Fuzzy quadratic minimum spanning tree problem

In this paper, a fuzzy quadratic minimum spanning tree problem is formulated as expected value model, chance-constrained programming and dependent-chance programming according to different decision criteria. Then the crisp equivalents are derived when the fuzzy costs are characterized by trapezoidal fuzzy numbers. Furthermore, a simulation-based genetic algorithm using Prüfer number representation is designed for solving the proposed fuzzy programming models as well as their crisp equivalents. Finally, a numerical example is provided for illustrating the effectiveness of the genetic algorithm.