Abstract:
In this project, Almost Distributive Fuzzy Lattice (ADFL) is characterized by ADL's
in terms of level se𝑡 𝐴
α
of a fuzzy Relation A. The Concept of ideals, filters, the
smallest ideals and the smallest filters containing a non-empty subset of R of an
ADFL are introduced, and some results are proved, In addition, the meet ``∧ ``
𝑎𝑛𝑑 𝑗𝑜𝑖𝑛 `` ∨`` of two ideals(filters) of an ADFL are defined, and finally it is proved
that for any two ideals I and J of an ADFL L, 𝐼 ∧ 𝐽 𝑎𝑛𝑑 𝐼 ∨ 𝐽 are also ideals of L,and
for any two filters F and G of an ADFL L, 𝐹 ∧ 𝐺 𝑎𝑛𝑑 𝐹 ∨ 𝐺 are also filters of L.