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Rank Functions of Fuzzy Greedoids

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DOI: 10.4236/ojdm.2015.54006    3,920 Downloads   4,319 Views   Citations

ABSTRACT

Fuzzy greedoids were recently introduced as a fuzzy set generalization of (crisp) greedoids. We characterize fuzzy languages which define fuzzy greedoids, give necessary properties and sufficient properties of the fuzzy rank function of a fuzzy greedoid, give a characterization of the rank function for a weighted greedoid, and discuss the rank closure of a fuzzy greedoid.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Tedford, S. (2015) Rank Functions of Fuzzy Greedoids. Open Journal of Discrete Mathematics, 5, 65-73. doi: 10.4236/ojdm.2015.54006.

References

[1] Zadeh, L.A. (1965) Fuzzy Sets. Information and Control, 8, 338-353.
http://dx.doi.org/10.1016/S0019-9958(65)90241-X
[2] Goetschel Jr., R. and Voxman, W. (1988) Fuzzy Matroids. Fuzzy Sets and Systems, 27, 291-301.
http://dx.doi.org/10.1016/0165-0114(88)90055-3
[3] Goetschel Jr., R. and Voxman, W. (1991) Fuzzy Rank Functions. Fuzzy Sets and Systems, 42, 245-258.
http://dx.doi.org/10.1016/0165-0114(91)90150-O
[4] Goetschel Jr., R. and Voxman, W. (1992) Spanning Properties for Fuzzy Matroids. Fuzzy Sets and Systems, 51, 313-321.
http://dx.doi.org/10.1016/0165-0114(92)90022-V
[5] Al-Hawary, T. (2011) Fuzzy Greedoids. International Journal of Pure and Applied Mathematics, 70, 285-295.
[6] Korte, B. and Lovász, L. (1981) Mathematical Structures Underlying Greedy Algorithms. Fundamentals of Computation Theory. Lecture Notes in Computer Sciences, 117, 205-209.
http://dx.doi.org/10.1007/3-540-10854-8_22
[7] Korte, B., Lovász, L. and Schrader, R. (1991) Greedoids. Springer-Verlag, New York.
http://dx.doi.org/10.1007/978-3-642-58191-5
[8] Gordon, G. and McMahon, E. (1989) A Greedoid Polynomial Which Distinguishes Rooted Arborescences. Proceedings of the American Mathematical Society, 107, 287-298.
http://dx.doi.org/10.1090/s0002-9939-1989-0967486-0

  
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