On fuzzy subalgebras of BE-algebras
Tóm tắt
In this paper the notion of fuzzy BE-algebras are introduced. We state and prove some theorems in fuzzy BE-algebras and level subalgebras. Some characterizations of fuzzy subalgebras of BE-algebras are given. Using fuzzy subalgebras, characterizations of Artinian and Noetherian BE-algebras are also established. Finally the notion of fuzzy topological BE-algebras is introduced. We state and prove the Foster’s results on homomorphic images and inverse images in fuzzy topological BE-algebras.
Tài liệu tham khảo
Foster D.H.: Fuzzy topological groups. J. Math. Anal. Appl. 67, 549–564 (1979)
Hu Q.P., Li X.: On BCH-algebras. Math. Semin. Notes 11, 313–320 (1983)
Hu Q.P., Li X.: On proper BCH-algebras. Math. Jpn. 30, 659–661 (1985)
Imai Y., Iseki K.: On axiom systems of propositional calculi. XIV Proc. Jpn. Acad. 42, 19–22 (1966)
Iseki K., Tanaka S.: An introduction to the theory of BCK-algebras. Math. Jpn. 23, 1–26 (1978)
Iseki K.: On BCI-algebras. Math. Semin. Notes 8, 125–130 (1980)
Jun Y.B., Roh E.H., Kim H.S.: On BH-algebras. Sci. Math. Jpn. 1, 347–354 (1998)
Kim, H.S., Kim, Y.H.: On BE-algebras, Scientiae Mathematicae Japonicae Online, e-2006, 1299–1302 (2006)
Neggers J., Kim H.S.: On d-algebras. Math. Slov. 49, 19–26 (1999)
Neggers J., Kim H.S.: On B-algebras. Math. Vensik 54, 21–29 (2002)
Rosenfeld A.: Fuzzy groups. J. Math. Anal. Appl. 35, 512–517 (1971)
Zadeh L.A.: Fuzzy sets. Inform. Control 8, 338–353 (1965)