To address the situation where the Multi-criteria decision-making (MCDM) problems with hesitant fuzzy preference relations (HFPRs), this study develops group decision-making considering the best and worst indexes simultaneously. First, the concepts of best and worst multiplicative consistency indexes of HFPRs are proposed, and then the concept of acceptable multiplicative consistent HFPRs is developed, which takes into accounted best consistency index (BCI) and worst consistency index (WCI). Second, several optimization models are constructed for improving the consistency of HFPRs when they are unacceptable. The main characteristic of the constructed optimization models is that two predefined thresholds for the BCI and WCI are taken into accounted. It requires all the fuzzy preference relations (FPRs) derived from original HFPRs meet the threshold of WCI, and there is a FPR meets the threshold of BCI. Third, the proposed consistency checking and improving processes are extended to incomplete evaluation information. Fourth, an algorithm is designed for deriving priority weights from acceptable consistent HFPRs/incomplete HFPRs. Finally, an illustrative example in conjunction with comparative analysis is used to demonstrate the proposed method is feasible and efficiency for practical MCDM problems.