The main purpose of this paper is to design a method for ranking the competitive advantages of container shipping liner companies. The major issue that arises in applying this method is capturing and dealing with qualitative and uncertain information in a complex decision-making environment. A novel hybrid scheme combining intuitionistic fuzzy linguistic variables with optimal determining weights is proposed to assess the competitive advantages of five representative shipping liner companies. Several experts in the related field are invited to adopt intuitionistic fuzzy sets into their group decision-making on the basis of four aspects of competitive advantage held by each shipping liner firm. The intuitionistic fuzzy linguistic variables are employed to evaluate data under each key attribute, which is extracted from the public reports issued by each company concerned. The result validates the effectiveness of the scheme with intuitionistic fuzzy linguistic variables, and it is found that the experts involved more easily grasp the classical intuitionistic fuzzy evaluation tool, benefiting the effectiveness of competitive advantage assessments of liner companies.