On fuzzy implicative ideals in BL-algebras

In this paper, the concept of fuzzy implicative ideal in BL-algebras is introduced and several properties of it are stated. Using the concept of level subsets, some characterizations of fuzzy implicative ideals are proved. Also, it is proved that the concepts of fuzzy implicative ideal and fuzzy Boolean ideal in BL-algebras are coincide. Moreover, it is shown that a BL-algebra L is a Boolean algebra if and only if any fuzzy ideal of L is a fuzzy implicative ideal. Finally, it is proved that the homomorphic image and preimage of fuzzy implicative ideals are fuzzy implicative ideal.