ŁUKASIEWICZ FUZZY FILTERS IN HOOPS | ||
| Journal of Algebraic Systems | ||
| دوره 12، شماره 1، آذر 2024، صفحه 1-20 اصل مقاله (176.44 K) | ||
| نوع مقاله: Original Manuscript | ||
| شناسه دیجیتال (DOI): 10.22044/jas.2022.12139.1632 | ||
| نویسندگان | ||
| Mohammad Mohseni Takallo1؛ Mona Aaly Kologani2؛ Young Bae Jun3؛ Rajab Ali Borzooei* 1 | ||
| 1Department of Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran. | ||
| 2Hatef Higher Education Institute, Zahedan, Iran. | ||
| 3Department of Mathematics Education, Gyeongsang National University, Jinju 52828, Korea. | ||
| چکیده | ||
| By applying the concept of the Lukasiewicz fuzzy set to the filter in hoops, the Lukasiewicz fuzzy filter is introduced and its properties are investigated. The relationship between fuzzy filter and Lukasiewicz fuzzy filter is discussed. Conditions for the Lukasiewicz fuzzy set to be a Lukasiewicz fuzzy filter are provided, and characterizations of Lukasiewicz fuzzy filter are displayed. The conditions under which the three subsets, $\in$-set, q-set, and O-set, will be filter are explored. | ||
| کلیدواژهها | ||
| Lukasiewicz fuzzy set؛ Lukasiewicz fuzzy filter؛ $\in$-set؛ q-set؛ O-set | ||
| مراجع | ||
|
1. M. Aaly Kologani, M. Mohseni Takallo and H. S. Kim, Fuzzy filters of hoops based on fuzzy points, Mathematics, 7 (2019), 430.
2. P. Aglianó, I. M. A. Ferreirim and F. Montagna, Basic hoops: an algebraic study of continuous t-norm, Studia Logica, 87 (2007), 73–98.
3. S. S. Ahn, E. H. Roh and Y. B. Jun, Ideals in BE-algebras based on Łukasiewicz fuzzy set, Eur. J. Pure Appl. Math., 15(3) (2022), 1307–1320.
4. W. J. Blok and I. M. A. Ferreirim, Hoops and their implicational reducts, Logic in Computer Science, 28 (1993), 219–230.
5. W. J. Blok and I. M. A. Ferreirim, On the structure of hoops, Algebra Universalis, 43 (2000), 233–257.
6. R. A. Borzooei and M. Aaly Kologani, Filter theory of hoop-algebras, Journal of Advanced Research in Pure Mathematics, 6(4) (2014), 72–86.
7. R. A. Borzooei and M. Aaly Kologani, On fuzzy filters of hoop-algebras, The Journal of Fuzzy Mathematics, 25(1) (2017), 177–195.
8. R. A. Borzooei, M. Mohseni Takallo, A. Aaly Kologani and Y. B. Jun, Fuzzy sub-hoops based on fuzzy points, Miskolc Math. Notes, 22(1) (2021), 91–106.
9. R. A. Borzooei, H. R. Varasteh and K. Borna, Fundamental hoop-algebras, Ratio Mathematica, 29 (2015), 25–40.
10. B. Bosbach, Komplementäre Halbgruppen, Axiomatik und Arithmetik, Fund. Math., 64 (1969), 257–287.
11. B. Bosbach, Komplementäre Halbgruppen, Kongruenzen and Quotienten, Fund. Math., 69 (1970), 1–14.
12. G. Georgescu, L. Leustean, V. Preoteasa, Pseudo-hoops, Journal of MultipleValued Logic and Soft Computing, 11(1-2) (2005), 153–184.
13. S. Ghorbani, Localization of hoop-algebras, Journal of Advanced Research in Pure Mathematics, 5(3) (2013), 1–13.
14. Y. B. Jun, Łukasiewicz anti fuzzy set and its application in BE-algebras, Transactions on fuzzy sets and systems, (in press).
15. Y. B. Jun, Łukasiewicz fuzzy ideals in BCK-algebras and BCI-algebras, J. Algebra Relat. Topics, (submitted).
16. Y. B. Jun, Łukasiewicz fuzzy subalgebras in BCK-algebras and BCI-algebras, Ann. Fuzzy Math. Inform., 23(2) (2022), 213–223.
17. Y. B. Jun and S. S. Ahn, Łukasiewicz fuzzy BE-algebras and BE-filters, Eur. J. Pure Appl. Math., 15(3) (2022), 924–937.
18. C. F. Luo, X. L. Xin and P. He, n-fold (positive) implicative filters of hoops, Italian Journal of Pure and Applied Mathematics, 38 (2017), 631–642.
19. P. M. Pu and y. M. Liu, Fuzzy topology I, Neighborhood structure of a fuzzy point and Moore-Smith convergence, J. Math. Anal. Appl., 76 (1980), 571–599.
20. G. R. Rezaei and Y. B. Jun, Commutative ideals of BCI-algebras based on Łukasiewicz fuzzy sets, Journal of Algebraic Hyperstructures and Logical Algebras, (submitted).
21. S. Z. Song and Y. B. Jun, Lukasiewicz fuzzy positive implicative ideals in BCKalgebras, Journal of Algebraic Hyperstructures and Logical Algebras, 3(2) (2022), 47–58.
22. R. Tayebi Khorami and A. Borumand Saeid, Some unitary operators on hoopalgebras, Fuzzy Information and Engineering, 9(2) (2017), 205–223.
23. Marta A. Zander, Decomposability of the finitely generated free hoop residuation algebra, Studia Logica, 88(2) (2008), 233–246. | ||
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