Linguistic summarization with fuzzy sets, extracting explicit and concise knowledge from data, has received a great attention because of its compatibility with human cognitive mechanism. The most crucial step in linguistic summarization is certainly the evaluation of linguistic summaries. In this study, a new fuzzy cardinality based possibilistic approach is proposed for evaluating linguistic summaries in interval type-2 fuzzy environment. It is proved that the proposed possibilistic approach satisfies the desired properties defined in the literature. An application of the proposed possibilistic approach is presented on financial time series including the three stocks in Borsa Istanbul (BIST) covering the period for the last 10 years. It is noticed that the proposed possibilistic approach generates more stable results than the probabilistic approach of Boran and Akay (IEEE Trans Cybern 44:1632-1645, 2014).