Fuzzy Sets and Systems
Fuzzy Sets and Systems
Abstract and concrete categories
Abstract and concrete categories
Fuzzy Sets and Systems
Fuzzy Sets and Systems
On fuzzy independence set systems
Fuzzy Sets and Systems
Fuzzy Sets and Systems
Axioms for bases of closed regular fuzzy matroids
Fuzzy Sets and Systems
Connectedness of refined Goetschel--Voxman fuzzy matroids
Fuzzy Sets and Systems
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This paper represents an attempt to define a closure operator which can determine Geotschel and Voxman fuzzy matroid (GV fuzzy matroid for short), and presents an application of the notion co-tower in GV fuzzy matroids. Two bijections are obtained for a given finite set X, one is from A"X={@d@?[0,1]^X|(X,@d)is a closed singular GV fuzzy matroid or a closed proper single GV fuzzy matroid} to B"X (the set of all triples of operators on X satisfying some fuzzy closure axioms), the other is from FM(X) (the set of all systems of GV independent fuzzy sets on X) to M^c(X) (the set of all co-tower structures on X). The first bijection shows that a triple of operators on X satisfying some fuzzy closure axioms can determine a closed singular GV fuzzy matroid or a closed proper single GV fuzzy matroid, and the second shows that a co-tower structure on X can determine a GV fuzzy matroid. As a result, it is proved that the category FM of all GV fuzzy matroids and continuous mappings is isomorphic to the category M^c of all co-towers in M (the category of all matroids and continuous mappings) and continuous mappings.