In this study, a fractile-based robust stochastic programming (FRSP) method is developed for planning electric power systems under uncertainty. FRSP can tackle uncertainties expressed as possibilistic and probabilistic distributions in constraints and objective function. The developed FRSP is applied to long-term electric power systems planning, where two cases are examined based on different greenhouse gas (GHG) and air-pollutant management policies. During power-generation processes, various losses may affect energy consumption rate, leading to uncertainties in energy conversion efficiency. From a long-term planning point of view, energy demands from multiple end-users may vary due to population increase and economic development. A variety of scenarios associated with different levels of energy conversion efficiency and energy demand are analyzed. Decision variables with p-necessity are useful for managers to sustain and/or modify the decision schemes for energy activities through incorporation of their implicit knowledge. The results obtained can not only be used for generating desired energy resource/service distribution, but also help decision makers identify desired policies for GHG and air-pollutant mitigation with a cost-effective manner.