Section-retraction-pairs between fuzzy domains

Fuzzy Galois connections on fuzzy posets

“…f : X −→ Y is called order-preserving or isotone (respectively, antitone) [16,17] if for all x, y ∈ X, e X (x, y) ≤ e Y (f (x), f(y)) (respectively, e X (x, y) ≤ e Y (f (y), f(x))).…”

“…[4,Theorem 3.12]), are exactly the three axioms of the definition of an L-order in [4,5] and that of a fuzzy poset in [16,17].…”

“…This paper is organized as follows. In Section 2, we recall some basic notions and properties of fuzzy posets proposed in [4,5,16,17]. In Section 3, fuzzy Galois connections are defined on fuzzy posets and their properties are investigated.…”

“…2 Fuzzy ordered sets Definition 2.1 [4,5,16,17] Let X be a nonempty set. A map e : X × X −→ L (called a degree function) is called a fuzzy partial order on X if (E1) for all x ∈ X, e(x, x) = 1;…”

“…Definition 2.4 [16,17] Let (X, e) be a fuzzy poset, x 0 ∈ X, A ∈ L X . x 0 is called a join (respectively, meet) of A (w. r. t. the fuzzy partial order e), in symbols…”