Skip to main content
SpringerLink
Log in

A Novel Approach in the Light of Fuzzy Multiset Topology

  • Scientific Research Paper
  • Published:
Proceedings of the National Academy of Sciences, India Section A: Physical Sciences Aims and scope Submit manuscript

Abstract

In the present article, we present the notions of fuzzy multiset interior and closure operator and study their basic characterizations and properties. Furthermore, using the fuzzy multiset closure operator we introduce the notion of fuzzy multiset closure space and present its related properties. Finally, the notion of connectedness in the context of fuzzy multiset topology is discussed and some properties are investigated.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Availability of data and material

The article does not contain any data for analysis.

Code Availability

Not applicable.

References

  1. Zadeh LA (1965) Fuzzy sets. Inf Control 8(3):338–353

    Article  MATH  Google Scholar 

  2. Knuth D (1981) The art of computer programming, Vol. 2: seminumerical algorithms. Addison- Wesley, Reading, MA

    MATH  Google Scholar 

  3. De Bruijn NG (1983) Denumerations of rooted trees and multisets. Discret Appl Math 6(1):25–33

    Article  MathSciNet  MATH  Google Scholar 

  4. Blizard WD (1989) Multiset theory. Notre Dame J Form Log 30(1):36–66

    MathSciNet  MATH  Google Scholar 

  5. Blizard WD (1991) The development of multiset theory. Mod Log 1(4):319–352

    MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  7. Kandil A, Tantawy OA, El-Sheikh SA, Zakaria A (2016) Multiset proximity spaces. J Egypt Math Soc 24(4):562–567

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  9. El-Sheikh S, Omar R, Raafat M (2015) Separation axioms on multiset topology. J New Theory 7:11–21

    Google Scholar 

  10. Girish KP, John SJ (2011) Rough multiset and its multiset topology. In: Transactions on Rough Sets XIV, Springer, Berlin, Heidelberg, pp 62–80

  11. Girish KP, John SJ (2012) On multiset topologies. Theory Appl Math Comput Sci 2:37–52

    MATH  Google Scholar 

  12. Mahalakshmi PM, Thangavelu P (2016) M-Connectedness in M-topology. Internat J Pure Appl Math 106(8):21–25

    Google Scholar 

  13. Shravan K, Tripathy BC (2018) Generalised closed sets in multiset topological space. Proyecciones (Antofagasta) 37(2):223–237

    Article  MATH  Google Scholar 

  14. Shravan K, Tripathy BC (2018) Multiset ideal topological spaces and local function. Proyecciones (Antofagasta) 37(4):699–711

    Article  MathSciNet  MATH  Google Scholar 

  15. Shravan K, Tripathy BC (2019) Multiset mixed topological space. Soft Comput 23(20):9801–9805

    Article  MATH  Google Scholar 

  16. Yager RR (1986) On the theory of bags. Int J Gen Syst 13(1):23–37

    Article  MathSciNet  Google Scholar 

  17. Chakrabarty K, Biswas R, Nanda S (1999) On Yager’s theory of bags and fuzzy bags. Comput Informat 18(1):1–17

    MathSciNet  MATH  Google Scholar 

  18. Miyamoto S (2000) Fuzzy multisets and their generalizations. Workshop on membrane computing. Springer, Berlin, Heidelberg, pp 225–235

    Google Scholar 

  19. Riesgo Á, Alonso P, Diaz I, Montes S (2018) Basic operations for fuzzy multisets. Int J Approx Reason 101:107–118

    Article  MathSciNet  MATH  Google Scholar 

  20. Rocacher D (2003) On fuzzy bags and their application to flexible querying. Fuzzy Sets Syst 140(1):93–110

    Article  MathSciNet  MATH  Google Scholar 

  21. Kim KS, Miyamoto S (1996) Application of fuzzy multisets to fuzzy database systems. In: Soft Computing in Intelligent Systems and Information Processing. Proceedings of the 1996 Asian Fuzzy Systems Symposium. IEEE, pp 115–120

  22. Biswas R (1999) An application of Yager’s bag theory in multicriteria based decision making problems. Int J Intell Syst 14(12):1231–1238

    Article  MATH  Google Scholar 

  23. LI B (1990) Fuzzy bags and applications. Fuzzy Sets Syst 34(1):61–71

    Article  MathSciNet  MATH  Google Scholar 

  24. Pisarski RD (2007) Fuzzy bags and Wilson lines. Prog Theor Phys Suppl 168:276–284

    Article  ADS  Google Scholar 

  25. Moshahary J (2017) Topological structure on fuzzy multisets. Int J Sci Res Manag 5:6461–6465

    Google Scholar 

  26. Dugundji J (1995) Topology. Universal Book stall, New Delhi

    MATH  Google Scholar 

  27. Munkres JR (2000) Topology—a first course. Prentice Hall of India

  28. Simmons GF (1963) Introduction to topology and modern analysis. In: International, vol 44. McGraw Hill

  29. Willard S (1970) General topology. Addison-Wesley

  30. Chang CL (1968) Fuzzy topological spaces. J Math Anal Appl 24(1):182–190

    Article  MathSciNet  MATH  Google Scholar 

Download references

Funding

Not applicable, the research is not supported by any funding agency.

Author information

Authors and Affiliations

  1. Department of Mathematics, NIT Agartala, Agartala, Tripura, 799046, India

    Md Mirazul Hoque & Baby Bhattacharya

  2. Department of Mathematics, Tripura University, Agartala, Tripura, 799022, India

    Binod Chandra Tripathy

Authors
  1. Md Mirazul Hoque
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Baby Bhattacharya
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Binod Chandra Tripathy
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

All the authors have equal contribution for the preparation of this article.

Corresponding author

Correspondence to Baby Bhattacharya.

Ethics declarations

Conflict of interest

The authors declare that the article is free from conflicts of interest.

Significant Statement

Fuzzy multiset topology introduced by J. Moshahary has a lot of scope for investigation. Here, we have studied fuzzy multiset closure and interior operators. In fuzzy relational databases, these two operators play an important role and certainly motivate the research community for further investigation and application in the domain.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hoque, M.M., Bhattacharya, B. & Tripathy, B.C. A Novel Approach in the Light of Fuzzy Multiset Topology. Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci. 93, 675–683 (2023). https://doi.org/10.1007/s40010-023-00834-y

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40010-023-00834-y

Keywords

Mathematics Subject Classification

Search

Navigation