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On relationship between generalized rough multisets and multiset topologies

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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.

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References

  1. Abo-Tabl EA (2013) Topological approximations of multisets. J Egypt Math Soc 21:123–132

    Article  MATH  MathSciNet  Google Scholar 

  2. Abo-Tabl EA (2013) Topological approaches to generalised rough multisets. Fuzzy Inform Eng 5:279–294

    Article  MathSciNet  Google Scholar 

  3. 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)

  4. Blizard WD (1989) Multiset theory. Notre Dame J Logic 30:346–368

    MATH  MathSciNet  Google Scholar 

  5. 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

  6. Girish KP, John SJ (2009) Relations and functions in multiset context. Inform Sci 179:758–768

    Article  MATH  MathSciNet  Google Scholar 

  7. 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

  8. Girish KP, John SJ (2012) Multiset topologies induced by multiset relations. Inform Sci 188:298–313

    Article  MATH  MathSciNet  Google Scholar 

  9. He YL, Wang XZ, Huang JZ (2016) Fuzzy nonlinear regression analysis using a random weight network. Inform Sci 364–365:222–240

    Article  Google Scholar 

  10. He YL, Liu JNK, Hu YX, Wang XZ (2015) OWA operator based link prediction ensemble for social network. Expert Syst Appl 42:21–50

    Article  Google Scholar 

  11. Jena SP, Ghosh SK, Tripathy BK (2001) On the theory of bags and lists. Inform Sci 132:241–254

    Article  MATH  MathSciNet  Google Scholar 

  12. Pawlak Z (1982) Rough sets. Int J Comput Inform Sci 11:341–356

    Article  MATH  Google Scholar 

  13. Peterson J (1976) Computation sequence sets. J Comput Syst Sci 13:1–24

    Article  MATH  MathSciNet  Google Scholar 

  14. Singh D, Ibrahim AM, Yohanna T, Singh JN (2007) An overview of the applications of multisets. Novi Sad J Math 37:73–92

    MATH  MathSciNet  Google Scholar 

  15. Wang XZ (2015) Learning from big data with uncertainty–editorial. J Intell Fuzzy Syst 28(5):2329–2330

    Article  MathSciNet  Google Scholar 

  16. Wang XZ, Ashfaq RAR, Fu AM (2015) Fuzziness based sample categorization for classifier performance improvement. J Intell Fuzzy Syst 29(3):1185–1196

    Article  MathSciNet  Google Scholar 

  17. Yager RR (1986) On the theory of bags. Int J Gen Syst 13:23–37

    Article  MathSciNet  Google Scholar 

Download references

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.

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Correspondence to Shambhu Sharan.

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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

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  • DOI: https://doi.org/10.1007/s13042-016-0581-4

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