In this study, an integrated fuzzy possibilistic-joint probabilistic mixed-integer programming (FPJPMIP) model is developed and applied to the expansion planning of power generation under uncertainty. As an extension of existing fuzzy possibilistic programming and joint probabilistic programming, the FPJPMIP addresses system uncertainties in the model's left- and right-hand sides (with the expression of possibilistic and probabilistic distributions). Its applicability has been demonstrated by the application to a hypothetic power generation problem. The developed method is applied to a case of power generation expansion planning, where desirable solutions are obtained. Willingness to pay higher costs will promise system stability. A desire to reduce the costs will get into the risk of potential system failure.