Abstract
Binary relations play an important role in rough set theory. This paper investigates the similarity of binary relations based on L-fuzzy topologies, where L is a boolean algebra. First, rough approximations based on a boolean algebra are proposed through successor neighborhoods on binary relations. Next, L-fuzzy topologies induced by binary relations are investigated. Finally, similarity of binary relations is introduced by using the L-fuzzy topologies and the fact that every binary relation is solely similar to some preorder relation is proved. It is worth mentioning that similarity of binary relations are both originated in the L-fuzzy topology and independent of the L-fuzzy topology.
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
Choudhury MA, Zaman SI (2006) Learning sets and topologies. Kybernetes 35:1567–1578
Goguen JA (1967) \(L\)-fuzzy sets. J Math Anal Appl 18:145–174
Hao J, Li Q (2011) The relationship between \(L\)-fuzzy rough set and \(L\)-topology. Fuzzy Sets Syst 178:74–83
Kortelainen J (1994) On the relationship between modified sets, topological spaces and rough sets. Fuzzy Sets Syst 61:91–95
Lashin EF, Kozae AM, Abo Khadra AA, Medhat T (2005) Rough set theory for topological spaces. Int J Approx Reason 40:35–43
Li Z, Cui R (2015) \(T\)-similarity of fuzzy relations and related algebraic structures. Fuzzy Sets Syst 275:130–143
Li Z, Cui R (2015) Similarity of fuzzy relations based on fuzzy topologies induced by fuzzy rough approximation operators. Inf Sci 305:219–233
Li Z, Xie T (2014) The relationship among soft sets, soft rough sets and topologies. Soft Comput 18:717–728
Li Z, Xie T (2015) Roughness of fuzzy soft sets and related results. Int J Comput Intell Syst 8:278–296
Li Z, Xie T, Li Q (2012) Topological structure of generalized rough sets. Comput Math Appl 63:1066–1071
Li Z, Xie N, Wen G (2015) Soft coverings and their parameter reductions. Appl Soft Comput 31:48–60
Liu G, Zhu W (2008) The algebraic structures of generalized rough set theory. Inf Sci 178:4105–4113
Pawlak Z (1982) Rough sets. Int J Comput Inf Sci 11:341–356
Pawlak Z, Skowron A (2007) Rudiments of rough sets. Inf Sci 177:3–27
Pawlak Z, Skowron A (2007) Rough sets: some extensions. Inf Sci 177:28–40
Pawlak Z, Skowron A (2007) Rough sets and Boolean reasoning. Inf Sci 177:41–73
Pei Z, Pei D, Zheng L (2011) Topology vs generalized rough sets. Int J Approx Reason 52:231–239
Wang G (1988) Theory of \(L\)-fuzzy topological spaces. Shaanxi Normal University Press, Xian
Wiweger R (1989) On topological rough sets. Bull Polish Acad Sci Math 37:89–93
Wu Q, Wang T, Huang Y, Li J (2008) Topology theory on rough sets. Trans Syst Man Cybern ( Part B ) 38:68–77
Yao YY (1996) Two views of the theory of rough sets in finite universes. Int J Approx Reason 15:291–317
Yao YY (1998) Relational interpretations of neighborhood operators and rough set approximation operators. Inf Sci 111:239–259
Yao YY (1998) Constructive and algebraic methods of the theory of rough sets. Inf Sci 109:21–47
Yang L, Xu L (2011) Topological properties of generalized approximation spaces. Inf Sci 181:3570–3580
Zhang W, Wu W, Liang J, Li D (2001) Rough set theory and methods. Chinese Scientific, Beijing
Zhang X, Dai J, Yu Y (2015) On the union and intersection operations of rough sets based on various approximation spaces. Inf Sci 292:214–229
Acknowledgments
The authors would like to thank the editors and the anonymous reviewers for their valuable comments and suggestions which have helped immensely in improving the quality of this paper. This work is supported by the NSF of China (11261005, 11161029, 11461002, 11461005), the NSF of Guangxi (2012GXNSFDA276040, 2014GXNSFAA118001), the NSF for Young Scholar of Guangxi (2013GXNSFBA019020), Guangxi Province Universities and Colleges Excellence Scholar and Innovation Team Funded Scheme, Key Discipline of Quantitative Economics in Guangxi University of Finance and Economics (2014YBKT07) and Quantitative Economics Key Laboratory Program of Guangxi University of Finance and Economics (2014SYS01).
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
All authors declare that there is no conflict of interest regarding the publication of this manuscript.
Additional information
Communicated by A. Di Nola.
Rights and permissions
About this article
Cite this article
Qin, B., Zeng, F. & Yan, K. Similarity of binary relations based on L-fuzzy topologies. Soft Comput 20, 3497–3504 (2016). https://doi.org/10.1007/s00500-015-1968-y
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00500-015-1968-y