SavedAdd your journal

Journals / Hacettepe Journal of Mathematics and Statistics / 2010 / Cilt: 39 - Sayı: 2

Based of [0, 1]-matroids

Fu Gui SHI
Chun E. HUANG
Pages
233–240
Publication Date
2022-10-18
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

It is proved that there is a one-to-one correspondence between the family of closed perfect [0, 1]-matroids on E and the set of their fuzzy bases.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, a characterization of [0, 1]-matroids is given.
📊
Key Findings & Data:It is proved that a [0, 1]-matroid is equivalent to a hereditary fuzzy pre-matroid, and that a perfect [0, 1]-matroid is equivalent to a Goetschel-Voxman fuzzy matroid.
💡
Conclusion & Impact:It is proved that there is a one-to-one correspondence between the family of closed perfect [0, 1]-matroids on E and the set of their fuzzy bases.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

In this paper, a characterization of [0, 1]-matroids is given. It is proved that a [0, 1]-matroid is equivalent to a hereditary fuzzy pre-matroid, and that a perfect [0, 1]-matroid is equivalent to a Goetschel-Voxman fuzzy matroid. It is proved that there is a one-to-one correspondence between the family of closed perfect [0, 1]-matroids on E and the set of their fuzzy bases.

🔖

Cite This Article

SHI, F. G., HUANG, C. E. (2022). Based of [0, 1]-matroids. Hacettepe Journal of Mathematics and Statistics, Cilt: 39 - Sayı: 2, 233–240. https://ajindex.com/articles/530662

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (11)

  1. Goetschel, R. and Voxman, W. Fuzzy matroids, Fuzzy Sets and Systems 27, 291–302, 1988
  2. Goetschel, R. and Voxman, W. Bases of fuzzy matroids, Fuzzy Sets and Systems 31, 253– 261, 1989
  3. Goetschel, R. and Voxman, W. Fuzzy rank functions, Fuzzy Sets and Systems 42, 245–258, 1991
  4. Novak, L.A. On fuzzy independence set systems, Fuzzy Sets and Systems 91, 365–374, 1997
  5. Novak, L.A. On Goetschel and Voxman fuzzy matroids, Fuzzy Sets and Systems 117, 407– 412, 2001
  6. Oxley, J.G. Matroid Theory (Oxford university press, 1992)
  7. Shi, F. -G. A new approach to the fuzzification of matroids, Fuzzy Sets and Systems, 160, 696–705, 2009
  8. Shi, F. -G. (L,M)-fuzzy matroids, Fuzzy Sets and Systems 160, 2387–2400, 2009
  9. Whitney, H. On the abstract properties of linear dependence, Amer. J. Math. 57, 509–533, 1935
  10. Xin, X. and Shi, F. -G. Rank functions for closed and perfect [0, 1]-matroids, Hacettepe J. Math. Stat. 39 (1), 31–39, 2010
  11. Zadeh, L.A. A computational approach to fuzzy quantifiers in natural languages, Comput. Math. Appl. 9, 149–184, 1983.