@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’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 Mélange, Tom and Deschrijver, Glad and Esmi, Estevão and Kerre, Etienne}},
  issn         = {{0924-9907}},
  journal      = {{JOURNAL OF MATHEMATICAL IMAGING AND VISION}},
  keywords     = {{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}},
  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://doi.org/10.1007/s10851-011-0283-1}},
  volume       = {{43}},
  year         = {{2012}},
}

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