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Bases of [0,1]-matroids
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.
Keywords
References
- 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.
- 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.
- Oxley, J. G. Matroid Theory (Oxford university press, 1992).
- Shi, F. -G. A new approach to the fuzzification of matroids, Fuzzy Sets and Systems, 160, 696–705, 2009.
- Shi, F. -G. (L, M )-fuzzy matroids, Fuzzy Sets and Systems 160, 2387–2400, 2009.
- 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.
- Zadeh, L. A. A computational approach to fuzzy quantifiers in natural languages, Comput. Math. Appl. 9, 149–184, 1983.
Details
Primary Language
English
Subjects
Statistics
Journal Section
Research Article
Publication Date
February 1, 2010
Submission Date
May 12, 2014
Acceptance Date
-
Published in Issue
Year 2010 Volume: 39 Number: 2
APA
Huang, C.- e., & Shi, F.- gui. (2010). Bases of [0,1]-matroids. Hacettepe Journal of Mathematics and Statistics, 39(2), 233-240. https://izlik.org/JA74CC92PU
AMA
1.Huang C e., Shi F gui. Bases of [0,1]-matroids. Hacettepe Journal of Mathematics and Statistics. 2010;39(2):233-240. https://izlik.org/JA74CC92PU
Chicago
Huang, Chun-e., and Fu-gui Shi. 2010. “Bases of [0,1]-Matroids”. Hacettepe Journal of Mathematics and Statistics 39 (2): 233-40. https://izlik.org/JA74CC92PU.
EndNote
Huang C- e., Shi F- gui (February 1, 2010) Bases of [0,1]-matroids. Hacettepe Journal of Mathematics and Statistics 39 2 233–240.
IEEE
[1]C.- e. Huang and F.- gui Shi, “Bases of [0,1]-matroids”, Hacettepe Journal of Mathematics and Statistics, vol. 39, no. 2, pp. 233–240, Feb. 2010, [Online]. Available: https://izlik.org/JA74CC92PU
ISNAD
Huang, Chun-e. - Shi, Fu-gui. “Bases of [0,1]-Matroids”. Hacettepe Journal of Mathematics and Statistics 39/2 (February 1, 2010): 233-240. https://izlik.org/JA74CC92PU.
JAMA
1.Huang C- e., Shi F- gui. Bases of [0,1]-matroids. Hacettepe Journal of Mathematics and Statistics. 2010;39:233–240.
MLA
Huang, Chun-e., and Fu-gui Shi. “Bases of [0,1]-Matroids”. Hacettepe Journal of Mathematics and Statistics, vol. 39, no. 2, Feb. 2010, pp. 233-40, https://izlik.org/JA74CC92PU.
Vancouver
1.Chun-e. Huang, Fu-gui Shi. Bases of [0,1]-matroids. Hacettepe Journal of Mathematics and Statistics [Internet]. 2010 Feb. 1;39(2):233-40. Available from: https://izlik.org/JA74CC92PU