Skip to main content

Advertisement

Log in

Three-way n-valued neutrosophic concept lattice at different granulation

  • Original Article
  • Published:
International Journal of Machine Learning and Cybernetics Aims and scope Submit manuscript

Abstract

In recent year, the mathematics of three-way fuzzy concept lattice is introduced to characterize the attributes based on its acceptation, rejection and uncertain part. One of the suitable example is descriptive analysis of opinion of people in a democratic country. This became complex for the country like India where opinion (i.e. vote) of people to choose the particular leader is based on 29 independent states and their distinct issues. Adequate analysis of these type of 29-valued data based on its acceptation, rejection and uncertain part is major issue for the government and private agencies. To resolve this issue current paper introduces n-valued neutrosophic context and its graphical structure visualization for descriptive analysis. In the same time an another method is proposed to some of the similar three-way n-valued concepts. To zoom in and zoom out the n-valued neutrosophic context at user required information granules with an illustrative example.

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

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

Notes

  1. https://en.wikipedia.org/wiki/Many_valued_logic.

  2. https://en.wikipedia.org/wiki/Multivalued_function.

  3. https://en.wikipedia.org/wiki/Polarity_international_relations.

  4. https://en.wikipedia.org/wiki/None_of_the_above.

  5. https://plato.stanford.edu/entries/logic-manyvalued/.

  6. http://katehon.com/article/india-and-multipolarity.

  7. http://www.e-ir.info/2013/06/03/towards-a-multi-polar-international-system-which-prospects-for-global-peace/.

References

  1. Alkhazaleh S (2017) N-Valued refined neutrosophic soft set theory. J Intell Fuzzy Syst 32(6):4311–4318

    Article  Google Scholar 

  2. Alkhazaleh S, Hazaymeh A (2018) N-valued refined neutrosophic soft sets and their applications in decision making problems and medical diagnosis. J Artif Intell Soft Comput Res 8(1):79–86

    Article  Google Scholar 

  3. Ascar E, Yener B (2009) Unsupervised multiway data analysis: a literature survey. IEEE Trans Data Knowl Eng 1(1):6–20

    Article  Google Scholar 

  4. Antoni L, Krajči S, Krídlo O, Macek B, Piskova L (2014) On heterogeneous formal contexts. Fuzzy Sets Syst 234:22–33

    Article  MathSciNet  Google Scholar 

  5. Bělohlávek R (2004) Concept lattices and order in fuzzy logic. Ann Pure Appl Logic 128(1–3):277–298

    Article  MathSciNet  Google Scholar 

  6. Burusco A, Fuentes-Gonzalez R (1994) The study of the L-fuzzy concept lattice. Mathew Soft Comput 1(3):209–218

    MathSciNet  MATH  Google Scholar 

  7. Broumi S, Deli I, Smarandache F (2015) N-valued interval neutrosophic sets and their application in medical diagnosis. Crit Rev Cent Math Uncertainty Creighton Univ USA 10:46–69

    Google Scholar 

  8. Broumi S, Son LH, Bakali A, Talea M, Smarandache F, Selvachandran G (2017) Computing operational matrices in neutrosophic environments: a matlab toolbox. Neutrosoph Sets Syst 18:58–66

    Google Scholar 

  9. Broumi S, Bakali A, Talea M, Smarandache F (2017) Shortest path problem on single valued neutrosophic graphs. In: International symposium on networks, computers and communications (ISNCC): wireless and mobile communications and networking 978-1-5090-4260-9/17/31.00. pp 1–6. https://doi.org/10.1109/ISNCC.2017.8071993

  10. Chen J, Li S, Ma S, Wang X (2014) \(m\)-polar fuzzy sets: an extension of bipolar fuzzy sets. Sci World J. https://doi.org/10.1155/2014/416530

    Article  Google Scholar 

  11. Djouadi Y, Prade H (2011) Possibility-theoretic extension of derivation operators in formal concept analysis over fuzzy lattices. Fuzzy Optim Decis Making 10:287–309

    Article  MathSciNet  Google Scholar 

  12. Ganter B, Wille R (1999) Formal concept analysis: mathematical foundation. Springer, Berlin

    Book  Google Scholar 

  13. Kandasamy WBV, Ilanthenral K, Smarandache F (2015) Neutrosophic graphs: a new dimension to graph theory, Kindle edn. EuropaNova ASBL, Clos du Parnasse, 3E (ISBN-13: 978-1-59973-362-3)

    Google Scholar 

  14. Kroonenberg PM (2008) Applied multiway data analysis. Wiley, Oxford

    Book  Google Scholar 

  15. Liu D, Li T, Ruan D (2011) Probabilistic model criteria with decision-theoretic rough sets. Inf Sci 181:3709–3722

    Article  MathSciNet  Google Scholar 

  16. Liu D, Liang D (2017) Three-way decisions in ordered decision system. Knowl Based Syst 137:182–195

    Article  Google Scholar 

  17. Li JH, Huanga C, Qi J, Qian J, Liu W (2017) Three-way cognitive concept learning via multi-granularity. Inf Sci 378:244–263

    Article  Google Scholar 

  18. Ma L, Mi JS, Xie B (2017) Multi-scaled concept lattices based on neighborhood systems. Int J Mach Learn Cybern 8(1):149–157

    Article  Google Scholar 

  19. Pedrycz W, Chen SM (2015) Granular computing and decision-making: interactive and iterative approaches. Springer, Berlin

    Book  Google Scholar 

  20. Singh PK, Gani A (2015) Fuzzy concept lattice reduction using Shannon entropy and Huffman coding. J Appl Non Class logic 25(2):101–119

    Article  MathSciNet  Google Scholar 

  21. Singh PK, Kumar CA, Gani A (2016) A comprehensive survey on formal concept analysis and its research trends. Int J Appl Math Comput Sci 26(2):495–516

    Article  MathSciNet  Google Scholar 

  22. Singh PK (2017) Three-way fuzzy concept lattice representation using neutrosophic set. Int J Mach Learn Cybern 8(1):69–79

    Article  Google Scholar 

  23. Singh PK (2017) Complex vague set based concept lattice. Chaos Solitons Fract 96:145–153

    Article  Google Scholar 

  24. Singh PK (2018) Medical diagnoses using three-way fuzzy concept lattice and their Euclidean distance. Comput Appl Math 37(3):3282–3306

    Article  Google Scholar 

  25. Singh PK (2018) Interval-valued neutrosophic graph representation of concept lattice and its (\(\alpha, \beta, \gamma\))-decomposition. Arab J Sci Eng 43(2):723–740. https://doi.org/10.1007/s13369-017-2718-5

    Article  Google Scholar 

  26. Singh PK (2018) \(m\)-polar fuzzy graph representation of concept lattice. Eng Appl Artif Intell 67:52–62

    Article  Google Scholar 

  27. Singh PK (2018) Complex neutrosophic concept lattice and its applications to air quality analysis. Chaos Solitons Fract 109:206–213

    Article  Google Scholar 

  28. Singh PK (2018) Concept lattice visualization of data with m-polar fuzzy attribute. Granul Comput 2(3):159–173. https://doi.org/10.1007/s41066-017-0060-7

    Article  Google Scholar 

  29. Rivieccio U (2007) Neutrosophic logics: prospects and problems. Fuzzy Sets Syst 159:1860–1868

    Article  MathSciNet  Google Scholar 

  30. Smarandache F (1998) Neutrosophy, Neutrosophic probability, set, and logic, proquest information & learning. American Research Press, Rehoboth, p 105 (ISBN 978-1-59973-080-6)

    MATH  Google Scholar 

  31. Smarandache F (2013) n-valued refined neutrosophic logic and its applications to physics. Prog Phys 9(4):143–146

    Google Scholar 

  32. Voutsadakis G (2002) Polyadic concept analysis. Order 19:295–304

    Article  MathSciNet  Google Scholar 

  33. Wille R (1982) Restructuring lattice theory: an approach based on hierarchies of concepts. In: Rival I (ed) Ordered sets, NATO advanced study institutes series, vol 83. Springer, Dordrecht, pp 445–470

    Google Scholar 

  34. Wu WZ, Leung Y, Mi JS (2009) Granular computing and knowledge reduction in formal context. IEEE Trans Knowl Data Eng 21(10):1461–1474

    Article  Google Scholar 

  35. Yao Y (2009) Three-way decision: an interpretation of rules in rough set theory. In: Wen P, Li Y, Polkowski L, Yao Y, Tsumoto S, Wang G (eds) RSKT 2009, vol 5589. Springer, Berlin, pp 642–649

    Google Scholar 

  36. Yao Y (2010) Three-way decisions with probabilistic rough sets. Inf Sci 180:341–353

    Article  MathSciNet  Google Scholar 

  37. Yao Y (2013) An outline of a theory of three-way decisions. In: Yao J, Yang Y, Slowinski R, Greco S, Li H, Mitra S, Polkowski L (eds) RSCTC 2012, vol 7413. Springer, Berlin, pp 1–17

    Google Scholar 

  38. Yao Y (2016) Three-way decisions and cognitive computing. Cogn Comput 8:543–554

    Article  Google Scholar 

  39. Zenzo SD (1988) A many-valued logic for approximate reasoning. IBM J Res Dev 32(4):552–565

    Article  Google Scholar 

Download references

Acknowledgements

Author sincerely thanks the reviewers and Editor for their opinion to improve this paper.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Prem Kumar Singh.

Ethics declarations

Conflict of interest

Author declares that there is no conflict of interest.

Additional information

Publisher’s Note

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

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Singh, P.K. Three-way n-valued neutrosophic concept lattice at different granulation. Int. J. Mach. Learn. & Cyber. 9, 1839–1855 (2018). https://doi.org/10.1007/s13042-018-0860-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13042-018-0860-3

Keywords