# A Important Double Twist On CK-636

Theorem forty ��Let X, Y be nonempty sets, and let A, B be fuzzy sublattices of X, Y, respectively. f : A �� B is definitely an L-fuzzy mapping, if for all a ��*(0), f[a] is often a lattice homomorphism how to order from A[a] to B[a], and then f : A �� B is often a fuzzy lattice homomorphism.Theorem 41 ��Let X, Y be nonempty sets, and let A, B be fuzzy sublattices of X, Y, respectively. f : A �� B is surely an L-fuzzy mapping, if forhttp://www.selleckchem.com/products/a-674563.html all b, c L, ��(bc) = ��(b)��(c), then the following conditions are equivalent:f : A �� B is a fuzzy lattice homomorphism;for all a ��*(0), f[a] is usually a lattice homomorphism from A[a] to B[a].5. Fuzzy LatticeIn Definitions 16, 17, and 18, allow A = X, and then the problems are real naturally. So we will get a further unique situation of bi-fuzzy lattice-fuzzy lattice. Now we give its definition and corresponding theorems.

Definition 42 ��Let L be a fully distributive lattice, X �� , and allow R be an L-fuzzy relation on X, if R satisfies for any x, y, z X, there exist s, t X this kind of that(S1)R(x, s) �� R(x, x), R(y, s) �� R(y, y),(S2)R(s, z) �� R(x, z)��R(y, z),(T1)R(t, x) �� R(x, x), R(t, y) �� R(y, y),(T2)R(z, t) �� R(z, x)��R(z, y). then CK-636we get in touch with s, t as supremum and infimum of x, y with respect to R, respectively.Definition 43 ��Let L be a absolutely distributive lattice, X �� , and let R be an L-fuzzy relation on X, if for just about any x, y X, the two supremum and infimum of x, y with respect to R exist, then we get in touch with X as a fuzzy lattice with respect to R.Exact same for the corresponding theorems in last segment,we have the following theorem.

Theorem 44 ��Let L be a totally distributive lattice, X �� , and allow R be an L-fuzzy relation; then (1), (2), (3), (6), (7), and (8) with the following conditions are equivalent, and (four)(five)(1) is accurate.X is often a fuzzy lattice with respect to R.For each a L0, (X, R[a]) can be a lattice.For every a M(L), (X, R[a]) is really a lattice.For each a ��(1), (X, R(a)) is usually a lattice.For each a ��*(one), (X, R(a)) is usually a lattice.For each a ��(0), (X, R[a]) is a lattice.For each a ��*(0), (X, R[a]) is a lattice.For each a P(L), (X, R(a)) is often a lattice.AcknowledgmentThis function was supported from the National Normal Science Basis of China (no. 61171195).

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