Further on Fuzzy Ideals of Lattices

Wondwosen, Zemene

dc.contributor.author	Wondwosen, Zemene
dc.date.accessioned	2020-09-15T12:42:35Z
dc.date.available	2020-09-15T12:42:35Z
dc.date.issued	2020-09-15
dc.identifier.uri	http://hdl.handle.net/123456789/11217
dc.description.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	en_US
dc.language.iso	en_US	en_US
dc.subject	Mathematics	en_US
dc.title	Further on Fuzzy Ideals of Lattices	en_US
dc.type	Thesis	en_US