This study contributes to formulate and solve a real-world problem in the field of healthcare facility location analysis. A new emergency center is to be located in one of the limited potential locations in Firouzabad city from Fars province of Iran in existence of several quantitative criteria where some of them take interval type values. The criteria are selected by the experts of healthcare management. Some data of the problem are obtained from the related databases of the city where some of them are measured practically. An analytical non-linear mathematical formulation with a solution approach based on Lagrange multipliers is proposed to find the importance weights of the criteria of the problem. Then a direct interval-based TOPSIS approach is applied to rank the potential locations and select the best one. Comparing the results obtained from the non-linear model and the interval TOPSIS approach to those of the literature and also the experts’ opinions, the robustness and superiority of the proposed approach can be realized.