Abstract:
In this project, we have seen the concept of principal ideals, principal filters and the fuzzy
lattice of ideals and filters of an almost distributive fuzzy lattice. It is proved that a fuzzy
poset (I
A
(L), B) and (F
A
(L), B) forms a fuzzy lattice, where I
A
(L) and F
A
(L) are the set
containing all ideals, and the set containing all filters of an Almost Distributive Fuzzy
Lattice(ADFL) respectively. And also proved that, a fuzzy poset (PI
A
(L), B) and (PF
A
(L),
B) forms fuzzy distributive lattice, where PI
A
(L) and PF
A
(L) denotes the set containing all
principal ideals and the set containing all principal filters of an ADFL. Finally, it is
proved that for any ideal I and filter F of an ADFL, I
i
A
= {(i]
A
: i ∈ I} and F
: f ∈ F}
are ideals of a fuzzy distributive lattice (PI
A
(L), B) and (PF
A
f
A
= {[f)
A
(L), B) respectively, and F
=
{(f ]
A
: f ∈ F} and I
f
A
= {[i)
A
: i ∈ I} are filters of a distributive fuzzy lattice (PI
A
(L), B) and
(PF
A
(L), B) respectively.
i
A