تعداد نشریات | 27 |
تعداد شمارهها | 604 |
تعداد مقالات | 6,159 |
تعداد مشاهده مقاله | 9,107,464 |
تعداد دریافت فایل اصل مقاله | 5,939,288 |
$L$-fuzzy approximation spaces and $L$-fuzzy topological spaces | ||
Iranian Journal of Fuzzy Systems | ||
مقاله 9، دوره 13، شماره 1، اردیبهشت 2016، صفحه 115-129 اصل مقاله (375.47 K) | ||
شناسه دیجیتال (DOI): 10.22111/ijfs.2016.2292 | ||
نویسندگان | ||
A. A. Ramadan* 1؛ E. H. Elkordy1؛ M. El-Dardery2 | ||
1Department of Mathematics, Faculty of Science, Beni-Suef Univer- sity, Beni-Suef, Egypt | ||
2Department of Mathematics, Faculty of Science, Fayoum University, Fayoum, Egypt | ||
چکیده | ||
The $L$-fuzzy approximation operator associated with an $L$-fuzzy approximation space $(X,R)$ turns out to be a saturated $L$-fuzzy closure (interior) operator on a set $X$ precisely when the relation $R$ is reflexive and transitive. We investigate the relations between $L$-fuzzy approximation spaces and $L$-(fuzzy) topological spaces. | ||
کلیدواژهها | ||
Complete residuated lattice؛ $L$-fuzzy approximation spaces؛ $L$-fuzzy topology؛ Continuity | ||
مراجع | ||
[1] R. Belohlavek, Fuzzy relational systems: foundations and principles, Kluwer Academic/ Plenum Press, New York (2002). [2] K. Blount and T. Tsinakis, The structure of residuated lattices, Int. J. Algebra and Computation, 13(4) (2004), 473{461. [3] D. Boixader, J. Jacas and J. Recasens, Upper and lower approximations of fuzzy sets, Int. Jour. of Gen. Sys., 29 (2000), 555{568. [4] X. Chen and Q. Li, Construction of rough approximations in fuzzy setting, Fuzzy Sets and Systems, 158 (2007), 2641{2653. [5] M. Chuchro, On rough sets in topological Boolean algebra. In: Ziarko, W.(ed.): Rough Sets, Fuzzy Sets and Knowledge Discovery, Springer-Verlage, New York, (1994), 157{160. [6] D. Dubois and H. Prade, Rough fuzzy sets and fuzzy rough sets, Int. J. Gen. Syst., 17(2-3) (1990), 191{208. [7] J. Fang, I-fuzzy Alexadrov topologies and specialization orders, Fuzzy Sets and Systems, 158 (2007), 2359{2374. [8] P. Hajek, Metamathematics of fuzzy logic, Kluwer, Dordrecht (1998). [9] U. Hohle and A. P. Sostak, Axiomatic foundations of xed-basis fuzzy topology, In: Hohle, S. E. Rodabaugh (Eds), Mathematics of Fuzzy Sets, Logic, Topology and Measure Theory, The Handbooks of Fuzzy Sets Series, Chapter 3, Kluwer Academic Publisher, Dordrechet (1999), 123{272. [10] Y. C. Kim and Y. S. Kim, (L,)-approximation spaces and (L,)-fuzzy quasi-uniform spaces, Information Sciences, 179 (2009), 2028{2048. [11] H. Lai and D. Zhang, Fuzzy pre order and fuzzy topology, Fuzzy Sets and Systems, 157 (2006), 1865{1885. [12] Z. M. Ma and B. Q. Hu, Topological and lattice structures of L-fuzzy rough sets determined by lower and upper sets, Information Sciences, 218 (2013), 194{204. [13] N. N. Morsi and M. M. Yakout, Axiomatics for fuzzy rough sets, Fuzzy Sets Systems, 100 (1998), 327-342. [14] Z. Pawlak, Rough sets, Inter. J. Comp. Info. Sci., 161 (2010), 2923-2944. [15] K. Qin and Z. Pei, On the topological properties of fuzzy rough sets, Fuzzy Sets and Systems, 151 (2005), 601{613. [16] K. Qin, J. Yang and Z. Pei, Generalized rough sets based on re exive and transitive, Info. Sci., 178 (2008), 4138{4141. [17] A. M. Radzikowoska and E. E. Kerre, Fuzzy rough sets based on residuated lattices, In: Transaction on Rough sets II, in Lincs, 3135 (2004), 278{296. [18] A. A. Ramadan, Smooth topological Spaces, Fuzzy Sets and Systems, 48(3) (1992), 371{357. [19] A. A. Ramadan, L-fuzzy interior systems, Comp. and Math. with Appl., 62 (2011), 4301{ 4307. [20] S. E. Rodabaugh and E. P. Kelment, Topological and algebraic structures in fuzzy sets, The Handbook of Recent Developments in the Mathematics of Fuzzy Sets, Trends in Logic 20, Kluwer Academic Publisher, Boston (2003). [21] A. Sostak, On a fuzzy topological structure, Rend. Circ. Mat. Palermo (Supp. Ser.II), 11 (1985), 89{103. [22] E. Turunen, Mathematics behind fuzzy logic, A Springer Verlag Co., Hiedelberg (1999). [23] C. Y. Wang and B. Q. Hu, Fuzzy rough sets based on generalized residuated lattices, Information Sciences, 248 (2013), 31{49. [24] W. Z. Wu, A study on relationship between fuzzy rough approximation operators and fuzzy topological spaces, c Springer-Verlag, Berlin, Heidelberg (2005). [25] W. Z. Wu, J. S. Mi and W. X. Zhang, Generalized fuzzy rough sets, Information Sciences, 151 (2003), 263{282. [26] Y. Y. Yao, Constructive and Algebraic methods of the theory of rough sets, Information Sciences, 109 (1998), 21{27. [27] W. X. Zhang, Y. Leung and W. Z.Wu, Information systems and knowledge discovery, Science Press,Beijing (2003). [28] P. Zhi, P. Daowu and Z. Li, Topology vs generalized rough sets, Fuzzy Sets and Systems, 52(2) (2011), 231{239. | ||
آمار تعداد مشاهده مقاله: 1,697 تعداد دریافت فایل اصل مقاله: 1,301 |