Rajab Ali Borzooei - Department of Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran.
Mohammad Mohseni Takallo - Department of Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran.
Mona Aaly Kologani - Hatef Higher Education Institute, Zahedan, Iran.
Young Bae Jun - Department of Mathematics Education, Gyeongsang National University, P.O. Box ۵۲۸۲۸, Jinju, Korea.

The notion of fuzzy ideal in bounded equality algebras is defined, and several properties are studied. Fuzzy ideal generated by a fuzzy set is established, and a fuzzy ideal is made by using the collection of ideals. Characterizations of fuzzy ideal are discussed. Conditions for a fuzzy ideal to attains its infimum on all ideals are provided. Homomorphic image and preimage of fuzzy ideal are considered. Finally, quotient structures of equality algebra induced by (fuzzy) ideal are studied.

Bounded equality algebra, fuzzy sets, ideal, fuzzy ideal, quotient structure