[go: up one dir, main page]
More Web Proxy on the site http://driver.im/ Skip to main content
Springer Nature Link
Log in

Complex Fuzzy Concept Lattice

  • Published:
Neural Processing Letters Aims and scope Submit manuscript

Abstract

Recently, several properties of complex fuzzy sets are introduced to measure the changes in dynamic or periodic fuzzy attributes using its amplitude and phase terms. In this process, a problem is observed while discovering some of the meaningful information from the given complex data sets for the knowledge processing tasks. The reason is lack of researches on complex fuzzy matrix and its graphical properties. To fill this backdrop, the current paper introduces a method for mathematical analysis of complex fuzzy context using the properties of lower neighbors and \(\delta \)-equality. The current paper also describes the application of the complex fuzzy concept lattice with an illustrative example.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
£29.99 /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 includes VAT (United Kingdom)

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

Explore related subjects

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

References

  1. Gajdos P, Snasel V (2014) A new FCA algorithm enabling analyzing of complex and dynamic data sets. Soft Comput 18(4):683–694

    Article  Google Scholar 

  2. Singh PK (2017) Complex vague set based concept lattice. Chaos Solitons Fractals 95:145–153

    Article  MATH  Google Scholar 

  3. Wille R (1982) Restructuring lattice theory: an approach based on hierarchies of concepts. In: Rival I (ed) Ordered sets. Reidel, Dordrect, pp 445–470

    Chapter  Google Scholar 

  4. Burusco A, Fuentes-Gonzales R (1994) The study of L-fuzzy concept lattice. Mathw Soft Comput 3:209–218

    MathSciNet  MATH  Google Scholar 

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

    Book  MATH  Google Scholar 

  6. Goguen JA (1967) L-fuzzy sets. J Math Anal Appl 18(1967):145–174

    Article  MathSciNet  MATH  Google Scholar 

  7. Ward M, Dilworth RP (1939) Residuated lattices. Trans. Am. Math. Soc. 45:335–354

    Article  MathSciNet  MATH  Google Scholar 

  8. Berry A, Sigayret A (2004) Representing concept lattice by a graph. Discrete Appl Math 144:27–42

    Article  MathSciNet  MATH  Google Scholar 

  9. Singh PK (2018) Concept learning using vague concept lattice. Neural Process Lett. https://doi.org/10.1007/s11063-017-9699-y

    Google Scholar 

  10. Singh PK (2018) Similar vague concepts selection using their Euclidean distance at different granulation. Cogn Comput 10(2):228–241. https://doi.org/10.1007/s12559-017-9527-8

    Article  Google Scholar 

  11. Ghosh P, Kundu K, Sarkar D (2010) Fuzzy graph representation of a fuzzy concept lattice. Fuzzy Sets Syst 161:1669–1675

    Article  MathSciNet  MATH  Google Scholar 

  12. Li JH, Mei C, Lv Y (2012) Knowledge reduction in real decision formal contexts. Inf Sci 189:191–207

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

  14. Ramot D, Friedman M, Langholz G, Kandel A (2003) Complex fuzzy logic. IEEE Trans Fuzzy Syst 11(4):450–461

    Article  Google Scholar 

  15. Ramot D, Milo R, Friedman M, Kandel A (2005) Complex fuzzy sets. IEEE Trans Fuzzy Syst 10(2):171–186

    Article  Google Scholar 

  16. Dick S (2005) Toward complex fuzzy logic. IEEE Trans Fuzzy Syst 13(3):405–414

    Article  Google Scholar 

  17. Tamir DE, Teodorescu HN, Last M, Kandel A (2012) Discrete complex fuzzy logic. In: NAFIPS, 6 p

  18. Selvachandrana G, Maji PK, Abed IE, Salleh AR (2016) Relations between complex vague soft sets. Appl Soft Comput 47:438–448

    Article  Google Scholar 

  19. Yazdanbakhsh O, Dick S (2015) Time-series forecasting via complex fuzzy logic. In: Sadeghian A, Tahayori H (eds) Frontiers of higher order fuzzy sets. Springer, New York, pp 147–165

    Google Scholar 

  20. Yazdanbakhsh O, Dick S (2017) A systematic review of complex fuzzy sets and logic. Fuzzy Sets Syst. https://doi.org/10.1016/j.fss.2017.01.010

    MATH  Google Scholar 

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

    Article  Google Scholar 

  22. Selvachandran G, Maji PK, Abed IE, Salleh AR (2016) Complex vague soft sets and its distance measures. J Intell Fuzzy Syst 31:55–68

    Article  MATH  Google Scholar 

  23. Singh PK, AKumar CA (2014) Bipolar fuzzy graph representation of concept lattice. Inf Sci 288:437–448

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  26. 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 

  27. Alkouri AS, Salleh AR (2014) Linguistic variables, hedges and several distances on complex fuzzy sets. J Intell Fuzzy Syst 26:2527–2535

    MathSciNet  MATH  Google Scholar 

  28. Li C, Chan FT (2012) Knowledge discovery by an intelligent approach using complex fuzzy sets. Lect Notes Comput Sci 7196:320–329

    Article  Google Scholar 

  29. Ali M, Smarandache F (2017) Complex neutrosophic set. Neural Comput Appl 28(7):1817–1834

    Article  Google Scholar 

  30. Ulazeez ABD, Alkouri M, Salleh AR (2014) Complex fuzzy soft multisets. The 2014 UKM FST postgraduate colloquium. In: Proceddings of 2014 AIP conference, vol 1614, pp 955–961. https://doi.org/10.1063/1.4895330

  31. Qudah YA, Hassan M (2017) Operations on complex multi-fuzzy sets. J Intell Fuzzy Syst. https://doi.org/10.3233/JIFS-162428

    MATH  Google Scholar 

  32. Dick S, Yager RR, Yazdanbakhsh O (2016) On Pythagorean and complex fuzzy set operations. IEEE Trans Fuzzy Syst 24:1009–1021

    Article  Google Scholar 

  33. Zhao ZQ, Ma SQ (2016) Complex fuzzy matrix and its convergence problem research. In: Cao BY et al (eds) Fuzzy systems and operations research and management. Springer, Cham, pp 157–162

    Chapter  Google Scholar 

  34. Zhang X, Mei C, Chen D, Li JH (2016) Feature selection in mixed data: a method using a novel fuzzy rough set-based information entropy. Pattern Recogn 56:1–15

    Article  Google Scholar 

  35. Tamir DE, Rishe ND, Kandel A (2015) Complex fuzzy sets and complex fuzzy logic: an overview of theory and applications. Fifty years of fuzzy logic and its applications. Springer, Cham, pp 661–681

    MATH  Google Scholar 

  36. Thirunavukarasu P, Suresh R, Viswanathan KK (2016) Energy of a complex fuzzy graph. Int J Math Sci Eng Appl (IJMSEA) 10(1):243–248

    Google Scholar 

  37. Singh PK (2015) Fuzzy concept lattice reduction using Shannon entropy and Huffman coding. J Appl Nonclassic Log 25(2):101–119

    Article  MathSciNet  MATH  Google Scholar 

  38. Kumar CA, Singh PK (2014) Knowledge representation using formal concept analysis: a study on concept generation. In: Tripathy BK, Acharjya DP (eds) Global trends in knowledge representation and computational intelligence. IGI Global International Publishers, New York, pp 306–336

    Google Scholar 

  39. Zhang G, Dillon TS, Cai KY, Ma J, Lu J (2009) Operation properties and \(\delta \)-equalities of complex fuzzy sets. Int J Approx Reason 50:1227–1249

    Article  MathSciNet  MATH  Google Scholar 

  40. Kumar CA, Srinivas S (2010) Concept lattice reduction using fuzzy K-means clustering. Expert Syst Appl 37(3):2696–2704

    Article  Google Scholar 

  41. Kumar CA, Dias SM, Vieira NJ (2015) Knowledge reduction in formal contexts using non-negative matrix factorization. Math Comput Simul 109:46–63

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

Author thanks the anonymous reviewers and Editor for their compliments to improve the quality of this paper.

Author information

Authors and Affiliations

  1. Amity Institute of Information Technology, Amity University, Sector-125, Noida, Uttar Pradesh, 201303, India

    Prem Kumar Singh

Authors
  1. Prem Kumar Singh
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Prem Kumar Singh.

Ethics declarations

Conflict of interest

Author declares that there is no conflict of interest.

Ethical Approval

This article does not contain any studies with human participants or animals.

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. Complex Fuzzy Concept Lattice. Neural Process Lett 49, 1511–1526 (2019). https://doi.org/10.1007/s11063-018-9884-7

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11063-018-9884-7

Keywords

Search

Navigation