Probabilistic Linguistic Group Decision-Making Based on Evidential Reasoning Considering Correlations Between Linguistic Terms

In recent years, evidential reasoning (ER) has provided an effective means to deal with uncertain information depicted by probabilistic linguistic terms sets (PLTSs) during fusion. However, it is worth noting that due to the differences in decision makers’ preferences and understanding of linguistic terms, there is a significant difference between the level of ER and the term in PLTSs, which hinders further development of ER in PLTSs. To fill this gap, this study modifies the existing ER algorithm with linguistic correlation and introduces it to multiple attribute group decision-making (MAGDM) problems within PLTSs. First, the correlations between different linguistic terms are defined based on the expressive preferences of decision-makers. Second, the correlation between different linguistic terms is integrated into the original ER to reduce the contradiction caused by expressive preferences. Moreover, linguistic correlation is also involved in the calculation of reliability to adjust the distance measure, which can reduce the unreliability caused by the preferences expressed by decision-makers. Then, nonlinear programming models are conducted to drive expert reliability. Thereafter, the modified ER algorithm is employed to integrate expert opinions into a comprehensive evaluation of alternatives. Finally, an illustrative example of an industry evaluation problem is conducted to verify the robustness and validity of the proposed method.