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Basic concepts of complete residuated lattice-valued fuzzy mathematical morphology.
- Source :
-
Journal of Intelligent & Fuzzy Systems . Apr2024, p1-10. 10p. - Publication Year :
- 2024
-
Abstract
- The aim of this paper is to present basic concepts of lattice-valued fuzzy mathematical morphology. We use a complete residuated lattice as the codomain of fuzzy sets, a pair of fuzzy powerset operators, called the fuzzy erosion operator and the fuzzy dilation operator, is defined and their properties and relationships are studied. The pair of two operators forms a Galois adjunction and so that the induced fuzzy opening operator and fuzzy closing are an interior operator and a closure operator respectively. It is shown that the dilation stable sets and the erosion stable sets are equivalent, which form a fuzzy Alexandrov topology. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 10641246
- Database :
- Academic Search Index
- Journal :
- Journal of Intelligent & Fuzzy Systems
- Publication Type :
- Academic Journal
- Accession number :
- 176637676
- Full Text :
- https://doi.org/10.3233/jifs-238540