The supplier selection process of a company depends on numerous criteria which can have differing importance factors. Solving this kind of multiple criteria decision making (MCDM) problem is essential for the long-term strategy of a company. While this problem is examined numerous times throughout the years, the consideration of involving economic, social and environmental factors, i.e. sustainability is becoming a growing necessity for this effort, especially in the recent years. We propose a Choquet integral based fuzzy model to use the data we obtain by converting the linguistic terms of perceived subcontractor performance values to trapezoidal fuzzy numbers. After the performance criteria values are normalized by the fuzzy integral, they are defuzzified into single data points which helps an evaluator to compare. A case study involving a curtain wall company in Turkey (and its 4 subcontractors) is used to demonstrate the effectiveness of the method. The defuzzified results showed which subcontractor is the optimal choice among 4 subcontractors and 17 criteria.