This paper deals with a minimum spanning tree programming problem
involving fuzzy random weights. New decision making 
models are proposed to maximize the probability that 
the degree of possibility or necessity that the fuzzy goal for 
the fuzzy random objective function is satisfied is greater 
than or equal to a satisficing level. 
It is shown that the original problems involving fuzzy random variables 
are transformed into deterministic equivalent ones which are nonlinear 
maximum spanning tree problems through the proposed models. 
An efficient tabu search algorithm is developed to solve the resulting 
nonlinear maximum spanning tree problems.