A study on fuzzy random minimum spanning tree problems through possibilistic programming and the expectation optimization model

In this paper, we deal with minimum spanning tree problems where each edge weight is a fuzzy random variable. In order to consider the imprecise nature of the decision maker´s judgment, a fuzzy goal for the objective function is introduced. The problem is to seek a spanning tree maximizing the expectation of a degree of possibility or necessity that the fuzzy goal is satisfied. After showing that the problem to be solved is a minimum ratio spanning tree problem, a polynomial-time algorithm is provided to solve the problem.