Abstract
The purpose of this paper is to investigate the relationship between multiset topology (M-topology) and generalized rough multiset induced by multiset relation. The notion of transitive closure of a relation is proposed in multiset context. The notable results we establish here are (1) any serial multiset relation induce an M-topology (2) any reflexive multiset relation R and its transitive closure t(R) induce the same M-topology, i.e., \(\tau (R)=\tau (t(R))\). The interior and closure operators of the M-topology \(\tau (R)\) is obtained and discuss their relationship with multiset relation R, when R is a reflexive multiset relation. On the other part, we consider the case when R is a tolerance multiset relation.
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
Abo-Tabl EA (2013) Topological approximations of multisets. J Egypt Math Soc 21:123–132
Abo-Tabl EA (2013) Topological approaches to generalised rough multisets. Fuzzy Inform Eng 5:279–294
Ashfaq RAR, Wang XZ, Huang JZ (2016) Fuzziness based semi-supervised learning approach for intrusion detection system. Inform Sci. doi:10.1016/j.ins.2016.04.019 (in press)
Blizard WD (1989) Multiset theory. Notre Dame J Logic 30:346–368
Cerf V, Fernandez E, Gostelow K, Volausky S (1971) Formal control and low properties of a model of computation. Report ENG 7178, Computer Science Department, University of California, Los Angeles, CA, December, 1971, p 81
Girish KP, John SJ (2009) Relations and functions in multiset context. Inform Sci 179:758–768
Girish KP, John SJ (2011) Rough multiset and its multisets topology. In: Peters JF et al (eds) Transactions on rough sets, XIV, LNCS, vol 6600, pp 62–80
Girish KP, John SJ (2012) Multiset topologies induced by multiset relations. Inform Sci 188:298–313
He YL, Wang XZ, Huang JZ (2016) Fuzzy nonlinear regression analysis using a random weight network. Inform Sci 364–365:222–240
He YL, Liu JNK, Hu YX, Wang XZ (2015) OWA operator based link prediction ensemble for social network. Expert Syst Appl 42:21–50
Jena SP, Ghosh SK, Tripathy BK (2001) On the theory of bags and lists. Inform Sci 132:241–254
Pawlak Z (1982) Rough sets. Int J Comput Inform Sci 11:341–356
Peterson J (1976) Computation sequence sets. J Comput Syst Sci 13:1–24
Singh D, Ibrahim AM, Yohanna T, Singh JN (2007) An overview of the applications of multisets. Novi Sad J Math 37:73–92
Wang XZ (2015) Learning from big data with uncertainty–editorial. J Intell Fuzzy Syst 28(5):2329–2330
Wang XZ, Ashfaq RAR, Fu AM (2015) Fuzziness based sample categorization for classifier performance improvement. J Intell Fuzzy Syst 29(3):1185–1196
Yager RR (1986) On the theory of bags. Int J Gen Syst 13:23–37
Acknowledgments
The authors are greatly indebted to the Editor-in-Chief, Associate Editor, and anonymous reviewers for their valuable comments and suggestions for improving the paper.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Sharan, S., Tiwari, S.P. & Kumari, N. On relationship between generalized rough multisets and multiset topologies. Int. J. Mach. Learn. & Cyber. 8, 2017–2024 (2017). https://doi.org/10.1007/s13042-016-0581-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13042-016-0581-4