Connectedness of refined Goetschel–Voxman fuzzy matroids

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.