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On fuzzy independence set systems. (English) Zbl 0921.04006
Summary: The concept of fuzzy pre-independence set system and that of fuzzy independence set system are introduced and investigated. For these systems, the properties “to be closed”, “to be perfect” and “to be strongly regular” are considered. Several propositions concerning bases of closed perfect fuzzy independence set systems are presented. An important subclass of perfect fuzzy independence set systems are fuzzy matroids, introduced by R. Goetschel and W. Voxman [Fuzzy Sets Syst. 27, 291-302 (1988; Zbl 0651.05024), ibid. 31, 253-261 (1989; Zbl 0686.05013)].

MSC:
03E72 Theory of fuzzy sets, etc.
05B35 Combinatorial aspects of matroids and geometric lattices
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References:
[1] Goetschel, R.; Voxman, W., Fuzzy matroids, Fuzzy sets and systems, 27, 291-302, (1988) · Zbl 0651.05024
[2] Goetschel, R.; Voxman, W., Bases of fuzzy matroids, Fuzzy sets and systems, 31, 253-261, (1989) · Zbl 0686.05013
[3] Negoita, C.V.; Ralescu, D.A., Applications of fuzzy sets to systems analysis, (1975), Wiley New York · Zbl 0326.94002
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