1School of Mathematics and Statistics, Xidian University, Xi'an, 710071, Shaanxi, China
2School of Information and Technology, Northwest University, Xi'an, 710069, Shaanxi, China
Matroids are important combinatorial structures and connect close-ly with graphs. Matroids and graphs were all generalized to fuzzy setting respectively. This paper tries to study connections between fuzzy matroids and fuzzy graphs. For a given fuzzy graph, we first induce a sequence of matroids from a sequence of crisp graph, i.e., cuts of the fuzzy graph. A fuzzy matroid, named graph fuzzy matroid, is then constructed by using the sequence of matroids. An equivalent description of graphic fuzzy matroids is given and their properties of fuzzy bases and fuzzy circuits are studied.
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