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Hesitant fuzzy linguistic term sets (HFLTSs) have attracted lots of attention recently due to their distinguished power and efficiency for dealing with multi-criteria decision making. To extend the applicability of HFLTSs, this paper first presents a more concise comparison formula of hesitant fuzzy linguistic term sets based on probability criterion of uniform distribution and develops novel distance measures considering the hesitance degree. Next, an aggregation scheme is designed to integrate OWD measure into the TOPSIS analysis procedure, in which we calculate different criterion weights according to the distance between criterion values and positive and negative ideal solutions. The weighted distances between the alternatives and positive and negative ideal solutions are calculated. Then the relative closeness degree to the positive ideal solution is calculated to rank all alternatives. Finally, an example is given to illustrate the capabilities and validation of the proposed algorithm.

The core information of hesitant fuzzy linguistic term sets is an important concept in hesitant fuzzy linguistic decision making, which is decided by “min_upper” and “max_lower” operators on hesitant fuzzy linguistic term sets. In the paper, we first provide t-norms and t-conorms on hesitant fuzzy linguistic term sets and discuss their properties. Then, we propose an alternative core information of hesitant fuzzy linguistic term sets based on t-norms and t-conorms. Finally, we utilize the new core information of hesitant fuzzy linguistic term sets for hesitant fuzzy linguistic decision making. We provide an example to illustrate the practicality of the new core information and comparison with the classical core information of hesitant fuzzy linguistic term sets, it seems that the new core information based on t-norms and t-conorms may be an alternative tool for hesitant fuzzy linguistic decision making.

In this paper, the concept of generalized hesitant fuzzy linguistic term set based on 2-tuple linguistic model is provided, then several operators on generalized hesitant fuzzy linguistic term sets and their properties are proposed and analyzed for aggregating generalized hesitant fuzzy linguistic information in linguistic decision making. Especially, based on these new operators, the likelihood-based comparison relations of generalized hesitant fuzzy linguistic term sets are presented, and the generalized hesitant fuzzy linguistic weighted average operator is designed to fuse generalized hesitant fuzzy linguistic term sets in linguistic decision making. An example is used to illustrate the practicality of the aggregation operator based on generalized hesitant fuzzy linguistic term sets, result shows that the proposed method is an useful and alternative method for hesitant fuzzy linguistic decision making.