In this paper, we have studied the constrained version of the fuzzy minimum spanning tree problem.Costs of all the edges are considered as fuzzy numbers.Using the measure, a generalization of credibility measure, the problem here is formulated as chance-constrained programming problem and dependent-chance programming problem according to different decision criteria.Then the crisp equivalents are derived when the fuzzy costs click here are characterized by trapezoidal fuzzy numbers.Furthermore, a fuzzy simulation based hybrid genetic algorithm is designed to solve the proposed models using Prüfer like code representation of labeled trees.