A hybrid multi-criteria decision-making framework of EWM-BWM-TODIM based on Linguistic Pythagorean fuzzy environment

Linguistic Pythagorean fuzzy set (LPFS) combines Pythagorean fuzzy sets and linguistic term sets, which can effectively deal with fuzzy information in multi-criteria decision-making (MCDM). The entropy weight method (EWM) can reflect the objectivity of decision information, while the best-worst method (BWM) can reflect the subjectivity of decision-makers. The interactive multi-criteria decision-making (TODIM) method can describe the different preferences of decision-makers for gains and losses. In this paper, EWM, BWM, and TODIM are combined and applied to LPFS for the first time. First, we calculate the objective weight and subjective weight of each criterion through EWM and BWM and combine them to get the final weight to balance subjectivity and objectivity. Then, this paper selects the best scheme through TODIM sorting. In conclusion, the LPFS-EWM-BWM-TODIM model is established in this paper. Finally, the paper applies this model to the selection of corporate investment strategy and green mine, verifies the effectiveness of the method, and carries out comparative analysis and sensitivity analysis, proving the rationality and robustness of the model.