In human language, there are plenty of fuzzy conceptions without exact bound, thus it is vital to establish some reasonable models for the investigations about human behaviors. Fuzzy linguistic is an emerging interdisciplinary, with an integration of fuzzy set theory and modern linguistics, and plays an important role in the handling of natural language, information extraction and decision support. The work attempts to bridge the extended fuzzy linguistics and scientific decision making. In this paper, we propose the linguistic probabilistic hesitant fuzzy set (LPHFS), and define some operations for these sets. Then the power average operator for LPHFSs are presented and a model for decision making on the perspective of information aggregation is developed. In the end, an illustrative example about the assessment of the investment on works of art shows the validity of the model.