Skip to main content
SpringerLink
Log in

Proto-Fuzzy Concepts Generation Technique Using Fuzzy Graph

  • Conference paper
Book cover Facets of Uncertainties and Applications

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 125))

  • 704 Accesses

Abstract

Since one major disadvantage of application of fuzzy formal concept analysis is that large numbers of fuzzy concepts are generated from fuzzy context, it is practically impossible to analyze such a large amount of concepts. Often it may be required to consider some particular concepts. For example, one might be interested to find out the fuzzy concepts containing all those objects which share some specific property with a specific/required degree from a given fuzzy context. Given such a situation, proto-fuzzy concepts may play a very useful role. This paper proposes a proto-fuzzy concept generation technique using fuzzy graph on uncertainty data. In this paper, we begin with defining a fuzzy graph corresponding to the L-context (fuzzy context). We then go on to demonstrate that t-concepts can be found to correspond with each maximal cliques of t-level graph of the defined fuzzy graph. After that, we determine all those cliques which corresponds to the proto-fuzzy concepts of degree \(t\). Finally, a demonstration has been made using an example with the proposed technique.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Bělohlávek, R.: Lattices generated by binary fuzzy relations (extended abstract). In: Abstract of the 4th International Conference on Fuzzy Sets Theory and Its Applications, Liptovsky Jan’, Slovakia, p. 11 (1998)

    Google Scholar 

  2. Bělohlávek, R.: Fuzzy Relational Systems: Foundations and Principles. Kluwer Academic/Plenum Publishers, New York (2002)

    Book  Google Scholar 

  3. Bělohlávek, R., Sklenar, V., Zacpal, J.: Crisply generated fuzzy concepts. In: Ganter, B., Godin, R. (eds.) ICFCA 2005. Lecturer Notes in Computer Science, vol. 3403, pp. 268–283. Springer, Berlin (2005)

    Google Scholar 

  4. Bělohlávek, R., Vychodil, V.: Reducing the size of fuzzy concept lattices by hedges. In: The IEEE International Conference on Fuzzy Systems, FUZZ-IEEE 2005 (Proceedings on CD), pp. 663–668, Reno, Nevada, USA, 22–25 May 2005, Abstract in Printed Proceedings, p. 44, ISBN: 0-7803-9158-6

    Google Scholar 

  5. Berry, A., Sigayret, A.: Representation a concept lattice by a graph. Discret. Appl. Math. 144, 27–42 (2004)

    Article  Google Scholar 

  6. Bhattacharya, P.: Some remarks on fuzzy graphs. Pattern Recognit. Lett. 6, 297–302 (1987)

    Article  Google Scholar 

  7. Bomze, I.M., Budinich, M., Pardalos, P.M., Pelillo, M.: The maximum clique problem. In: Du, D.-Z., Pardalos, P.M. (eds.) Handbook of Combinatorial Optimization, Supplement vol. A, pp. 1–74. Kluwer, Dordrecht (1999)

    Google Scholar 

  8. Bron, C., Kerbosch, J.: Algorithm 457, finding all cliques of an undirected graph. Commun. ACM 16, 575–577 (1973)

    Article  Google Scholar 

  9. Burusco, A., Fuentes-Gonzalez, R.: The study of the L-fuzzy concept lattices. Mathw. Soft Comput. 3, 209–218 (1994)

    MathSciNet  MATH  Google Scholar 

  10. Burusco, A., Fuentes-Gonzalez, R.: Construction of the L-fuzzy concept lattice. Fuzzy Sets Syst. 97, 109–114 (1998)

    Article  MathSciNet  Google Scholar 

  11. Chakroborthy, M.K., Das, M.: Study in fuzzy relations over fuzzy subsets. Fuzzy Sets Syst. 9, 79–89 (1983)

    Article  Google Scholar 

  12. Chakroborthy, M.K., Das, M.: Fuzzy hypergraphs. In: Proceedings of International Conference on Logic Programming Born (1997)

    Google Scholar 

  13. Chiba, N., Nishizeki, T.: Arboricity and subgraph listing algorithms. SIAM J. Comput. 14, 210–223 (1985)

    Article  MathSciNet  Google Scholar 

  14. Dubois, D., Prade, H.: Fuzzy Sets and Systems, Theory and Applications. Academic Press, New York (1980)

    MATH  Google Scholar 

  15. Ganter, B.: Two Basic Algorithms in Concept Analysis, Preprint 831. Technische Hochschule Darmstadt, Darmstadt (1984)

    Google Scholar 

  16. Ganter, B., Wille, R.: Formal Concept Analysis, Mathematical Foundation. Springer, Berlin (1999)

    Book  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  18. Goguen, J.A.: L-fuzzy set. J. Math. Anal. Appl. 18(1), 145–174 (1967)

    Article  MathSciNet  Google Scholar 

  19. HöHle, U.: On the fundamentals of fuzzy set theory. J. Math Anal. Appl. 201, 786–826 (1996)

    Article  MathSciNet  Google Scholar 

  20. Jhonson, D.S., Yannakakis, M., Papadimitriou, C.H.: On generating all maximal independent sets. Inf. Process. Lett. 27, 119–123 (1988)

    Article  MathSciNet  Google Scholar 

  21. John, N.M., Premchand, S.N.: Fuzzy Graphs Fuzzy Hyper Graph. Springer, Berlin (2000)

    MATH  Google Scholar 

  22. Kaufmann, A.: Introduction a lathèorielath des sous-ensembles flous. Masson, Paris (1973)

    Google Scholar 

  23. Koch, I.: Enumerating all connected maximal common subgraphs in two graphs. Theor. Comput. Sci. 250, 1–30 (2001)

    Article  MathSciNet  Google Scholar 

  24. Krajči, S.: Cluster based efficient generation of fuzzy concepts. Neural Netw. World 5, 521–530 (2003)

    Google Scholar 

  25. Krídlo, O., Krajči, S., Proto-fuzzy concepts, their retrieval and usage. In: Proceedings of Sixth International Conference on Concept Lattices and their Applications (CLA 2008), pp. 83–96

    Google Scholar 

  26. Krídlo, O., Krajči, S., Fuzzy concept lattice is made by proto-fuzzy concepts. IFSA-EUSFLAT (2009)

    Google Scholar 

  27. Pollandt, S.: Fuzzy Begriffe. Springer, Berlin (1997)

    Book  Google Scholar 

  28. Rosenfield, A.: Fuzzy graphs. In: Zadeh, L.A., Fu, K.-S., Tanaka, K., Shimura, M. (eds.) Fuzzy Sets and their Applications to Cognitive and Decision Process, pp. 77–96. Academic Press, New York (1975)

    Google Scholar 

  29. Takeda, E.: Connectvity in fuzzy graphs. Tech. Rep. Osaka Univ. 23, 343–352 (1973)

    MathSciNet  Google Scholar 

  30. Tomitaa, E., Tanakaa, A., Takahashia, H.: The worst-case time complexity for generating all maximal cliques and computational experiments. Theor. Comput. Sci. 363, 28–42 (2006)

    Article  MathSciNet  Google Scholar 

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

    Chapter  Google Scholar 

  32. Yeh, R.T., Bang, S.Y.: Fuzzy relations, fuzzy graphs, and their applications to clustering analysis. In: Zadeh, L.A., Fu, K.S., Shimura, M. (eds.) Fuzzy Sets and their Applications, pp. 125–149. Academic Press, New York (1975)

    Google Scholar 

  33. Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–353 (1965)

    Article  Google Scholar 

  34. Zaman, W., Ghosh, P., Dutta, K.K., Basu, P.N.: A framework to incorporate domain knowledge modeling. Math. Sci. Int. Res. J. 2, 474–478 (2013)

    Google Scholar 

  35. Zaman, W., Ghosh, P., Basu, P. N.: A Prototype to incorporate domain knowledge computation in an education system. Br. J. Educ. Technol. (communicated)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Haldia Government College, P.O. Debhog, Purba Medinipur District, 721657, India

    Partha Ghosh

  2. Department of Applied Mathematics, University of Calcutta, 92 A.P.C. Road, Kolkata, 700009, India

    Krishna Kundu

Authors
  1. Partha Ghosh
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Krishna Kundu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Partha Ghosh .

Editor information

Editors and Affiliations

  1. Jadavpur University, Kolkata, India

    Mihir K. Chakraborty

  2. Institute of Mathematics, University of Warsaw, Warszawa, Poland

    Andrzej Skowron

  3. Vidyasagar University, Paschim Medinipur, West Bengal, India

    Manoranjan Maiti

  4. Department of Mathematics, National Institute of Technology (NIT), Durgapur, India

    Samarjit Kar

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer India

About this paper

Cite this paper

Ghosh, P., Kundu, K. (2015). Proto-Fuzzy Concepts Generation Technique Using Fuzzy Graph. In: Chakraborty, M.K., Skowron, A., Maiti, M., Kar, S. (eds) Facets of Uncertainties and Applications. Springer Proceedings in Mathematics & Statistics, vol 125. Springer, New Delhi. https://doi.org/10.1007/978-81-322-2301-6_5

Download citation

Publish with us

Policies and ethics

Search

Navigation