Managing incomplete general hesitant linguistic preference relations and their application

Hesitant linguistic preference relations (HLPRs) are useful tools for decision makers (DMs) to express their qualitative judgements. However, the traditional HLPRs have one prominent drawback, which is to sort the linguistic values in a hesitant linguistic set. This will distort the DMs' initial judgements. In the present paper, a revised definition of HLPR, called general HLPR (GHLPR), was proposed. A characterization was explored for LPRs. Then, the characterization was extended to GHLPRs. Based on the characterization, the estimation of unknown entries in incomplete GHLPRs were carried out by two algorithms. The group decision-making problems with incomplete GHLPRs were settled by another algorithm. Finally, a case study was illustrated, and comparisons showed that our methods were more reasonable than the existent methods.