When expressing preferences with different probability weights for different linguistic terms, only partial assessment information is usually to be provided. Then the probability information can be normalized to the interval probability, hence, using interval probabilistic linguistic term sets (IPLTs) is more appropriate. Considering this situation, interval probabilistic linguistic preference relation (IPLPR) is proposed. To measure the consistency of IPLPR, the consistency definition of IPLPR is put forward. For the consistent IPLPR, from which an expected consistent PLPR can be obtained, we can obtain interval weights as the final priorities by using the pairs of linear programming models. We also create the probabilistic linguistic geometric consistency index (PLGCI) of PLPRs to judge whether the IPLPR is satisfactorily consistent. For an unsatisfied consistency IPLPR, the adjusting algorithm is proposed. Probability information is firstly considered to be adjusted. If it is not possible to achieve satisfactory consistency through the adjustment of probability information, then the linguistic terms will be adjusted. In addition to examples of different situations, such as the consistency, satisfactory consistency and consistency improvement, the application example is also given to show the practicability of the proposed methods.

Best-Worst method (BWM) is a new multi-criteria decision-making method based on pairwise comparisons, but only the comparisons concerning the best and the worst alternatives or criteria. This method shows some significant advantages in the simplicity with a less requirement of comparison data and reliability with better consistency. This paper proposes a new consistency measure method based on the distance of the vectors of reference comparisons in BWM because the difference of the preference in two vectors directly affects the reliability of results. Through the establishment of the threshold of consistency ratio, we supplement the definition of satisfactory consistency of the comparisons in BWM. With comparisons satisfying the acceptable consistency, we use linear programming models to find all possible priority weights between the preferences given by decision maker and derive interval weights. For comparisons with unacceptable consistency, another approach is presented to find the interval weights meeting the consistent requirement. At last, several examples are used to illustrate the details of process.