تعداد نشریات | 31 |
تعداد شمارهها | 705 |
تعداد مقالات | 6,886 |
تعداد مشاهده مقاله | 11,262,428 |
تعداد دریافت فایل اصل مقاله | 7,556,486 |
ON ( $\alpha, \beta$ )-FUZZY Hv-IDEALS OF H_{v}-RINGS | ||
Iranian Journal of Fuzzy Systems | ||
مقاله 4، دوره 5، شماره 2، شهریور 2008، صفحه 35-47 اصل مقاله (192.63 K) | ||
نوع مقاله: Research Paper | ||
شناسه دیجیتال (DOI): 10.22111/ijfs.2008.331 | ||
نویسندگان | ||
B. Davvaz* 1؛ P. Corsini2 | ||
1Department of Mathematics, Yazd University, Yazd, Iran | ||
2Dipartimento di Matematica e Informatica, Via delle Scienze 206, 33100 Udine, Italy | ||
چکیده | ||
Using the notion of “belongingness ($\epsilon$)” and “quasi-coincidence (q)” of fuzzy points with fuzzy sets, we introduce the concept of an ($ \alpha, \beta$)- fuzzyHv-ideal of an Hv-ring, where , are any two of {$\epsilon$, q,$\epsilon$ $\vee$ q, $\epsilon$ $\wedge$ q} with $ \alpha$ $\neq$ $\epsilon$ $\wedge$ q. Since the concept of ($\epsilon$, $\epsilon$ $\vee$ q)-fuzzy Hv-ideals is an important and useful generalization of ordinary fuzzy Hv-ideals, we discuss some fundamental aspects of ($\epsilon$, $\epsilon$ $\vee$ q)-fuzzy Hv-ideals. A fuzzy subset A of an Hv-ring R is an ($\epsilon$, $\epsilon$ $\vee$ q)-fuzzy Hv-ideal if and only if an At, level cut of A, is an Hv-ideal of R, for all t$\epsilon$(0, 0.5]. This shows that an($\epsilon$, $\epsilon$ $\vee$ q)-fuzzy Hv-ideal is a generalization of the existing concept of fuzzy Hv-ideal. Finally, we extend the concept of a fuzzy subgroup with thresholds to the concept of a fuzzy H_{v}-ideal with thresholds. | ||
کلیدواژهها | ||
Hyperstructure؛ H_{v}-ring؛ Fuzzy set؛ Fuzzy H_{v}-ideal | ||
مراجع | ||
[1] S. K. Bhakat, ($\epsilon$ $\vee$ q)-fuzzy normal, quasinormal and maximal subgroups, Fuzzy Sets and Systems,112 (2000), 299-312. [2] S. K. Bhakat and P. Das,Fuzzy subrings and ideals, Fuzzy Sets and Systems, 81 (1996),383-393. [3] S. K. Bhakat and P. Das, ($\epsilon$ $\vee$ q)-fuzzy subgroup, Fuzzy Sets and Systems, 80 (1996), 359-368. [4] P. Corsini,Prolegomena of hypergroup theory, Second Edition, Aviani Editor, 1993. [5] P. Corsini and V. Leoreanu,Applications of hyperstructures theory, Advanced in Mathematics, Kluwer Academic Publishers, 2003. [6] B. Davvaz, ($\epsilon$ $\vee$ q)-fuzzy subnear-rings and ideals, Soft Computing 10 (2006), 206-211. [7] B. Davvaz,A brief survey of the theory of H_{v}-structures, in: Proc. 8th International Congress on Algebraic Hyperstructures and Applications, 1-9 Sep., 2002, Samothraki, Greece, Spanidis Press, 2003, 39-70. [8] B. Davvaz,Fuzzy H_{v}-groups, Fuzzy Sets and Systems, 101 (1999), 191-195. [9] B. Davvaz,Fuzzy H_{v}-submodules, Fuzzy Sets and Systems, 117 (2001), 477-484. [10] B. Davvaz,T-fuzzy H_{v}-subrings of an H_{v}-ring, J. Fuzzy Math., 11 (2003), 215-224. [11] B. Davvaz,On Hv-rings and fuzzy H_{v}-ideals, J. Fuzzy Math., 6 (1998), 33-42. [12] B. Davvaz,Product of fuzzy H_{v}-ideals in Hv-rings, Korean J. Compu. Appl. Math., 8 (2001), 685-693. [13] Y. B. Jun,On ( $\alpha, \beta$ )-fuzzy subalgebra of BCK/BCI-algebras, Bull. Korean Math. Soc., 42 (2005), 703-711. [14] W. J. Liu,Fuzzy invariant subgroups and fuzzy ideals, Fuzzy Sets and Systems, 8 (1982), 133-139. [15] F. Marty,Sur une generalization de la notion de group, 8th Congress Math. Scandenaves, Stockholm, 1934, 45-49. [16] 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. [17] A. Rosenfeld,Fuzzy groups, J. Math. Anal. Appl., 35 (1971), 512-517. [18] T. Vougiouklis,Hyperstructures and their representations, Hadronic Press, Inc, 115, Palm Harber, USA, 1994. [19] T. Vougiouklis,The fundamental relation in hyperrings. The general hyperfield, in: Proc. 4th International Congress on Algebraic Hyperstructures and Applications, Xanthi, 1990, World Sci. Publishing, Teaneck, NJ, (1991), 203-211. [20] X. Yuan, C. Zhang and Y. Ren,Generalized fuzzy groups and many-valued implications, Fuzzy Sets and Systems,138 (2003), 205-211. [21] L. A. Zadeh,Fuzzy sets, Inform. Control, 8 (1965), 338-353. | ||
آمار تعداد مشاهده مقاله: 2,490 تعداد دریافت فایل اصل مقاله: 1,283 |