×

Rough approximation operators based on quantale-valued fuzzy generalized neighborhood systems. (English) Zbl 1429.68308

Summary: Let \(L\) be an integral and commutative quantale. In this paper, by fuzzifying the notion of generalized neighborhood systems, the notion of \(L\)-fuzzy generalized neighborhood system is introduced and then a pair of lower and upper approximation operators based on it are defined and discussed. It is proved that these approximation operators include generalized neighborhood system-based approximation operators, \(L\)-fuzzy relation-based approximation operators and \(L\)-fuzzy covering-based approximation operators as their special circumstances. Therefore, the research on \(L\)-fuzzy generalized neighborhood system-based approximation operators has more general significance. In addition, when the \(L\)-fuzzy generalized neighborhood system is serial, reflexive, unary and transitive, then the corresponding approximation operators are discussed and characterized, respectively.

MSC:

68T37 Reasoning under uncertainty in the context of artificial intelligence
54A40 Fuzzy topology
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] E. Bartl, M. Krupka,Residuated lattices of block relations: Size reduction of concept lattices, International Journal of General Systems,45(7-8) (2016), 773-789. · Zbl 1404.68154
[2] R. Belohlavek,Fuzzy relational systems, Foundations and Principles, Kluwer Academic Publishers, New York, 2002. · Zbl 1067.03059
[3] R. Belohlavek,Fuzzy closure operators II: Induced relations, representation, and examples, Soft Computing,7(1) (2002), 53-64. · Zbl 1027.06008
[4] R. A. Borzooei, A. A. Estaji, M. Mobini,On the category of rough sets, Soft Computing,21(9) (2017), 2201-2214. · Zbl 1381.18001
[5] X. Y. Chen, Q. G. Li,Construction of rough approximations in fuzzy setting, Fuzzy Sets and Systems,158(2007), 2641-653. · Zbl 1127.68105
[6] T. Q. Deng, Y. M. Chen, W. L. Xu, Q. H. Dai,A novel approach to fuzzy rough sets based on a fuzzy covering, Information Sciences,177(2007), 2308-2326. · Zbl 1119.03051
[7] J. A. Goguen,L-fuzzy sets, Journal of Mathematical Analysis and Applications,18(1967), 145-174. · Zbl 0145.24404
[8] S. E. Han, L. X. Lu, W. Yao,Quantale-valued fuzzy scott topology, Iranian Journal of Fuzzy Systems,16(3) (2019), 175-188. · Zbl 1429.54007
[9] P. H´ajek,Metamathematics of fuzzy logic, Kluwer Academic Publishers, Dordrecht, 1998. · Zbl 0937.03030
[10] J. Hao, S. S. Huang,Topological similarity ofL-relations, Iranian Journal of Fuzzy Systems,14(4) (2017), 99-115. · Zbl 1398.54016
[11] J. Hao, Q. G. Li,The relationship betweenL-fuzzy rough set andL-topology, Fuzzy Sets and Systems,178(2011), 74-83. · Zbl 1238.54005
[12] K. Hu, J. Q. Li,The entropy and similarity measure of interval valued intuitionistic fuzzy sets and their relationship, International Journal of Fuzzy Systems,15(3) (2013), 279-288.
[13] Q. Jin, L. Q. Li,One-axiom characterizations on lattice-valued closure (interior) operators, Journal of Intelligent and Fuzzy Systems,31(2016), 1679-1688. · Zbl 1367.54008
[14] Q. Jin, L. Q. Li,Modified Top-convergence spaces and their relationships to lattice-valued convergence spaces, Journal of Intelligent and Fuzzy Systems,35(2018), 2537-2546.
[15] Q. Jin, L. Q Li, Y. R. Lv, etal.,Connectedness for lattice-valued subsets in lattice-valued convergence spaces, Quaestiones Mathematicae,42(2) (2019), 135-150. · Zbl 1502.54004
[16] Y. C. Kim,Join-meet approximation operators and fuzzy preorders, Journal of Intelligent and Fuzzy Systems,28(2015), 1089-1097. · Zbl 1351.06001
[17] H. L. Lai, D. X. Zhang,Fuzzy topological spaces with conical neighborhood system, Fuzzy Sets and Systems,330(2018), 87-104. · Zbl 1380.54009
[18] L. Q. Li,p-topologicalness-A relative topologicalness in⊤-convergence spaces, Mathematics,7(3) (2019), 228.
[19] L. Q. Li, Q. Jin,On adjunctions between Lim, SL-Top, and SL-Lim, Fuzzy Sets and Systems,182(2011), 66-78. · Zbl 1244.54018
[20] L. Q. Li, Q. Jin,On stratifiedL-convergence spaces: Pretopological axioms and diagonal axioms, Fuzzy Sets and Systems, 204(2012), 40-52. · Zbl 1254.54010
[21] L. Q. Li, Q. Jin, K. Hu,Lattice-valued convergence associated with CNS spaces, Fuzzy Sets and Systems,370(1) (2019), 91-98. · Zbl 1423.54010
[22] L. Q Li, Q. Jin, K. Hu, F. F. Zhao,The axiomatic characterizations onL-fuzzy covering-based approximation operators, International Journal of General Systems,46(4) (2017), 332-353.
[23] L. Q. Li, Q. G. Li,On enrichedL-topologies: Base and subbase, Journal of Intelligent and Fuzzy Systems,28(2015), 2423-2432. · Zbl 1352.54006
[24] T. J. Li, Y. Leung, W. X. Zhang,Generalized fuzzy rough approximation operators based on fuzzy coverings, International Journal of Approximate Reasoning,48(2008), 836-856. · Zbl 1186.68464
[25] T. Y. Lin,Neighborhood systems: A qualitative theory for fuzzy and rough sets, Advances in Machine Intelligence and Soft Computing,4(1997), 132-155.
[26] Z. M. Ma, B. Q. Hu,Topological and lattice structures ofL-fuzzy rough sets determined by lower and upper sets, Information Sciences,218(2013), 194-204. · Zbl 1293.03025
[27] J. B. Michael, T. Y. Lin,Neighborhoods, rough sets and query relaxation in cooperative answering, Rough Sets and Data Mining: Analysis of Imprecise Data, Kluwer Academic Publisher, 1997.
[28] B. Pang,Degrees of separation properties in stratifiedL-generalized convergence spaces using residual implication, Filomat, 31(20) (2017), 6293-6305. · Zbl 1499.54057
[29] B. Pang, F. G. Shi,Subcategories of the category ofL-convex spaces, Fuzzy Sets and Systems,313(2017), 61-74. · Zbl 1372.52001
[30] B. Pang, Z. Y. Xiu,StratifiedL-prefilter convergence structures in stratifiedL-topological spaces, Soft Computing,22(2018), 7539-7551. · Zbl 1402.54015
[31] Z. Pawlak,Rough sets, Internatinal Journal of Computer and Information Sciences,11(1982), 341-356. · Zbl 0501.68053
[32] A. M. Radzikowska, E. E. Kerre,Fuzzy rough sets based on residuated lattices, LNCS,3135(2004), 278-296. · Zbl 1109.68118
[33] A. A. Ramadan, E. H. Elkordy, M. El-Dardery,L-fuzzy approximation spaces andL-fuzzy topological spaces, Iranian Journal of Fuzzy Systems,13(1) (2016), 115-129. · Zbl 1338.54056
[34] Y. H. She, G. J. Wang,An axiomatic approach of fuzzy rough sets based on residuated lattices, Computers and Mathematics with Applications,58(2009), 189-201. · Zbl 1189.03059
[35] Y. R. Syau, E. B. Lin,Neighborhood systems and covering approximation spaces, Knowledge-Based Systems,66(2014), 61-67.
[36] S. P. Tiwari, A. K. Srivastava,Fuzzy rough sets, fuzzy preorders and fuzzy topologies, Fuzzy Sets and Systems,210(2013), 63-68. · Zbl 1260.54024
[37] W. Z. Wu, Y. Leung, J. S. Mi,On characterizations of(ℓ,T)-fuzzy rough approximation operators, Fuzzy Sets and Systems, 154(2005), 76-102. · Zbl 1074.03027
[38] W. Z. Wu, J. S. Mi, W. X. Zhang,Generalized fuzzy rough sets, Information Sciences,151(2003), 263-282. · Zbl 1019.03037
[39] W. Z. Wu, W. X. Zhang,Constructive and axiomatic approaches of fuzzy approximation operators, Information Sciences, 159(2004), 233-254. · Zbl 1071.68095
[40] Z. Y Xiu, B. Pang,Base axioms and subbase axioms inM-fuzzifying convex spaces, Iranian Journal of Fuzzy Systems,15(2) (2018), 75-87. · Zbl 1398.06006
[41] B. Yang, B. Q. Hu,Matrix representations and interdependency onL-fuzzy covering-based approximation operators, International Journal of Approximate Reasoning,96(2018), 57-77. · Zbl 1446.03098
[42] W. Yao, B. Zhao,Kernel systems onL-ordered sets, Fuzzy Sets and Systems,182(2011), 101-109. · Zbl 1241.06004
[43] Y.Y. Yao,Neighborhood systems and approximate retrieval, Information Sciences,176(2006), 3431-3452. · Zbl 1119.68074
[44] Y. Y. Yao, B. X. Yao,Covering based rough set approximations, Information Sciences,200(2012), 91-107. · Zbl 1248.68496
[45] D. S. Yeung, D. G. Chen, E. Tsang, J. Lee, X. Z. Wang,On the generalization of fuzzy rough sets, IEEE Transactions on Fuzzy Systems,13(2005), 343-361.
[46] J. M. Zhan, B. Sun, J. C. R. Alcantud,Covering based multigranulation(I, T)-fuzzy rough set models and applications in multi-attribute group decision-making, Information Sciences,476(2019), 290-318. · Zbl 1442.68236
[47] Y. L. Zhang, C. Q. Li, M. L. Lin, Y. J. Lin,Relationships between generalized rough sets based on covering and reflexive neighborhood system, Information Sciences,319(2015), 56-67. · Zbl 1390.68688
[48] F. F. Zhao, L. Q. Li,Axiomatization on generalized neighborhood system-based rough sets, Soft Computing,22(18) (2018), 6099-6110. · Zbl 1398.03207
[49] W. Zhu,Topological approaches to covering rough sets, Information Sciences,177(2007), 1499-1508. · Zbl 1109.68121
[50] W. Zhu,Generalized rough sets based on relations, Information Sciences,177(2007), 4997-5011. · Zbl 1129.68088
[51] W. Zhu,Relationship between generalized rough sets based on binary relation and covering, Information Science,179(2009), 210-225. · Zbl 1163.68339
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.