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In group decision making (GDM), due to complexity of various factors, decision makers (DMs) often provide incomplete preference relations (PRs) in preference matrix. Interval-valued probabilistic uncertain linguistic term set (IVPULTS) is a flexible and accurate tool to depict evaluation information of experts. In this paper, we mainly propose a new concept pertaining to interval-valued probabilistic uncertain linguistic preference relation (IVPULPR) that applies the IVPULTS to preference relations. Firstly, some new basic theoretical concepts of IVPULTS are developed including ordered IVPULTS, normalization method and new expectation function. Secondly, we establish several goal programming models to estimate the unknown elements in incomplete IVPULPR and propose the expected additive consistency of IVPULPR. To improve the consistency level, two optimization models are constructed based on the idea of minimum adjustment. Thirdly, we derive the experts' weights in terms of information uncertainty, where a new method to measure information uncertainty of IVPULTS is proposed. For the sake of improving group consensus, we construct a group consensus index (GCI) and two optimization models depending on the adjustment mechanism of expert weight. Finally, a complete GDM framework with incomplete IVPULPR is devised based on the analysis of IVPULPR consistency and group consensus. Through an experiment analysis by using an UCI dataset, we find that the proposed GDM model can not only precisely express fuzzy preference information of DMs, but also ensure achievement of acceptable consistency and group consensus under the condition of not changing the initial preference as much as possible. [ABSTRACT FROM AUTHOR]