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\L{}ukasiewicz fuzzy ideals in BCK-algebras and BCI-algebras | ||
| Journal of Algebra and Related Topics | ||
| دوره 11، شماره 1، شهریور 2023، صفحه 1-14 اصل مقاله (289.78 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22124/jart.2022.21963.1393 | ||
| نویسنده | ||
| Y. B. Jun | ||
| Department of Mathematics Education, Gyeongsang National University, Jinju 52828, Korea | ||
| چکیده | ||
| The notion of (closed) \L{}ukasiewicz fuzzy ideal is introduced, and several properties are investigated. The relationship between \L{}ukasiewicz fuzzy subalgebra and \L{}ukasiewicz fuzzy ideal is discussed, and characterization of a \L{}ukasiewicz fuzzy ideal is considered. Conditions for a \L{}ukasiewicz fuzzy subalgebra to be a \L{}ukasiewicz fuzzy ideal are provided, and conditions for the $\in$-set, $q$-set and $O$-set to be ideals are explored. | ||
| کلیدواژه‌ها | ||
| \L{}ukasiewicz fuzzy set؛ (strong) \L{}ukasiewicz fuzzy subalgebra؛ (closed) \L{}ukasiewicz fuzzy ideal؛ $q$-set؛ $O$-set | ||
| مراجع | ||
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1. Y. Huang, BCI-algebra, Science Press: Beijing, China, 2006. 2. K. Is´eki, On BCI-algebras, Math. Seminar Notes, 8 (1980), 125–130. 3. K. Is´eki and S. Tanaka, An introduction to the theory of BCK-algebras, Math. Japon. 23 (1978), 1–26. 4. Y. B. Jun, Lukasiewicz fuzzy subalgebras in BCK-algebras and BCI-algebras, Ann. Fuzzy Math. Inform. (2) 23 (2022), 213–223. 5. Y. B. Jun, S. M. Hong, S. J. Kim and S. Z. Song, Fuzzy ideals and fuzzy subalgebras of BCK-algebras, J. Fuzzy Math. 7 (1999), 411–418. 6. J. Meng and Y. B. Jun, BCK-algebras, Kyungmoonsa Co. Seoul, Korea 1994. 7. A. Paad and A. Jafari, n-fold obstinate and n-fold fantastic (pre)filters of EQalgebras, J. Algebra Relat. Topics, (1) 9 (2021), 31–50. 8. 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. 9. O. G. Xi, Fuzzy BCK-algebras, Math. Japon. 36 (1991), 935–942. 10. L. A. Zadeh, Fuzzy sets, Information and Control, (3) 8 (1965), 338–353. | ||
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