Prospect theory based method for heterogeneous group decision making with hybrid truth degrees of alternative comparisons

This paper develops a new prospect theory based method for heterogeneous multi-attribute group decision making with hybrid fuzzy truth degrees of alternative comparisons. The heterogeneous evaluations of attributes are expressed by intuitionistic fuzzy sets (IFSs), hesitant fuzzy sets (HFSs), trapezoidal fuzzy numbers (TrFNs), intervals, real numbers and probabilistic linguistic term sets (PLTSs), respectively. The fuzzy truth degrees contain five kinds of different forms: HFSs, IFSs, TrFNs, intervals and PLTSs. Firstly, based on prospect theory, the individual overall prospect value of alternative is defined considering the positive ideal solution (PIS) and negative ideal solution (NIS) simultaneously. Then, a multi-objective fuzzy program of maximizing all the importance of preference relations is built to determine the decision makers' weights. The group consistency index (GCI) and group inconsistency index (GICI) are defined using the overall prospect values of alternatives. By minimizing GICI and maximizing GCI, a bi-objective hybrid fuzzy program is constructed to acquire the attribute weights, PIS, and NIS simultaneously. Employing the defuzzified technology, the bi-objective hybrid fuzzy program is converted into a single objective crisp program for resolution. Subsequently, the collective overall prospect values are computed to generate the collective ranking of alternatives. An example is analyzed to validate the proposed method.