اخبار و اعلانات
آمار
| تعداد نشریات | 27 |
| تعداد شماره‌ها | 604 |
| تعداد مقالات | 6,159 |
| تعداد مشاهده مقاله | 9,098,446 |
| تعداد دریافت فایل اصل مقاله | 5,935,375 |
L-FUZZIFYING TOPOLOGICAL GROUPS | ||
| Iranian Journal of Fuzzy Systems | ||
| مقاله 9، دوره 9، شماره 4، دی 2012، صفحه 115-132 اصل مقاله (377.39 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2012.136 | ||
| نویسندگان | ||
Shai-yan Zhang1؛ Cong-hua Yan  2
| ||
| 1School of Science, Southern Yangtze University, Wuxi, Jiangsu 214122, People0 s Republic of China | ||
| 2school of Math. Sciences, Nanjing Normal Uni- versity, Nanjing Jiangsu 210046, People0 s Republic of China | ||
| چکیده | ||
| The main purpose of this paper is to introduce a concept of $L$-fuzzifying topological groups (here $L$ is a completely distributive lattice) and discuss some of their basic properties and the structures. We prove that its corresponding $L$-fuzzifying neighborhood structure is translation invariant. A characterization of such topological groups in terms of the corresponding $L$-fuzzifying neighborhood structure of the unit is given. It is shown that the category of $L$-fuzzifying topological groups $L$-{\bf FYTPG} is topological over the category of groups {\bf GRP} with respect to the forgetful functor. As an application, the conclusion that the product of $L$-fuzzifying topological groups is also an $L$-fuzzifying topological group is proved. Finally, it is proved the forgetful functor preserves the product. | ||
| کلیدواژه‌ها | ||
| L-fuzzifying topological groups؛ L-fuzzifying topology؛ L-fuzzifying neighborhood structure؛ category | ||
| مراجع | ||
|
[1] J. Adamek, H. Herrlich and G. E. Strecker, Abstract and concrete categories, John Wiley & Sons, 1990. [2] D. H. Foster, Fuzzy topological groups, J. Math. Anal. Appl., 67 (1979), 549-564. [3] G. Gierz, K. H. Hofmann, K. Keimel, J. D. Lawson, M. W. Mislove and D. S. Scott, A compendium of continuous lattices, Springer, Berlin, 1980. [4] E. Hewitt and K. Stromberg, Real and abstract analysis, Springer, Berlin, 1975. [5] U. Hohle, Characterization of L-topologies by L-valued neighborhoods, In S. E. Rodabaugh, E. P. Klement, U. Hohle, eds., Applications of Category Theory to Fuzzy Subsets, Kluwer Academic Publishers, (1999), 389-432. [6] X. Luo and J. Fang, Fuzzifying closure systems and closure operators, Iranian Journal of Fuzzy Systems, 8(1) (2011), 77-94. [7] J. L. Ma and C. H. Yu, Fuzzy topological groups, Fuzzy Sets and Systems, 12 (1984), 289-299. [8] S. E. Rodabaugh, Powerset operator foundations for point-set lattice-theoretic (POSLAT) fuzzy set theories and topologies, Questions Mathematicae, 20 (1997), 463-530. [9] J. Z. Shen, Fuzzifying topological groups based on completely distributive residuated lattice- valued logic (I), Proceedings of IEEE 22th International Symposium on Multiple-Valued Logic, Sendai, (1992), 198-205. [10] J. Z. Shen, Topological groups based on continuous valued logic [0,1], Journal of Engineering Math., 114 (1994), 52-64. [11] J. Z. Shen, Fuzzifying topological groups(II), [J]. J. Jiangxi Normal Univ., in Chinese, 1 (1994), 72-80. [12] J. Z. Shen, Fuzzifying topological groups based on completely distributive residuated lattice- valued logic (II), Information Sciences, 80 (1994), 319-339. [13] F. G. Shi and H. Y. Li, Almost S{Compactness in L-toplogical Spaces, Iranian Journal of Fuzzy Systems, 5(3) (2008), 31-44. [14] W. Yao, On L-fuzzifying convergence spaces, Iranian Journal of Fuzzy Systems, 6(1) (2009), 63-80. [15] M. Ying, A new approach for fuzzy topology (I), Fuzzy Sets and Systems, 39 (1991), 303-321. [16] M. Ying, A new approach for fuzzy topology (III), Fuzzy Sets and Systems, 55 (1993), 193-207. [17] C. H. Yu and J. L. Ma, Fuzzy topological groups I, J. Northeastern Normal Univ., in Chinese, 3 (1982), 13-18. [18] C. H. Yu and J. L. Ma, L-fuzzy topological groups, Fuzzy Sets and Systems, 47 (1992), 247-252. [19] D. Zhang, On the re ectivity and core ectivity of L-fuzzifying topological spaces in L- topological spaces, Acta Math. Sin. (Engl.Ser), 18(1) (2002), 55-68. [20] D. Zhang, L-fuzzifying topologies as L-topologies, Fuzzy Sets and Systems, 125 (2002), 135-144. | ||
|
آمار تعداد مشاهده مقاله: 2,371 تعداد دریافت فایل اصل مقاله: 1,573 |
||
