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TOPOLOGICAL SIMILARITY OF L-RELATIONS | ||
Iranian Journal of Fuzzy Systems | ||
مقاله 7، دوره 14، شماره 4، آبان 2017، صفحه 99-115 اصل مقاله (407.46 K) | ||
نوع مقاله: Research Paper | ||
شناسه دیجیتال (DOI): 10.22111/ijfs.2017.3328 | ||
نویسندگان | ||
Jing Hao ![]() | ||
1College of Mathematics and Information Science, Henan University of Economics and Law, Zhengzhou, 450000, China | ||
2College of Mathematics and Information, North China University of Water Resources and Electric Power, Zhengzhou, 450045, China | ||
چکیده | ||
$L$-fuzzy rough sets are extensions of the classical rough sets by relaxing the equivalence relations to $L$-relations. The topological structures induced by $L$-fuzzy rough sets have opened up the way for applications of topological facts and methods in granular computing. In this paper, we firstly prove that each arbitrary $L$-relation can generate an Alexandrov $L$-topology. Based on this fact, we introduce the topological similarity of $L$-relations, denote it by T-similarity, and we give intuitive characterization of T-similarity. Then we introduce the variations of a given $L$-relation and investigate the relationship among them. Moreover, we prove that each $L$-relation is uniquely topological similar to an $L$-preorder. Finally, we investigate the related algebraic structures of different sets of $L$-relations on the universe. | ||
کلیدواژهها | ||
$L$-fuzzy rough set؛ $L$-relation؛ Alexandrov $L$-topology؛ $L$-preorder؛ Topological similarity | ||
مراجع | ||
[1] K. Blount and C. Tsinakis, The structure of residuated lattices, International Journal of Algebra and Computation, 13(4) (2003), 437{461. [2] D. Boixader, J. Jacas and J. Recasens, Upper and lower approximations of fuzzy sets, International Journal of General System, 29(4) (2000), 555{568. [3] C. L. Chang, Fuzzy topological spaces, Journal of Mathematical Analysis and Applications, 24(1) (1968), 182{190. [4] X. Chen and Q. Li, Construction of rough approximations in fuzzy setting, Fuzzy sets and Systems, 158(23) (2007), 2641{2653. [5] M. De Cock, C. Cornelis and E. Kerre, Fuzzy rough sets: beyond the obvious, Proceedings of 2004 IEEE International Conference on Fuzzy Systems, 1 (2004), 103{108. [6] D. Dubois and H. Prade, Rough fuzzy sets and fuzzy rough sets, International Journal of General System, 17(2-3) (1990), 191{209. [7] J. A. Goguen, L-fuzzy sets, Journal of Mathematical Analysis and Applications, 18(1) (1967), 145{174. [8] J. Hao and Q. Li, The relationship between L-fuzzy rough set and L-topology, Fuzzy Sets and Systems, 178(1) (2011), 74{83. [9] J. Jarvinen and J. Kortelainen, A unifying study between modal-like operators, topologies and fuzzy sets, Fuzzy Sets and Systems, 158(11) (2007), 1217{1225. [10] H. Lai and D. Zhang, Fuzzy preorder and fuzzy topology, Fuzzy Sets and Systems, 157(14) (2006), 1865{1885. [11] Z. Li and R. Cui, T-similarity of fuzzy relations and related algebraic structures, Fuzzy Sets and Systems, 275 (2015), 130{143. [12] G. Liu, Generalized rough sets over fuzzy lattices, Information Sciences, 178(6) (2008), 1651{ 1662. [13] G. Liu and W. Zhu, The algebraic structures of generalized rough set theory, Information Sciences, 178(21) (2008), 4105{4113. [14] R. Lowen, Fuzzy topological spaces and fuzzy compactness, Journal of Mathematical Analysis and Applications, 56(3) (1976), 621{633. [15] 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. [16] N. N. Morsi and M. Yakout, Axiomatics for fuzzy rough sets, Fuzzy sets and Systems, 100(1) (1998), 327{342. [17] Z. Pawlak, Rough sets, International Journal of Computer & Information Sciences, 11(5) (1982), 341{356. [18] K. Qin and Z. Pei, On the topological properties of fuzzy rough sets, Fuzzy Sets and Systems, 151(3) (2005), 601{613. [19] A. M. Radzikowska and E. E. Kerre, A comparative study of fuzzy rough sets, Fuzzy Sets and Systems, 126(2) (2002), 137{155. [20] A. M. Radzikowska and E. E. Kerre, Fuzzy rough sets based on residuated lattices, In: Transactions on Rough Sets II, LNCS 3135, (2004), 278{296. [21] A. M. Radzikowska and E. E. Kerre, Characterisation of main classes of fuzzy relations using fuzzy modal operators, Fuzzy Sets and Systems, 152(2) (2005), 223{247. [22] Y. H. She and G. J. Wang, An axiomatic approach of fuzzy rough sets based on residuated lattices, Computers & Mathematics with Applications, 58(1) (2009), 189{201. [23] A. Skowron and J. Stepaniuk, Tolerance approximation spaces, Fundamenta Informaticae, 27(2-3) (1996), 245{253. [24] H. Thiele, On axiomatic characterization of fuzzy approximation operators II, the rough fuzzy set based case, Proceedings of the 31st IEEE International Symposium on Multiple-Valued Logic, (2001), 330{335. [25] H. Thiele, On axiomatic characterization of fuzzy approximation operators III, the fuzzy dia- mond and fuzzy box based cases, The 10th IEEE International Conference on Fuzzy Systems, 2 (2001), 1148{1151. [26] D. Vanderpooten, Similarity relation as a basis for rough approximations, Advances in Machine Intelligence and Soft Computing, 4 (1997), 17{33. [27] C. Y. Wang and B. Q. Hu, Fuzzy rough sets based on generalized residuated lattices, Information Sciences, 248 (2013), 31{49. [28] M.Ward and R. P. Dilworth, Residuated lattices, Transactions of the American Mathematical Society, 45(3) (1939), 335{354. [29] W. Z.Wu, Y. Leung and J. S. Mi, On characterizations of (I;T )-fuzzy rough approximation operators, Fuzzy Sets and Systems, 154(1) (2005), 76{102. [30] W. Z. Wu, J. S. Mi and W. X. Zhang, Generalized fuzzy rough sets, Information Sciences, 151 (2003), 263{282. [31] Y. Yao, Constructive and algebraic methods of the theory of rough sets, Information Sciences, 109(1) (1998), 21{47. [32] W. Zhu, Topological approaches to covering rough sets, Information Sciences, 177(6) (2007), 1499{1508. | ||
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