اخبار و اعلانات
آمار
| تعداد نشریات | 32 |
| تعداد شمارهها | 735 |
| تعداد مقالات | 7,132 |
| تعداد مشاهده مقاله | 11,592,605 |
| تعداد دریافت فایل اصل مقاله | 7,946,898 |
SOME PROPERTIES OF T-FUZZY GENERALIZED SUBGROUPS | ||
| Iranian Journal of Fuzzy Systems | ||
| مقاله 9، دوره 6، شماره 4، اسفند 2009، صفحه 73-87 اصل مقاله (294.65 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2009.542 | ||
| نویسندگان | ||
| Mahmood Bakhshi1؛ Rajab Ali Borzooei* 2 | ||
| 1Department of Mathematics, University of Bojnord, Bojnord, Iran | ||
| 2Department of Mathematics, Shahid Beheshti University, Tehran, Iran | ||
| چکیده | ||
| In this paper, we deal with Molaei’s generalized groups. We define the notion of a fuzzy generalized subgroup with respect to a t-norm (or T-fuzzy generalized subgroup) and give some related properties. Especially, we state and prove the Representation Theorem for these fuzzy generalized subgroups. Next, using the concept of continuity of t-norms we obtain a correspondence between TF(G), the set of all T-fuzzy generalized subgroups of a generalized group G, and the set of all T-fuzzy generalized subgroups of the corresponding quotient generalized group. Subsequently, we study the quotient structure of T-fuzzy generalized subgroups: we define the notion of a T-fuzzy normal generalized subgroup, give some related properties, construct the quotient generalized group, state and prove the homomorphism theorem. Finally, we study the lattice of T-fuzzy generalized subgroups and prove that TF(G) is a Heyting algebra. | ||
| کلیدواژهها | ||
| Generalized groups؛ Fuzzy generalized subgroups؛ t-norm؛ Heyting algebra | ||
| مراجع | ||
|
[1] R. Ameri, M. Bakhshi, S. A. Nematollahzadeh and R. A. Borzooei, Fuzzy (strong) congruence relations on a hypergroupoid and hyper BCK-algebra, Quasigroups and Related Systems, 15 (2007), 11-24. [2] J. M. Anthony and H. Sherwood, A characterization of fuzzy subgroups, Fuzzy Sets and Systems, 7 (1982), 297-305. [3] M. Bakhshi and R. A. Borzooei, Lattice structure on fuzzy congruence relations of a hypergroupoid, Inform. Sci., 177(16) (2007), 3305-3313. [4] G. Birkhoff, Lattice theory, Amer. Math. Soc., Providence, R. I., 1967. [5] R. A. Borzooei, M. Bakhshi and M. Mashinchi, Lattice structure on some fuzzy algebraic systems, Soft Computing, 12(8) (2008), 739-749. [6] R. A. Borzooei, G. R. Rezaei, M. R. Molaei and M. M. Zahedi, Characterization of generalized groups of orders 2 and 3, Pure Math. Appl., 11(4) (2000), 1-74. [7] E. P. Klement and R. Mesiar, Logical, algebraic, analytic and probabilistic aspects of triangular norms, Elsevier, Netherlands, 2005. [8] W. J. Liu, Fuzzy invariant subgroups and fuzzy ideals, Fuzzy Sets and Sysems, 8 (1982), 133-139. [9] M. Mehrabi, M. R. Molaei and A. Oloomi, Generalized subgroups and homomorphisms, Arab J. Math. Sci., 6(2) (2000), 1-7. [10] M. R. Molaei, Generalized groups, Buletinul Institului Polithnic Din Iasi, Tomul XLV(XLIX), (1999), 21-24. [11] J. N. Mordeson, K. R. Bhutani and A. Rosenfeld, Fuzzy group theory, Springer-Verlag Berlin Heidelberg, Netherlands, 2005. [12] N. P. Mukherjee and P. Bhattacharya, Fuzzy normal subgroups and fuzzy cosets, Inform. Sci., 34 (1984), 225-239. [13] M. T. Abu Osman, On some product of fuzzy subgroups, Fuzzy Sets and Systems, 24 (1987), 79-86. [14] H. T. Nguyen and E. A.Walker, A first course in fuzzy logic, 3rd ed. Chapman and Hall/CRC, USA, Florida, 2006. [15] E. H. Roh, B. Davvaz and K. H. Kim, T-fuzzy subhypernear-rings of hypernear-rings, Sci. Math. Jpn., 61(3) (2005), 535-545. [16] A. Rosenfeld, Fuzzy groups, J. Math. Anal. Appl., 35 (1971), 512-517. [17] S. Sessa, On fuzzy subgroups and fuzzy ideals under triangular norms: short communiction, Fuzzy Sets and Systems, 13 (1984), 95-100. [18] L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338-353. [19] J. Zhang, On properties of fuzzy hyperideals in hypernear-rings with t-norms, J. Appl. Math. Comput., 20 (2006), 255-277. | ||
|
آمار تعداد مشاهده مقاله: 2,771 تعداد دریافت فایل اصل مقاله: 2,683 |
||