The reference ideal TOPSIS method for linguistic q-rung orthopair fuzzy decision making based on linguistic scale function

The linguistic q-rung orthopair fuzzy set is a powerful tool in representing linguistic assessments. Considering that the traditional decision making methods cannot deal with the situation that the best choice may not be the minimum or the maximum but between them, we propose an innovative TOPSIS method with linguistic q-rung orthopair fuzzy numbers based on the reference ideal theory. Firstly, the new operations of linguistic q-rung orthopair fuzzy sets are introduced based on the linguistic scale function. In addition, we propose the Minkowski distance measure of linguistic q-rung orthopair fuzzy numbers to make up for the defects of the existing distance measures based on the linguistic scale function. By using the new operations of linguistic q-rung orthopair fuzzy numbers, we propose the linguistic q-rung orthopair fuzzy weighted averaging operator and the linguistic q-rung orthopair fuzzy weighted geometric operator to aggregate linguistic decision information. Furthermore, we develop a reference ideal TOPSIS method to the linguistic q-rung orthopair fuzzy decision making problems. Finally, an example concerning the postgraduate entrance qualification assessment is given to illustrate the feasibility of the proposed method. Some comparative analysis is also given to show the efficiency of the method, in addition, the sensitivity analysis and stability analysis of the proposed method are also given.