Fuzzy congruence relations on pseudo BE-algebras

Document Type : Original Article

Authors

1 Department of Mathematics, Payame Noor University, P.o.box. 19395-3697, Tehran, Iran

2 Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran

3 Department of Mathematics, Beihang University (BUAA), BUA-Haidian School of Applied Technology, china

Abstract

In this paper, we introduce the concept of fuzzy congruence relations on a pseudo BE-algebra and some of properties are investigated. We show that the set of all fuzzy congruence relations is a modular lattice and the quotient structure induced by fuzzy congruence relations is studied.

Keywords

References

[1] A. Borumand Saeid, A. Rezaei, R.A. Borzooei, Some types of filters in BE-algebras, Mathematics in Computer Science, 7(3) (2013), 341–352.
[2] R.A. Borzooei, M. Bakhsi, T-fuzzy congruences and T-fuzzy filters of a BL-algebra, Iranian
Journal of Fuzzy Systtems, 6(4) (2009), 37–47.
[3] R.A. Borzooei, A. Borumand Saeid, A. Rezaei, A. Radfar, R. Ameri, On pseudo BE-algebras,
Discussiones Mathematica, General Algebra and Applications, 33 (2013), 95–108.
[4] R.A. Borzooei, A. Borumand Saeid, A. Rezaei, A. Radfar, R. Ameri, On distributive pseudo
BE-algebras, Fasciculi Mathematici, 54 (2015), 21–39.
[5] L.C. Ciungu, Commutative pseudo BE-algebras, Iranian Journal of Fuzzy Systtems, 13(1)
(2016), 131–144.
[6] G. Dymek, A. Walendziak, Fuzzy ideals of pseudo BCK algebras, Demonstratio Mathematica,
XLV, 1 (2012), 1–15.
[7] H.S. Kim, Y.H. Kim, On BE-algebras, Scientiae Mathematicae Japonicae, 66(1) (2007), 113–
117.
[8] M. Kondo, Fuzzy congruences on groups, Quasigroups and Related Systems, 11 (2004), 59–70.
[9] K.J. Lee, Fuzzy ideals of pseudo BCI-algebras, Journal of Applied Mathematics and Informatics,
27 (2009), 795–807.
[10] V. Murali, Fuzzy congruence relations, Fuzzy Sets and Systems, 30 (1989), 155–163.
[11] V. Murali, Fuzzy congruence relations, Fuzzy Sets and Systems, 41 (1991), 359–369.
[12] A. Rezaei, Fuzzy medial filters on pseudo BE-algebras, Submitted.
[13] A. Rezaei, A. Borumand Saeid, On fuzzy subalgebras of BE-algebras, Afrika Matematika, 22(2)
(2011), 115–127.
[14] A. Rezaei, A. Borumand Saeid, Fuzzy congruence relations in CI-algebras, Neural Computing
and Applications, 21(1) (2012), 319–328.
[15] A. Rezaei, A. Borumand Saeid, A. Radfar, R.A. Borzooei, Congruence relations on pseudo
BE-algebras, Annals of the University of Craivova, Mathematics and Computer Science Series,
41(2) (2014), 166–176.
[16] A. Walendziak, A. Rezaei, Fuzzy filters of pseudo BE-algebras, Afrika Matematika, (on line),
(2019), 1–12.
[17] A. Walendziak, M. Wojciechowska-Rysiawa, Fuzzy ideals of pseudo BCH-algebras, Mathematica Aeterna, 5(5) (2015), 867–881.
[18] L.A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338–353.
Journal of Algebraic Hyperstructures and Logical Algebras
Volume 1, Issue 2
May 2020
Pages 31-43

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