presented the intuitionistic fuzzy ordered weighted cosine similarity measure and applied it to the group decision-making problem about the choice of investment plan. Ye proposed the cosine similarity measure and the weighted cosine similarity measure between IFSs. One of the important similarity measures is the cosine similarity measure, which is defined in vector space. On the other hand, similarity measure is an important topic in the fuzzy set theory, and it is widely used in some fields, such as pattern recognition, medical diagnosis, and citation analysis. The research on this field has been growing rapidly. The intuitionistic fuzzy linguistic sets (IFLSs) have made great progress in describing linguistic information and to some extent it can be regarded as an innovative construct. For example, is an intuitionistic fuzzy linguistic number (IFLN), 0.2 is the membership degree of the linguistic term, and is the nonmembership degree of the linguistic term. proposed the intuitionistic fuzzy linguistic aggregation operators and applied them to multicriteria group decision-making problems. However, in some practical decision-making problems, the decision-makers may have some indeterminacy in their linguistic evaluation they cannot express their preferences by using only membership degree of a linguistic term. Furthermore, Xu presented the linguistic hybrid aggregation (LHA) operator and applied it to group decision-making. Later, Xu proposed a group decision-making method based on the uncertain linguistic ordered weighted geometric (LOWG) operators and the induced uncertain LOWG operators. considered several group decision-making processes using linguistic ordered weighted averaging (LOWA) operator. proposed a consensus model for group decision-making based on linguistic evaluations information, and Herrera et al. In some practical decision-making problems, the decision-maker regards the linguistic information as the values of linguistic variables that is to say, the values of the variables are not represented by numerical values but are represented by linguistic values, such as “good,” “better,” “fair,” “slightly worse,” and “poor.” Up to now, many people have studied the problem of linguistic multiple criteria decision-making, Herrera and Verdegay proposed the linguistic assessments in group decision-making (GDM) problem in 1993, then Herrera et al. At this time, people often provide their opinions in linguistic term sets. However, due to the fuzziness and uncertainty in the multiple criteria decision-making problems, it is difficult to use the exact values to present qualitative evaluation. A typical feature of IFS is that the membership relations are represented by the membership degree and nonmembership degree, respectively. One of the generalizations of fuzzy set is intuitionistic fuzzy set (IFS), which was introduced by Atanassov. Since the fuzzy set was put forward, it was extended in different aspects. The fuzzy set was proposed by Zadeh and has achieved a great success in various fields, which is considered to be an effective tool to solve the decision-making problems, pattern recognition, and fuzzy inference. Finally, we present the application of the cosine similarity measures for intuitionistic fuzzy linguistic term sets and interval-valued intuitionistic fuzzy linguistic term sets to pattern recognition and medical diagnosis, and the existing cosine similarity measures are compared with the proposed cosine similarity measures by the illustrative example. The main advantage of the proposed cosine similarity measures is that the decision-makers can flexibly select the linguistic scale function depending on the actual semantic situation. Then, the weighted cosine similarity measure and the ordered weighted cosine similarity measure for IFLSs and IVIFLSs are introduced by taking into account the importance of each element, and the properties of the cosine similarity measures are also given. We propose the cosine similarity measures for intuitionistic fuzzy linguistic sets (IFLSs) and interval-valued intuitionistic fuzzy linguistic sets (IVIFLSs), which are expressed by the linguistic scale function based on the cosine function.
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