Abstract:
Abstract
In this dissertation Birkho center of almost distributive fuzzy lattice, properties
of stone almost distributive fuzzy lattice,B-almost distributive fuzzy lattice, P0
almost distributive fuzzy lattice and P1 almost distributive fuzzy lattice are in-
troduced as extension of Birkho center of almost distributive lattice, properties of
stone almost distributive lattice,B-almost distributive lattice,P0 almost distribu-
tive lattice,and P1 almost distributive lattice respectively. They are conceived as
extensions of their analogous operations on the classical theory .
One of the result found here is the connection of almost distributive lattice in
lattice theory and almost distributive fuzzy lattice in fuzzy lattice theory. The con-
cept of Birkho center BA(R) of an almost distributive fuzzy lattice (R;A) with
maximal element is introduced.
We also prove that product of almost distributive fuzzy lattice is again almost
distributive fuzzy lattice. We develop the concept of properties of stone almost
distributive fuzzy lattice(Stone ADFL) as an extension of properties of stone al-
most distributive lattice (Stone ADL) and necessary and su cient conditions for
properties of stone almost distributive fuzzy lattice are investigated.
Again the notion of B-almost distributive fuzzy lattice(B-ADFL) interms of its
principal ideal fuzzy lattice is introduced. We also explained the concept of P0
almost distributive fuzzy lattice (P0ADFL) with a nite chain base and we prove
basic properties about P0 almost distributive fuzzy lattice as an extension of P0
almost distributive lattice and product of family of P0ADFL is also P0ADFL.
Finaly, the idea of P1 almost distributive fuzzy lattice as an extension of P1
almost distributive lattice is introduced and we set necessary and su cient con-
ditions for a P1 almost distributive lattice to become a P1 almost distributive
fuzzy lattice.