The linguistic term set is an applicable and flexible technique in qualitative decision making (QDM). To further develop the linguistic term set, this paper proposes a generalized asymmetric linguistic term set (GALTS) based on the asymmetric sigmoid semantics, which belongs to an asymmetric and non-uniform linguistic term set, and can be used to address the QDM problems involving risk appetites of the decision maker (DM). Then, a value-at-risk fitting (VARF) approach is designed for obtaining the risk appetite parameters of the GALTS and six desirable properties of the GALTS are analyzed, i.e., asymmetry, non-uniformity, generality, variability, range consistency, and diminishing-utility. Based on the above approaches and the generalized asymmetric linguistic preference relations (GALPRs), a QDM process involving risk appetites of the DM is designed. Because the GALPRs consist of subjective information provided by the DM, the process is not perfectly consistent and is usually difficult to change or repeat. Thus, a transitivity improvement approach is investigated, and the corresponding calculation steps are provided. Finally, an example dealing with the problem of investment decision making is provided, and the results fully demonstrate the validity of the proposed methods for QDM involving risk appetites. 
Generalized asymmetric linguistic term set and its application to qualitative decision making involving risk appetites