This paper presents a fuzzy-based genetic algorithm to maximize total system social welfare by best the placement and sizing of TCSC and SSSC devices, considering their investment cost in a doublesided auction market. To introduce more accurate modeling, the valve loading effects are incorporated into the conventional quadratic smooth generator cost curves. In addition, quadratic consumer benefit functions are integrated into the objective function to guarantee that locational marginal prices charged at the demand buses are less than, or equal to, the DisCos benefit, earned by selling the power to retail customers. The proposed approach utilizes fuzzy-based genetic algorithms for optimal scheduling of GenCos and DisCos, as well as optimal placement and sizing of SSSC and TCSC units. In addition, the Newton-Raphson approach is used to minimize the mismatch of the power flow equation. Simulation results on the modified IEEE 14-bus and IEEE 30-bus test systems (with/without line flow constraints, before and after the compensation) are used to examine the impact of SSSC and TCSC on total system social welfare improvement versus their cost. To validate the accuracy of the proposed method, several case studies are presented and simulation results are compared with those generated by genetic and Sequential Quadratic Programming (SQP) approaches.