Ghent University Academic Bibliography

Advanced

Interval-valued and intuitionistic fuzzy mathematical morphologies as special cases of L-fuzzy mathematical morphology

Peter Sussner, Mike Nachtegael UGent, Tom Mélange UGent, Glad Deschrijver UGent, Estevão Esmi and Etienne Kerre UGent (2012) JOURNAL OF MATHEMATICAL IMAGING AND VISION. 43(1). p.50-71
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.
Please use this url to cite or link to this publication:
author
organization
year
type
journalArticle (original)
publication status
published
subject
keyword
SET-THEORY, Duality, ASSOCIATIVE MEMORIES, L-fuzzy mathematical morphology, L-fuzzy connectives, Inclusion measure, TYPE-2 FUZZISTICS, Mathematical morphology, L-fuzzy sets, Atanassov’s intuitionistic fuzzy sets, Adjunction, Negation, Complete lattice, Interval-valued fuzzy sets, GRAY-SCALE, LOGIC, OPERATORS, BINARY, CLASSIFICATION, DECOMPOSITION, FUNDAMENTALS
journal title
JOURNAL OF MATHEMATICAL IMAGING AND VISION
J. Math. Imaging Vis.
volume
43
issue
1
pages
50 - 71
Web of Science type
Article
Web of Science id
000302346000005
JCR category
MATHEMATICS, APPLIED
JCR impact factor
1.767 (2012)
JCR rank
20/247 (2012)
JCR quartile
1 (2012)
ISSN
0924-9907
DOI
10.1007/s10851-011-0283-1
language
English
UGent publication?
yes
classification
A1
copyright statement
I have transferred the copyright for this publication to the publisher
id
2128176
handle
http://hdl.handle.net/1854/LU-2128176
date created
2012-06-01 10:14:17
date last changed
2012-06-18 13:31:01
@article{2128176,
  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{\textquoteright}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.},
  author       = {Sussner, Peter and Nachtegael, Mike and M{\'e}lange, Tom and Deschrijver, Glad and Esmi, Estev{\~a}o and Kerre, Etienne},
  issn         = {0924-9907},
  journal      = {JOURNAL OF MATHEMATICAL IMAGING AND VISION},
  keyword      = {SET-THEORY,Duality,ASSOCIATIVE MEMORIES,L-fuzzy mathematical morphology,L-fuzzy connectives,Inclusion measure,TYPE-2 FUZZISTICS,Mathematical morphology,L-fuzzy sets,Atanassov{\textquoteright}s intuitionistic fuzzy sets,Adjunction,Negation,Complete lattice,Interval-valued fuzzy sets,GRAY-SCALE,LOGIC,OPERATORS,BINARY,CLASSIFICATION,DECOMPOSITION,FUNDAMENTALS},
  language     = {eng},
  number       = {1},
  pages        = {50--71},
  title        = {Interval-valued and intuitionistic fuzzy mathematical morphologies as special cases of L-fuzzy mathematical morphology},
  url          = {http://dx.doi.org/10.1007/s10851-011-0283-1},
  volume       = {43},
  year         = {2012},
}

Chicago
Sussner, Peter, Mike Nachtegael, Tom Mélange, Glad Deschrijver, Estevão Esmi, and Etienne Kerre. 2012. “Interval-valued and Intuitionistic Fuzzy Mathematical Morphologies as Special Cases of L-fuzzy Mathematical Morphology.” Journal of Mathematical Imaging and Vision 43 (1): 50–71.
APA
Sussner, P., Nachtegael, M., Mélange, T., Deschrijver, G., Esmi, E., & Kerre, E. (2012). Interval-valued and intuitionistic fuzzy mathematical morphologies as special cases of L-fuzzy mathematical morphology. JOURNAL OF MATHEMATICAL IMAGING AND VISION, 43(1), 50–71.
Vancouver
1.
Sussner P, Nachtegael M, Mélange T, Deschrijver G, Esmi E, Kerre E. Interval-valued and intuitionistic fuzzy mathematical morphologies as special cases of L-fuzzy mathematical morphology. JOURNAL OF MATHEMATICAL IMAGING AND VISION. 2012;43(1):50–71.
MLA
Sussner, Peter, Mike Nachtegael, Tom Mélange, et al. “Interval-valued and Intuitionistic Fuzzy Mathematical Morphologies as Special Cases of L-fuzzy Mathematical Morphology.” JOURNAL OF MATHEMATICAL IMAGING AND VISION 43.1 (2012): 50–71. Print.