Abstract:
In this thesis, we introduce the concept of relative fuzzy annihilator ideals in distributive
lattices. We give a set of equivalent conditions for a fuzzy annihilator to be a fuzzy ideal
and we characterize distributive lattice with the help of fuzzy annihilator ideals. We also
characterize relative fuzzy annihilators in terms of fuzzy points. Using the concept of
relative fuzzy annihilator, we show that the class of fuzzy ideals of distributive lattices
forms a Heything algebra. We define fuzzy annihilator ideals and we show that the class
of fuzzy annihilator ideals can be made a complete Boolean algebra. Furthermore, we
study fuzzy annihilator preserving homomorphism. Next, we introduce the concept of
a-fuzzy ideals in distributive lattices with least element "0". We also study the special
class of fuzzy ideals called a-fuzzy ideals, which is isomorphic to the set of all fuzzy
filters of the lattice of annulates. We give a set of equivalent conditions for a fuzzy ideal
to be an a-fuzzy ideal, which leads to a characterization of disjunctive lattices. Moreover,
we study the space of prime a-fuzzy ideals of distributive lattices. It is shown that the
class of a-fuzzy ideals is isomorphic to the set of all open sets of prime a-fuzzy ideals.
We give a necessary and sufficient condition for the space of prime a-fuzzy ideals to be a
regular space.
The concept of d-fuzzy ideals and O-fuzzy ideals in distributive lattices is also introduced.
We define d-fuzzy ideals in terms of pseudo-complementation and fuzzy filter.
We give a set of equivalent conditions for the class of d-fuzzy ideals to be a sublattice
to the lattice of all fuzzy ideals, which leads to a characterization of Stone lattices. We
characterize d-fuzzy ideals in terms of fuzzy congruence. We study the image and inverse
image of d-fuzzy ideals under a homomorphism mapping. Moreover, we define O-fuzzy
ideals in distributive lattices as a generalization of d-fuzzy ideals. We also show that every
O-fuzzy ideal is an a-fuzzy ideal. Furthermore, we prove that every a-fuzzy ideal is not