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Fuzzy bases of fuzzy independent set systems. (English) Zbl 1368.05018
Summary: Compactness, closeness and SC are conditions to ensure the existence of fuzzy bases for polymatroids, G-V fuzzy matroids and H fuzzy matroids respectively. In this work, relations of these three conditions with different fuzzy independent systems are studied. Furthermore, the equivalence of compactness, closeness and SC for G-V fuzzy matroids is proved and the existence of fuzzy bases of H fuzzy matroids is verified. Finally, it has been pointed out that H fuzzy matroids and E fuzzy matroids induced from polymatroids are the same and the question whether an H fuzzy matroid is a fuzzy pre-matroid is solved.

MSC:
05B35 Combinatorial aspects of matroids and geometric lattices
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[1] Edmonds, J., Submodular functions, matroids and certain polyhedra, (Guy, R.; etal., Combinatorial Structures and Their Applications, (1970), Gordon and Breach New York), 69-87 · Zbl 0268.05019
[2] Goetschel, R.; Voxman, W., Fuzzy matroids, Fuzzy Sets Syst., 27, 291-302, (1988) · Zbl 0651.05024
[3] Goetschel, R.; Voxman, W., Bases of fuzzy matroids, Fuzzy Sets Syst., 31, 253-261, (1989) · Zbl 0686.05013
[4] Goetschel, R.; Voxman, W., Fuzzy circuits, Fuzzy Sets Syst., 32, 35-43, (1989) · Zbl 0669.05025
[5] Goetschel, R.; Voxman, W., Fuzzy matroids and a greedy algorithm, Fuzzy Sets Syst., 37, 201-213, (1990) · Zbl 0736.05023
[6] Hsueh, Y. C., On fuzzification of matroids, Fuzzy Sets Syst., 53, 317-327, (1993) · Zbl 0789.05020
[7] Li, S. G.; Xin, X.; Li, Y. L., Closure axioms for a class of fuzzy matroids and co-towers of matroids, Fuzzy Sets Syst., 158, 1246-1257, (2007) · Zbl 1115.05013
[8] Li, X. N.; Liu, S. Y.; Li, S. G., Connectedness of refined GV-fuzzy matroids, Fuzzy Sets Syst., 161, 2709-2723, (2010) · Zbl 1205.05042
[9] Li, Y. L.; Zhang, G. J.; Lu, L. X., Axioms for bases of closed regular fuzzy matroids, Fuzzy Sets Syst., 161, 1711-1725, (2010) · Zbl 1215.05023
[10] Xin, X.; Shi, F. G., Categories of bi-fuzzy pre-matroids, Comput. Math. Appl., 59, 1548-1558, (2010) · Zbl 1189.05044
[11] Novak, L. A., On fuzzy independence set systems, Fuzzy Sets Syst., 91, 365-374, (1997) · Zbl 0921.04006
[12] Novak, L. A., On goetschel and voxman fuzzy matroids, Fuzzy Sets Syst., 117, 407-412, (2001) · Zbl 0966.05017
[13] Welsh, D. J.A., Matroid theory, (1976), Academic Press London · Zbl 0343.05002
[14] Whitney, H., On the abstract properties of linear dependence, Am. J. Math., 57, 509-533, (1935) · JFM 61.0073.03
[15] Shi, F. G., A new approach to the fuzzification of matroids, Fuzzy Sets Syst., 160, 696-705, (2009) · Zbl 1188.05046
[16] Yao, W., Basis axioms and circuits axioms for fuzzifying matroids, Fuzzy Sets Syst., 161, 3155-3165, (2010) · Zbl 1205.05043
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