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Connectedness of refined Goetschel-Voxman fuzzy matroids. (English) Zbl 1205.05042
Summary: This paper studies connectedness of Goetschel-Voxman fuzzy matroids (briefly, G-V fuzzy matroids), an analog of connectedness of crisp finite matroids. Based on the results of fuzzy circuits given by Goetschel and Voxman, the transitivity theorem concerning fuzzy circuits of G-V fuzzy matroids is established, and thus the useful notion of refined G-V fuzzy matroid is introduced. The connectedness of refined G-V fuzzy matroids is then defined by using an equivalence relation on the set of all fuzzy points on the ground set, and some expected properties of these G-V fuzzy matroids are presented. Additionally, five kinds of fuzzy matroids are compared.

MSC:
05B35 Combinatorial aspects of matroids and geometric lattices
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