Document Type : Original Manuscript


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.


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.


 1. M. Aaly Kologani, M. Mohseni Takallo and H. S. Kim, Fuzzy filters of hoops based on fuzzy points, Math., 7(5) (2019), 430–441.
2. R. A. Borzooei and M. Aaly Kologani, Minimal prime ideals in hoops, J. Algebr. Hyperstruc. Log. Algebr., 2(3) (2020), 109–120.
3. R. A. Borzooei and M. Aaly Kologani, Results on hoops, J. Algebr. Hyperstruc. Log. Algebr., 1(1) (2020), 61–77.
4. R. A. Borzooei, F. Zebardast and M. Aaly Kologani, Some type filters in equality algebras, Categ. Gen. Algebr, 7 (2017), 33–55.
5. L. C. Ciungu, On pseudo-equality algebras, Arch. Math. Log, 53 (2014), 561–570.
6. A. Dvurečenskij and O. Zahiri, Pseudo equality algebras-revision, Soft. Comput., 20 (2016), 2091–2101.
7. S. Jenei, Equality algebras, IEEE International Symposium on Computational Intelligence and Informatics, Budapest, Hungary, 2010.
8. S. Jenei, Equality algebras, Stud. Log., 100 (2012), 1201–1209.
9. S. Jenei and Kóródi, On the variety of equality algebras, Fuzzy Log. Tech., (2011), 153–155.
10. S. Jenei and Kóródi, Pseudo equality algebras, Arch. Math. Log, (2013), 469– 481.
11. Y. B. Jun and E. H. Roh, Fuzzy commutative ideals of BCK-algebras, Fuzzy Sets Syst., 64(3) (1994), 401–405.
12. M. Mohseni Takallo, S. S. Ahn, R. A. Borzooei and Y. B. Jun, Multipolar Fuzzy p-Ideals of BCI-algebras, Math., 7(11) (2019), 1094–1107.
13. M. Mohseni Takallo, H. Bordbar, Y. B. Jun and R. A. Borzooei, BMBJneutrosophic ideals in BCK/BCI-algebras, N.S.S., 27 (2019), 1–16.
14. V. Novák, Fuzzy type theory as higher-order fuzzy logic, Proceedings of the 6th International Conference on Intelligent Technologies, 2005.
15. V. Novák, On fuzzy type theory, Fuzzy Set. Syst., 149 (2005), 235–273.
16. V. Novák and B. De Baets, EQ-algebras, Fuzzy Set. Syst., 160(20) (2009), 2956–2978.
17. A. Paad, Ideals in bounded equality algebras, Filomat, 33(7) (2019), 2113– 2123.
18. A. Rosenfeld, Fuzzy groups, J. Math. Anal. Appl, 35(3) (1971), 512–517.
19. U. M. Swamy, D. Viswanadha Raju, Fuzzy ideals and congruences of lattices, Fuzzy Set. Syst., 95(2) (1998), 249–253.
20. F. Xie and H. Liu, Ideals in pseudo-hoop algebras, J. Algebr. Hyperstruc. Log. Algebr., 1(4) (2020), 39–53.
21. L. A. Zadeh, Fuzzy sets, Inf. Control, 8 (1965), 338–353.
22. F. Zebardast, R. A. Borzooei and M. Aaly Kologani, Results on equality algebras, Inf. Sci., 381 (2017), 270–282