Voltage sag, caused by faults, is an important power quality problem. Static transfer switches (STSes) are considered to be one of the efficient remedies for voltage sags. Determination of the installation locations for STSes in a distribution system, therefore, becomes essential for planning a system with sensitive loads. In this paper, the problem is formulated as a fuzzy multi-objective programming problem considering STS investment cost, sensitive bus voltage deviations and total voltage sags. Genetic Algorithms (GAs) using a vertex encoding/decoding are used to solve the problem. The vertex-based Prufer number is used in GAs for encoding/decoding the chromosomes (strings). The Prufer number ensures that the distribution system structure is radial in the iterations. The simulation results obtained from a 33-bus system are used to show the applicability of the proposed method.