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AN INVESTIGATION ON THE CO-ANNIHILATORS IN TRIANGLE ALGEBRAS | ||
| Iranian Journal of Fuzzy Systems | ||
| مقاله 8، دوره 15، شماره 7، آذر و دی 2018، صفحه 91-102 اصل مقاله (352.82 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2018.4287 | ||
| نویسندگان | ||
| Saeide Zahiri1؛ Arsham Borumand Saeid* 2؛ Masoome Zahiri1 | ||
| 1Department of Mathematics, Faculty of Science, Higher Education Center of Eghlid, Eghlid, Iran | ||
| 2Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Triangle algebra؛ IVRL-filter؛ Co-annihilator؛ congruence | ||
| مراجع | ||
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[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), 1042-1060. [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. | ||
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