Cosine similarity measures between q-rung orthopair linguistic sets and their application to group decision making problems

The q-rung orthopair linguistic set (q-ROLS), a combined version of linguistic term sets and q-rung orthopair fuzzy set, is an efficient mathematical tool to accomplish the imprecise information while solving the decision-making problems. Under this environment, we propose additional operations and relations to deal with the decision information, and some properties are well proved. Furthermore, we propound some cosine similarity measures and weighted cosine similarity measures for q-ROLSs based on the traditional cosine similarity measures with a brief study of related properties. In the proposed similarity measures, various linguistic scale functions are utilized in order to take into account the semantics of linguistic terms. Besides this, we employ the stated q-rung orthopair linguistic similarity measures to multi-criteria group decision making problems, in which the weights of DMs are delineated by the projection of individual decisions on the ideal decision results. At last, a numerical example is used to demonstrate the practicality of the suggested technique, and its efficacy is validated by comparison with prevailing techniques. The suggested method’s sensitivity and stability analyses are also provided.