Document Type: Research Paper


1 Department of Mathematics, Faculty of Science, Higher Education Center of Eghlid, Eghlid, Iran

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


In this paper, we introduce the notion of co-annihilator of a subset
in a triangle algebra. It is shown that the co-annihilator of a
subset is an interval valued residuated lattice (IVRL)-filter. Also, a
special set of a triangle algebra is defined and the relationship
between this set and co-annihilator of a subset in triangle algebra
is considered. Finally, co-annihilators preserving congruence
relation, or $CP$-congruence are defined and some results of them
are given.


[1] S. A. Celani, Remarks on Annihilators preserving congruence relations, Math. Slovaca, 62
(2012), 389-398.
[2] H. Ono, substructural logics and residualted lattices- An introduction, Trends in Logic, 20
(2003), 177-212.
[3] D. Piciu, Algebras of Fuzzy Logic, Ed. Universtaria Craiova, 2007.
[4] E. Turunen, BL-algebras of basic fuzzy logic, Mathware and Soft Computing, 6 (1999), 49-61.
[5] B. Van Gasse, G. Deschrijver, C. Cornelis and E. E. Kerre, Filters of residuated lattices and
triangle algebras, Information Sciences, 180 (2010), 3006-3020.
[6] B. Van Gasse, G. Deschrijver, C. Cornelis and E. E. Kerre, Triangle algebras: a formal
logic approach to interval-valued residuated lattices, Fuzzy Sets and Systems, 159 (2008),
[7] M. Ward and R. Dilworth, Residuated lattices, Transactions of the American Mathematical
Society, 45 (1939), 335-354.
[8] S. Zahiri, A. Borumand Saeid and E. Eslami, A new approach to fi lters in triangle algebras,
Publications de l'Institut Mathematique, 101(115) (2017), 267-283.
[9] S. Zahiri, A. Borumand Saeid and E. Eslami, On maximal filters in triangle algebras, Journal
of Intelligent and Fuzzy Systems, 30 (2016), 1181-1193.