L always denotes a completely distributive lattice and if the lattices L does not contain the zero element and unit element I

M), [intersection],[union],[phi],M }is a complete distributive lattice and it's represented by following Hass diagram

We generalize the classical map concept into the L- fuzzy map which combines all elements in the domain with elements in the co domain giving correlation degrees which takes its values from a complete distributive lattice in a way that forgets the elements whose membership degrees equal to lattice's zero in the domain and co domain.

Wu: Fuzzy ideals on a

distributive lattice, Fuzzy Sets and Systems, 35(1990), 231-240.

Finally, in Section 5 we make some remarks about a new partial order on TSSCPPs obtained via boolean triangles, which reduces in the permutation case to the distributive lattice which is the product of chains of lengths 2, 3, .

In [10], we examined a poset structure on TSSCPPs, which turned out to be a distributive lattice with poset of join irreducibles very similar to that of the ASM lattice.

5] Every distributive lattice is a modular lattice.

Let L be a distributive lattice and D be a generalized f- derivation on L where f : L [right arrow] L is a join-homomorphism.

l) if and only if S is a subdirect product of distributive lattice and a member in [?

Let S be a bi-semilattice, if S satisfies the additional identity x + xy [approximately equal to] x and x + yz [approximately equal to] (x + y)(x + z), then S is said to be a distributive lattice.

Farley and Schmidt answer a similar question for distributive lattices in [6].

Schmidt, Posets that locally resemble distributive lattices, J.