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.
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