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Dergiler / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 39 Issue: 2

Bases of [0,1]-matroids

Chun-e. Huang
Fu-gui Shi
Sayfa
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Yayın Tarihi
2010-02-01
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

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 Maddede Bu Makale

🎯
Amaç & Hipotez:In this paper, a characterization of [0, 1]-matroids is given.
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Temel Bulgular & Veri: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.
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Sonuç & Katkı: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.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Basis · 2000 AMS Classification: 03 E 70

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.

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Bu Makaleye Atıf Yap

Huang, C., Shi, F. (2010). Bases of [0,1]-matroids. Hacettepe Journal of Mathematics and Statistics, Volume: 39 Issue: 2. https://ajindex.com/articles/1403709

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Kaynakça (7)

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  2. 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.
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  4. Shi, F. -G. A new approach to the fuzzification of matroids, Fuzzy Sets and Systems, 160, 696–705, 2009.
  5. Shi, F. -G. (L, M )-fuzzy matroids, Fuzzy Sets and Systems 160, 2387–2400, 2009.
  6. 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.
  7. Zadeh, L. A. A computational approach to fuzzy quantifiers in natural languages, Comput. Math. Appl. 9, 149–184, 1983.