In practical decision-making problems, the coexistence of several complex situations increases the difficulty for decision makers to make reasonable decision, such as attributes outnumber alternatives, heterogeneous relationships among multiple attributes, and individual risk tendency of decision maker. In view of the advantage of probabilistic linguistic term sets (PLTSs) in presenting qualitative information, a novel decision-making approach with PLTSs is constructed to deal with the above special situations simultaneously. To realize this goal, some basic models have been proposed. First of all, to truly reflect the importance of attributes from the heterogeneous relationships, a weight determination model with generalized Banzhaf values is developed to analyze the interaction between combinations of attributes. Then, for analyzing the individual risk tendency of decision maker, the generalized Banzhaf TODIM method with PLTSs is constructed. Moreover, based on the above research results, the generalized Banzhaf TODIM-QUALIFLEX method with PLTSs is developed to solve decision-making problems where the number of attributes exceeds the number of alternatives, the combinations of attributes are interacted with each other, and decision maker is affected by individual risk propensity. Lastly, smartphones selection through online ratings is a typical case of decision-making problems with the above situations, which is designed to illustrate the performance of the proposed method. And its rationality and advantages are further demonstrated through some comparative analyses with other methods.

The power average (PA) operator and Maclaurin symmetric mean (MSM) operator are two important tools to handle the multiple attribute group decision-making (MAGDM) problems, and the combination of two operators can eliminate the influence of unreasonable information from biased decision makers (DMs) and can capture the interrelationship among any number of arguments. The Pythagorean fuzzy linguistic set (PFLS) is parallel to the intuitionistic linguistic set (ILS), which is more powerful to convey the uncertainty and ambiguity of the DMs than ILS. In this paper, we propose some power MSM aggregation operators for Pythagorean fuzzy linguistic information, such as Pythagorean fuzzy linguistic power MSM operator and Pythagorean fuzzy linguistic power weighted MSM (PFLPWMSM) operator. At the same time, we further discuss the properties and special cases of these operators. Then, we propose a new method to solve the MAGDM problems with Pythagorean fuzzy linguistic information based on the PFLPWMSM operator. Finally, some illustrative examples are utilized to show the effectiveness of the proposed method.