L-Fuzzy Ideals and Filters of a Poset By

DERSO, ABEJE

dc.contributor.author	DERSO, ABEJE
dc.date.accessioned	2020-09-15T12:26:58Z
dc.date.available	2020-09-15T12:26:58Z
dc.date.issued	2020-09-15
dc.identifier.uri	http://hdl.handle.net/123456789/11213
dc.description.abstract	In different literatures, we have found several generalizations of ideals and ﬁlters of a lattice to an arbitrarily partially ordered set which has been studied by different scholars . In this thesis we introduce several generalizations of L-fuzzy ideals and ﬁlters of a lattice to an arbitrarily partially ordered set whose truth values are in a complete lattice satisfying the inﬁnite meet distributive law. These are: L-fuzzy closed ideal and ﬁlter of a poset, L-fuzzy Frink ideal and ﬁlter of a poset, L-fuzzy ideal and ﬁlter of a poset in the sense of Halaš, L-fuzzy semi ideals and ﬁlters of a poset, L-fuzzy V-ideals and V-ﬁlters of a poset and m-L-fuzzy ideals and ﬁlters of a poset, where m is any cardinal number. All the deﬁnitions of L-fuzzy ideals and ﬁlters of a poset that we introduce in this thesis are generalizations of the notions of L-fuzzy ideals and ﬁlters of a lattice. We also study and establish some characterizations of them and we prove that the set of all L-fuzzy ideals of a poset forms a complete lattice with respect to point-wise ordering. Next, by choosing the L-fuzzy ideals and ﬁlters of a poset in the sense of Halaš as an L-fuzzy ideals of a poset, we introduce the notion of L-fuzzy prime ideals, prime Lfuzzy ideals, maximal L-fuzzy ideals and L-fuzzy maximal ideals. We also study and give sufﬁcient conditions for the existence of L-fuzzy prime ideals and prime L-fuzzy ideals in the lattice of all L-fuzzy ideals of a poset. Lastly, we introduce the concept of L-fuzzy semi-prime ideals in a general poset. Characterizations of L-fuzzy semi-prime ideals in posets as well as characterizations of an L-fuzzy semi-prime ideal to be L-fuzzy prime ideal are obtained. Also, the relations between the L-fuzzy semi-prime (respectively, L-fuzzy prime) ideals of a poset and the L-fuzzy semi-prime (respectively, L-fuzzy prime) ideals of the lattice of all ideals of a poset are established. We also extend and prove an analogue of Stone’s Theorem for ﬁnite posets, which has been studied by V. S. Kharat and K. A. Mokbel[35] using L-fuzzy semi-prime ideals.	en_US
dc.language.iso	en_US	en_US
dc.subject	Mathematics	en_US
dc.title	L-Fuzzy Ideals and Filters of a Poset By	en_US
dc.type	Thesis	en_US