measure
Duality
Negation
Adjunction
Country: Holanda
Editor: Springer
Rights: fechado
Identifier DOI: 10.1007/s10851-011-0283-1
Date Issue: 2012
Appears in Collections:Unicamp - Artigos e Outros Documentos

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