This paper formulates a risk-based robust decision making framework for a Smart Building (SB) energy management system under demand and supply uncertainty. The last aim of the resulting multi-objective mixed integer linear programming is to minimize the total day-ahead cost of the system, in which the objective functions are the total cost of heat and power co-generation, and the total emissions cost. In this way, the first trade-off is made between economy and environmental impacts, while the second trade-off is occurred between solution robustness and model robustness. The results from a numerical example demonstrate the robustness and flexibility of the overall framework in dealing with Decision Makers (DMs) risk aversion level. In average, a more conservative decision maker faces a 75% increase in total cost, a 90% increase in electricity generation cost, and an increase of 8% in emissions cost compared with a more risk-seeker DM. Compared with the conventional power generation system, using the proposed Microgrid-based system brings about 92%, 93%, and 85% savings in total cost, cost of power supply, and total emissions cost, respectively. (C) 2018 Elsevier Ltd. All rights reserved.