Probabilistic linguistic term sets (PLTSs) have many applications in the field of group decision making (GDM) because it includes both linguistic evaluation and probabilistic distribution when expressing preference information. However, the difference of information credibility in PLTSs is ignored, resulting in an inaccurate representation of decision information and unreasonable probability calculation. In this paper, we first consider the credibility of the information and propose the concept of Z-uncertain probabilistic linguistic variables (Z-UPLVs). Subsequently, the operational rules, normalization, distance and similarity measures, and comparison method of Z-UPLVs are introduced. Then, a probability calculation method based on credibility, an extended TOPSIS method, and some operators are proposed, which can be applied to emergency decision making in the Z-uncertain probabilistic linguistic (Z-UPL) environment. Finally, an emergency decision-making case of COVID-19 patients and comparative analysis illustrate the necessity and effectiveness of this method.

To solve the problems of making decision with uncertain and imprecise information, Zadeh proposed the concept of Z-number as an ordered pair, the first component of which is a restriction of variable, and the second one is a measure of reliability of the first component. But the decision-makers’ confidence in decision-making was neglected. In this paper, firstly, we present a new method to evaluate and rank -numbers based on the operations of trapezoidal Type 2 fuzzy numbers and generalized trapezoidal fuzzy numbers. Then, linguistic-induced ordered weighted averaging operator and linguistic combined weighted averaging aggregation operator are developed to solve multiple attribute group decision-making problems. And we analyze the main properties of them by utilizing some operational laws of fuzzy linguistic variables. Finally, a numerical example is provided to illustrate the rationality of the proposed method.

The linguistic aggregation operator is an important decision-making model that is proving effective for dealing with the input data that takes the form of uncertain information. In this paper, considering the principal component of the intuitionistic fuzzy linguistic variables, we develop a new intuitionistic fuzzy linguistic hybrid aggregation (NIFLHA) operator to solve group decision-making problems under the situation with intuitionistic fuzzy linguistic information. Then, we study some of its main properties by utilizing some operational laws of intuitionistic fuzzy linguistic variables and the different families of the NIFLHA operator. Moreover, the multiperson NIFLHA (MP-NIFLHA) operator is introduced to evaluate the opinions of experts. Finally, an illustrative example about a multiperson decision-making problem is developed to reveal the applicability and the availability of the raised operator.