Skip to main content

M-Fuzzifying P-Closure Operators

  • Conference paper
Fuzzy Information and Engineering Volume 2

Part of the book series: Advances in Intelligent and Soft Computing ((AINSC,volume 62))

  • 1014 Accesses

Abstract

In this paper, the notion of closure operators is generalized to M-fuzzy setting, which is called M-fuzzifying P-closure operators. It is proved that there exists a one-to-one corresponding between an M-fuzzifying matroid and its M-fuzzifying P-closure operator.

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

Access this chapter

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

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Dwinger, P.: Characterizations of the complete homomorphic images of a completely distributive complete lattice I. In: Indagationes Mathematicae (Proceedings), vol. 85, pp. 403–414 (1982)

    Google Scholar 

  2. Fortin, J., Kasperski, A., Zielinski, P.: Efficient methods for computing optimality degrees of elements in fuzzy weighted matroids. In: Bloch, I., Petrosino, A., Tettamanzi, A. (eds.) Fuzzy Logic and Applications, The 6th International Workshop, WILF, Crema, Italy, pp. 99–107 (2005)

    Google Scholar 

  3. Goetschel, R., Voxman, W.: Fuzzy matroids. Fuzzy Sets and Systems 27, 291–302 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  4. Goetschel, R., Voxman, W.: Bases of fuzzy matroids. Fuzzy Sets and Systems 31, 253–261 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  5. Goetschel, R., Voxman, W.: Fuzzy rank functions. Fuzzy Sets and Systems 42, 245–258 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  6. Hsueh, I.-C.: On fuzzication of matroids. Fuzzy Sets and Systems 53, 319–327 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  7. Huang, H.-L., Shi, F.-G.: M-fuzzy numbers and their properties. Information Sciences 178, 1141–1151 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  8. Kasperski, A., Zielinski, P.: A possibilistic approach to combinatorial optimization problems on fuzzy-valued matroids. In: Bloch, I., Petrosino, A., Tettamanzi, A. (eds.) Fuzzy Logic and Applications, The 6th International Workshop, WILF, Crema, Italy, pp. 46–52 (2005)

    Google Scholar 

  9. Kasperski, A., Zielinski, P.: On combinatorial optimization problems on matroids with uncertain weights. European Journal of Operational Research 177, 851–864 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  10. Kasperski, A., Zielinski, P.: Using gradual numbers for solving fuzzy-valued combinatorial Optimization problems. In: Melin, P., Castillo, O., Aguilar, L.T., Kacprzyk, J., Pedrycz, W. (eds.) Foundations of Fuzzy Logic and Soft Computing, The 12th International Fuzzy Systems Association World Congress, Cancun, Mexico, pp. 656–665 (2007)

    Google Scholar 

  11. Raney, G.N.: Completely distributive complete lattices. Proceedings of the American Mathematical Society 3, 677–680 (1952)

    Article  MATH  MathSciNet  Google Scholar 

  12. Shi, F.-G.: Theory of L β -nested sets and L α -nested sets and its applications. Fuzzy Systems and Mathematics 4, 65–72 (1995) (in Chinese)

    Google Scholar 

  13. Shi, F.-G.: M-fuzzy relation and M-fuzzy subgroup. The Journal of Fuzzy Mathematics 8, 491–499 (2000)

    MATH  Google Scholar 

  14. Shi, F.-G.: A new approach to the fuzzification of matroids. Fuzzy Sets and Systems (2008), doi:10.1016/j.fss.2008.05.007

    Google Scholar 

  15. Shi, F.-G.: (L,M)-fuzzy matroids. Fuzzy Sets and Systems (submitted)

    Google Scholar 

  16. Wang, G.-J.: Theory of topological molecular lattices. Fuzzy Sets and Systems 47, 351–376 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  17. Welsh, D.J.A.: Matroid theory. Academic Press, London (1976)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Wang, L., Wei, YP. (2009). M-Fuzzifying P-Closure Operators. In: Cao, B., Li, TF., Zhang, CY. (eds) Fuzzy Information and Engineering Volume 2. Advances in Intelligent and Soft Computing, vol 62. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03664-4_60

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-03664-4_60

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-03663-7

  • Online ISBN: 978-3-642-03664-4

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics