QUOTIENT STRUCTURES IN EQUALITY ALGEBRAS

نویسندگان
Borzooei, Rajab Ali ID 1
Aaly Kologani, Mona ID 2
Jun, Young Bae ID 3
Mohseni Takallo, Mohammad ID 4

1 Department of Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran.

2 Hatef Higher Education Institute, Zahedan, Iran.

3 Department of Mathematics Education, Gyeongsang National University, P.O. Box 52828, Jinju, Korea.

4 Department of Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran.

doi
10.22044/jas.2022.11919.1608
چکیده

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.

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