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.
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