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

(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:
http://hdl.handle.net/1854/LU-2128176

- author
- Peter Sussner, Mike Nachtegael UGent, Tom Mélange UGent, Glad Deschrijver, Estevão Esmi and Etienne Kerre UGent
- organization
- year
- 2012
- 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
- 2016-12-19 15:39:01

@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.