Spanning Tree Problem of Uncertain Network

In this paper we consider a spanning tree problem of uncertain network, which is a natural uncertain variation of the deterministic minimum spanning tree problem. By means of uncertainty theory, we propose three types of minimum spanning tree models for uncertain network, i.e., expected minimum spanning tree, α-minimum spanning tree, and distribution minimum spanning tree. Generally, we can theoretically give the inverse uncertainty distributions of uncertain spanning trees of an uncertain network. A 99-table algorithm for finding the inverse uncertainty distribution of uncertain spanning tree is given. Some numerical examples are illustrated according to the graphical topology structure of the uncertain spanning tree problem.