Fuzzy Ideals and Fuzzy Congruence Relations of MS-algebras

Teferi, Getachew

dc.contributor.author	Teferi, Getachew
dc.date.accessioned	2020-09-15T12:29:52Z
dc.date.available	2020-09-15T12:29:52Z
dc.date.issued	2020-09-15
dc.identifier.uri	http://hdl.handle.net/123456789/11214
dc.description.abstract	In this thesis, we introduce different types of fuzzy ideals and fuzzy ﬁlters of MS-algebras such as closure fuzzy ideals, d-fuzzy ideals, e-fuzzy ﬁlters and b-fuzzy ﬁlters of MSalgebras, and we study their properties. Also we introduce the fuzzy congruence relations of MS-algebras, and we study the properties of fuzzy congruences generated by a product of fuzzy ideal m by itself. We prove that the set of fuzzy congruence relations of an MS-algebra is a complete lattice. Finally, we introduce the fuzzy congruences of demi-pseudocomplemented MS-algebras and study their basic properties. We study the properties of fuzzy congruence generated by a product of fuzzy ideal m by itself. We introduce kernel fuzzy ideals and cokernel fuzzy ﬁlters of demi-pseudocomplemented MSalgebra. We characterized fuzzy congruence relations using kernel fuzzy ideals. Also we introduce ( ; )-fuzzy ideals of a demi-pseudocomplemented MS-algebra L. We show that these fuzzy ideals are precisely the kernel of fuzzy congruence J of L such that (L=J; ) is Boolean. Also we prove that ( ; )-fuzzy ideals form a sublattice of fuzzy ideals of L, and the set of these fuzzy ideals is isomorphic to the closed interval G F and c of the fuzzy congruence lattice of L where G F is Glievenko fuzzy congruence and c is the universal fuzzy congruence. i i	en_US
dc.language.iso	en_US	en_US
dc.subject	Mathematics	en_US
dc.title	Fuzzy Ideals and Fuzzy Congruence Relations of MS-algebras	en_US
dc.type	Thesis	en_US