Bases of fuzzy matroids (Q1262318)

The authors pursue their research on fuzzy matroids, a concept they introduced in a previous paper [see these authors, Fuzzy matroids, Fuzzy Sets and Systems 27, 291-302 (1988)]. They now deal with bases of fuzzy matroids. They show that not all matroids have fuzzy bases. They define a special class of fuzzy matroids that have them, called closed fuzzy metroids. They associate to a given fuzzy matroid another one called its closure and using the bases of this closure they induce bases in the given one, called closure bases. Finally they investigate the cardinality of the bases and characterize a class of fuzzy matroids, called regular, whose bases are equicardinal.