esraa Kareem kadhim marid

Fuzzy Bd-ideals provide a useful framework for studying Bd-algebras. This paper focuses on the Cartesian and direct products of finite prime fuzzy Bd-ideals. We extend the idea of primeness to these constructions and analyze how it behaves under product operations. Key properties of the Cartesian product are obtained, including conditions that keep primeness intact. We also study the direct product case and identify when the prime structure is preserved. These findings give a clearer view of how fuzzy ideals interact within product structures in Bd-algebras.

In this thesis, the concept Interval-valued Fuzzy AT-ideal of AT-algebra has been introduced This concept and give some Properties of it have studied. The image of the homomorphism formation and the invers image for the interval-valued fuzzy AT-ideal have been investigated. The quotient AT-algebras is induced by interval-valued Fuzzy AT-ideal of AT-algebra has proved. The concept of Interval-valued Intuitionistic Fuzzy AT-ideal of AT-algebra has been introduced. Also, the subalgebra, homomorphism and cartesian product of interval-valued intuitionistic fuzzy AT-ideal of AT-algebra have been investigated for this concept. The concept of the -translation of Intuitionistic Fuzzy AT-ideals of AT-algebras has been presented as well, and some of its properties have been discussed under the intersection and the cartesian product.

uzzy AT-ideal; intuitionistic fuzzy AT-subalgebra; intuitionistic fuzzy AT-ideal; α-translation of intuitionistic fuzzy; intuitionistic fuzzy extension; intuitionistic fuzzy multiplication. 2010 AMS Subject Classification: 06F35, 03G25, 08A72.

uzzy AT-ideal; intuitionistic fuzzy AT-subalgebra; intuitionistic fuzzy AT-ideal; α-translation of intuitionistic fuzzy; intuitionistic fuzzy extension; intuitionistic fuzzy multiplication. 2010 AMS Subject Classification: 06F35, 03G25, 08A72.

uzzy AT-ideal; intuitionistic fuzzy AT-subalgebra; intuitionistic fuzzy AT-ideal; α-translation of intuitionistic fuzzy; intuitionistic fuzzy extension; intuitionistic fuzzy multiplication. 2010 AMS Subject Classification: 06F35, 03G25, 08A72.