By multi-objective optimization of designing integrated energy systems for buildings, the Pareto frontier can be obtained consisting of a series of optimal compromise solutions. Since all solutions on Pareto frontiers are non-dominated, it is challenging to identify one "best of the best" solution, which requires posteriori multi-criteria decision-making. However, most existing research only presented the obtained Pareto frontiers, while neglected the decision-making. Therefore, this paper compares four posteriori decision-making approaches in recent publications by solving one identical problem to emphasize the importance of decision-making. An illustrative Pareto frontier is generated by two multi-objective optimization approaches, i.e., eps (epsilon)-constraint and Non-dominated Sorting Genetic Algorithm (NSGA-II). Four categories of multi-criteria decision-making methods, i.e., Shannon entropy, Eulerian distance, fuzzy membership function and evidential reasoning, are further implemented. The decision-making results are different when various approaches are applied. The underlying reasons are analyzed including two key factors, i.e. selection of objectives and shape of Pareto frontier, which provides suggestions of using decision-making approaches in future multi-objective optimization research on building energy systems. (C) 2019 Elsevier B.V. All rights reserved.