Abstract A possibilistic framework is proposed to assess the risk possibility of transmission capacity in long-term planning studies. Because the detailed forecasting data always include massive uncertainties relating to environment, the uncertainties in load variations can be dealt with using fuzzy set theory. A promising algorithm is developed to incorporate these uncertainties into the possibility distribution of nodal load power. To explore the impacts of uncertainties in load variations on transfer capacity assessment, nine cases with various future states are compared and classified by different linguistic aspects in terms of load growth rates and forecasting errors. The results of the possibility model are compared with the results of the probability analysis. Results show that the proposed possibility model can consider the exposure to risk of some possible states, and a confident result is attained. Furthermore, some useful rules for assessing transmission capacity are summarized to help planners in the process of decision making. The proposed technique is implemented on the IEEE 25-bus system to demonstrate its feasibility.