In this paper, an interval single-sided fuzzy chance-constrained mixed-integer programming model is developed for the fossil fuel management of a multi-source district heating system under multiple uncertainties, where the heat-supply-capacity expansion planning can also be reflected. The non-dimensional comprehensive equations method is simultaneously improved to quantify the ambiguous heat provisions, utilized as a type of boundary condition inputs to the proposed model. A real-world case study of a heating system located in northeastern China is undertaken to show the feasibility and applicability of the proposed methods. To obtain the reasonable fossil-fuel management schemes, multi-dimensional constraints are incorporated into the model based on a comprehensive consideration in terms of fuel supply and demand, quality and quantity, economic cost and environment protection, as well as their interactions. Results obtained from the case study indicate that the solutions for both continuous and binary variables have been generated, which are useful for identifying suitable fuel-supply patterns and heat-source operational modes for a heating system under different system reliabilities and heating-load distribution states. In addition, the results also reveal that the fossil-fuel management and heating-capacity-expansion pattern, as well as the economic cost and pollutant emission performances are sensitive to the thermal coefficient and system reliability level, which may provide in-depth analyses of tradeoffs for further supporting robust fossil-fuel management under uncertainty.