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FUZZY (POSITIVE, WEAK) IMPLICATIVE HYPER BCK-IDEALS | ||
| Iranian Journal of Fuzzy Systems | ||
| مقاله 6، دوره 1، شماره 2، دی 2004، صفحه 63-79 اصل مقاله (209.13 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2004.506 | ||
| نویسندگان | ||
Mahmood Bakhshi  1؛ Rajab Ali Borzooei1؛ Mohammad Mehdi Zahedi2
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| 1Department of Mathematics, Sistan and Baluchestan University, Zahedan, Iran | ||
| 2Department of Mathematics, Shahid Bahonar University of Kerman, Kerman, Iran | ||
| چکیده | ||
| In this note first we define the notions of fuzzy positive implicative hyper BCK-ideals of types 1,2,3 and 4. Then we prove some theorems which characterize the above notions according to the level subsets. Also we obtain the relationships among these notions, fuzzy (strong, weak, reflexive) hyper BCK-ideals and fuzzy positive implicative hyper BCK-ideals of types 5,6,7 and 8. Then, we define the notions of fuzzy (weak) implicative hyper BCKideals and we obtain some related results. Finally, by considering the product of two hyper BCK-algebras we give some theorems which show that how the projections of a fuzzy (positive implicative, implicative) hyper BCK-ideal is again a fuzzy (positive implicative, implicative) hyper BCK-ideal. | ||
| کلیدواژه‌ها | ||
| Hyper BCK-algebra؛ Fuzzy (strong؛ weak؛ reflexive) hyper BCKideal؛ Fuzzy (positive؛ weak) implicative hyper BCK-ideals | ||
| مراجع | ||
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[1] R. A. Borzooei, M. Bakhshi, On positive implicative hyper BCK-ideals, Scientiae Mathematicae Japonicae, Vol. 9(2003), 303-314. [2] R.A. Borzooei, M. Bakhshi, Some Results on Hyper BCK-algebras, Quasigroups and Related Systems, Vol.11 (2004), 9-24. [3] R. A. Borzooei, M. Bakhshi, (Weak) Implicative Hyper BCK-ideals, Quasigroups and Related Systems, Vol.12, to appear [4] R. A. Borzooei, A. Hasankhani, M. M. Zahedi, Y. B. Jun, On hyper K-algebras, Math. Japon., Vol. 52, No.1(2000), 13-121. [5] R. A. Borzooei, M. M. Zahedi, Fuzzy structures on hyper K-algebras, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, Vol. 10, No. 1(2002) 77-93. [6] Y. Imai, K. Is´eki, On axiom systems of propositional calculi XIV, Proc. Japan Academy, 42 (1966) 19-22. [7] Y. B. Jun, W. H. Shim, Fuzzy implicative hyper BCK-ideals of hyper BCK-algebras, Internat. J. Math. Sci., 29 (2002), No. 2, 63-70. [8] Y. B. Jun, W. H. Shim, Fuzzy structures of PI( ,,)BCK-ideals in hyper BCK-algebras, Internat. J. Math. Sci. (2003), No. 9, 549-556. [9] Y. B. Jun, M. M. Zahedi, X. L. Xin, R. A. Borzooei, On hyper BCK-algebras, Italian Journal of Pure and Applied Mathematics, No. 10 (2000), 127-136. [10] Y. B. Jun, X. L. Xin, E. H. Roh, M. M. Zahedi, Strong hyper BCK-ideals of hyper BCKalgebras, Mathematicae Japonicae, Vol.51, 3 (2000), 493-498. [11] Y. B. Jun, X. L. Xin, Implicative hyper BCK-ideals of hyper BCK-algebras, Mathematicae Japonicae, Vol. 52, No. 3, (2000), 435-443. [12] Y. B. Jun, X. L. Xin, Fuzzy hyper BCK-ideals of hyper BCK-algebras, Scientiae Mathematicae Japonicae, 53, No. 2(2001), 353-360. [13] F. Marty, Sur une generalization de la notion de groups, 8th congress Math. Scandinaves, Stockholm (1934) 45-49. [14] M. M. Zahedi, M. Bakhshi, R. A. Borzooei, Fuzzy positive implicative hyper BCK-ideals of types 5,6,7 and 8, Journal of Basic Science, University of Mazandaran, Vol. 2, No. 2, (2003), 61-69. [15] M. M. Zahedi, R. A. Borzooei, H. Rezaei, Fuzzy positive implicative hyper K-ideals of type 1,2,3 and 4, 9th IFSA World Congress and 20th NAFIPS 2001, July 25-28 (2001), Vancover (Canada), 1210-1215. | ||
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