Distance measure for Fermatean fuzzy linguistic term sets based on linguistic scale function: An illustration of the TODIM and TOPSIS methods

In this paper, we propose the Fermatean fuzzy linguistic term set (FFLTS) based on the linguistic scale function. A new similarity measure between FFLTSs is constructed, which not only includes the linguistic scale function but also combines the cosine similarity measure and Euclidean distance measure, and then the related properties of the similarity measure are proven. A corresponding distance measure is obtained according to the relationship between the distance measure and similarity measure. Furthermore, we extend the Tomada de Decisão Interativa Multicritério (TODIM) method and the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) method to the corresponding distance measure under the Fermatean fuzzy linguistic environment. The main advantages of the proposed methods are that they can not only transform linguistic information effectively in different decision environments but also improve the adaptability of FFLTS in decision-making problems. Finally, a numerical example is provided to illustrate the effectiveness and feasibility of the proposed methods, which are also compared with other existing methods. The sensitivity analysis of the parameters and the influence of linguistic scale function on the ranking results are also discussed.