This paper investigates multiple attribute group decision making (MAGDM) with probabilistic linguistic term sets (PLTSs) and proposes an integrated decision method for solving such problems. First, a novel distance measure of PLTSs is defined, and then a distance-based entropy measure and similarity measure are proposed. Subsequently, supposing that elements are independent of each other, an induced generalized PL-ordered weighted average (IG-PLOWA) operator and an induced generalized PL hybrid average (IG-PLHA) operator are introduced. Afterwards, considering some cases in which elements are interactive, an induced generalized probabilistic linguistic Shapley hybrid average (IG-PLSHA) operator is presented, and some desirable properties of this operator are further studied. Fusing the entropy and similarity degrees of decision makers (DMs), DM weights are determined objectively. Then, considering the interactions among attributes and the psychological behaviors of DMs, the models for obtaining the fuzzy measures on the attribute set are built based on the Shapley values and the prospect theory. Finally, taking DMs' risk attitudes into account, an integrated decision making method based on the IG-PLSHA operator is developed. At length, an example is provided to illustrate the feasibility and practicality of the developed method.