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Interval-valued and intuitionistic fuzzy mathematical morphologies as special cases of L-fuzzy mathematical morphology
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- journalArticle
- info:eu-repo/semantics/article
- info:eu-repo/semantics/publishedVersion
- Mathematics and Statistics
- 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