In this paper, we deal with a minimum spanning tree programming problem
involving fuzzy random weights and propose a fuzzy random programming model
using possibility and necessity measures. First, we focus on the degree of possibility
or necessity that the objective function satisfies a fuzzy goal. Next, we formulate
the problem to minimize the variance of the degree that the objective function value
satisfies a fuzzy goal. It is shown that the problem is transformed into a deterministic
equivalent one, which is a nonlinear minimum ratio spanning tree problem with a
constraint. In order to solve the problem, a Tabu Search (TS) algorithm is developed.