پیوندهای مفید
اخبار و اعلانات
آمار
| تعداد نشریات | 31 |
| تعداد شمارهها | 834 |
| تعداد مقالات | 8,015 |
| تعداد مشاهده مقاله | 14,853,726 |
| تعداد دریافت فایل اصل مقاله | 9,587,173 |
FUZZY SUBGROUPS AND CERTAIN EQUIVALENCE RELATIONS | ||
| Iranian Journal of Fuzzy Systems | ||
| مقاله 7، دوره 3، شماره 2، دی 2006، صفحه 75-91 اصل مقاله (284.44 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2006.469 | ||
| نویسنده | ||
| APARNA JAIN | ||
| DEPARTMENT OF MATHEMATICS, SHIVAJI COLLEGE, UNIVERSITY OF DELHI, NEW DELHI, INDIA | ||
| چکیده | ||
| In this paper, we study an equivalence relation on the set of fuzzy subgroups of an arbitrary group G and give four equivalent conditions each of which characterizes this relation. We demonstrate that with this equivalence relation each equivalence class constitutes a lattice under the ordering of fuzzy set inclusion. Moreover, we study the behavior of these equivalence classes under the action of a group homomorphism. | ||
| کلیدواژهها | ||
| Fuzzy subgroup؛ Equivalence relation؛ Lattice؛ $alpha$– cut؛ Strong $alpha$– cut؛ homomorphism | ||
| مراجع | ||
|
[1] N. Ajmal, Homomorphism of fuzzy groups, correspondence theorem and fuzzy quotient groups, Fuzzy Sets and Systems, 61 (1994), 329-339. [2] N. Ajmal, Fuzzy group theory : A comparison of different notions of product of fuzzy sets, Fuzzy Sets and Systems, 110 (2000), 437-446. [3] N. Ajmal and K. V. Thomas, The lattices of fuzzy subgroups and fuzzy normal subgroups, Inform. Sci., 76 (1994), 1-11. [4] N. Ajmal, The lattice of fuzzy normal subgroups is modular, Inform. Sci., 83 (1995), 199- 209. [5] N. Ajmal and K. V. Thomas, The lattices of fuzzy ideals of a ring, Fuzzy Sets and Systems, 74 (1995), 371-379. [6] P. S. Das, Fuzzy groups and level subgroups, Journal of Math. Anal. Appl., 84 (1981), 264- 269. [7] C. Degang, J. Jiashang, W. Congxin and E. C. C. Tsang, Some notes on equivalent fuzzy sets and fuzzy subgroups, Fuzzy Sets and Systems, 152 (2005), 403-409. [8] V. N. Dixit, R. Kumar and N. Ajmal, Level subgroups and union of fuzzy subgroups, Fuzzy Sets and Systems, 37 (1990), 359-371. [9] A. Jain and N. Ajmal, A new approach to the theory of fuzzy groups, Journal of Fuzzy Math., 12 (2) (2004), 341-355. [10] A. Jain, Tom Head’s join structure of fuzzy subgroups, Fuzzy Sets and Systems, 125 (2002), 191-200. [11] J. G. Kim and S. -J. Cho, Structure of a lattice of fuzzy subgroups, Fuzzy Sets and Systems, 89 (1997), 263-266. [12] M. Mashinchi and M. Mukaidono, A classification of fuzzy subgroups, Ninth Fuzzy System Symposium, Sapporo, Japan, (1992), 649-652. [13] M. Mashinchi and M. Mukaidono, On fuzzy subgroups classification, Research report of Meiji University, Japan, 9 (65) (1993), 31-36. [14] M. Mashinchi and M. M. Zahedi, A counter example of P. S. Das’s paper, Journal of Math. Anal. & Appl., 153 (2) (1990), 591-592. [15] J. N. Mordeson, Lecture notes in fuzzy mathematics and computer science, L-Subspaces and L-Subfields, Creighton University, Omaha, Nebraska 68178 USA, 1996. [16] V. Murali and B. B. Makamba, On an equivalence of fuzzy subgroups I, Fuzzy Sets and Systems, 123 (2001), 259-264. [17] V. Murali and B. B. Makamba, On an equivalence of fuzzy subgroups II, Fuzzy Sets and Systems, 136 (2003), 93-104. [18] V. Murali and B. B. Makamba, On an equivalence of fuzzy subgroups III, The International Journal of Math. And Math. Sciences, 36 (2003), 2303-2313. [19] S. Ray, Isomorphic fuzzy groups, Fuzzy Sets and Systems, 50 (1992), 201-207. [20] A. Rosenfeld, Fuzzy groups, Journal of Math. Anal. Appl., 35 (1971), 512-517. [21] L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338-353. | ||
|
آمار تعداد مشاهده مقاله: 3,015 تعداد دریافت فایل اصل مقاله: 1,998 |
||