*5.2. Comparison Analysis*

To illustrate the feasibility and effectiveness of the proposed method, different approaches are used to compare with the same numerical example. The comparison is displayed in Table 8.

From Table 8, we know that the optimal alternative obtained by the proposed method is *H*4; it is same as Liao et al. [31], Wang et al. [38], and Zhang et al. [41], which illustrates the feasibility and effectiveness of the proposed decision method.

**Table 8.** Comparison of different methods.


In Liao et al. [9], we can see the best alternative is different from other methods. The reason is that the approach from Liao et al. [9] only considers the algebraic relations of two HFLTSs, and they use the subscript of the linguistic terms directly in the process of operations, which may cause the loss of decision information. The method proposed in this paper is superior to the method in Liao et al. [9] for considering the distance measure, not only from the point of view of algebra, but also from the point of view of geometry.

Furthermore, in the MCDM method proposed by Liao et al. [31], the cosine similarity measure defined by them is not a regular similarity measure, as it cannot precisely deal with the hesitant fuzzy linguistic information that the subscripts of two linguistic terms have in the linear relationship, so that the result obtained in Liao et al. [31] seems unreliable. The proposed similarity measure combining the existing cosine similarity measure and the Euclidean distance measure overcomes this disadvantage; it can improve the accuracy of calculations to some extent, and it appears that the similarity measure that is proposed in this paper outperforms the existing similarity measure of HFLTSs.

In Wang et al. [38], the ranking results are a little different from the proposed method. Because the TODIM method in Wang et al. [38] has complicated parameters, the parameters selected by the expert will affect the ranking results. The proposed approach in this paper is capable of expressing the fuzzy linguistic information more flexibly; it can improve the adaptability of HFLTSs in practice.

In the method proposed by Zhang et al. [41], the evaluation values of each provider were aggregated independently. Because the best evaluation information under one criterion were usually offset by the worst evaluation information under another criterion in the process of aggregation, this may cause the decision information to be distorted. Compared with the method in Zhang et al. [41], the proposed method takes notice of the differences between different alternatives, and it is more meaningful in representing practical examples.

According to the results of comparative analysis, the benefits and advantages of this approach can be given in the following:

