On a Paradox of Extended Linguistic Summaries

Continued developments in information technologies allows for increasingly more data to be collected for decision making purposes. While statistical summaries and aggregations are commonly applied to such data, linguistic summaries capture essential features and relationships in the data and better support human users to understand complex data sets. The basic quality measure of linguistic summaries is the truth value, describing the validity of the sentence. Several methods for calculating the truth value have been proposed. In this paper we analyze several popular methods and show a strange, contradictory behavior in case of extended protoforms, which can result in misleading or non-intuitive results to the user. These results highlight the need for further research into linguistic summarization and the computation of truth values for real data sets.