Abstract—An inverse spanning tree problem is to make theleast modification on the edge weights such that apredetermined spanning tree is a minimum spanning tree. In thispaper, based on the notion of fuzzy α-minimum spanning tree,the inverse spanning tree problem with fuzzy edge weights isdiscussed and formulated as a fuzzy programming model withsome chance constraints. It shows that when all the edgeweights are assumed to be independent fuzzy variables withregular credibility distributions, the proposed model can bereformulated into a traditional nonlinear programmingaccording to the equivalent condition of fuzzy α-minimumspanning tree characterized by a set of constraints on non-treeedges and their tree paths. Moreover, if all the fuzzy weights aretriangular fuzzy numbers, a linear programming problem can beobtained and solved efficiently with the help of some welldeveloped software packages.