On consistency and priority weights for interval probabilistic linguistic preference relations

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.