Prospect theory based method for heterogeneous group decision making with hybrid truth degrees of alternative comparisons Abstract   This paper develops a new prospect theory based method for heterogeneous multiattribute 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 multiobjective fuzzy program of maximizing all the importance of preference relations is built to determine the decision makersxe2x80x99 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 biobjective hybrid fuzzy program is constructed to acquire the attribute weights, PIS, and NIS simultaneously. Employing the defuzzified technology, the biobjective 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.

Multicriteria outranking method based on probability distribution with probabilistic linguistic information Abstract   The probabilistic linguistic term set (PLTS) is a powerful tool for describing qualitative evaluations derived from teams of experts, and it has adequate description capability in identifying preferences among different evaluations. The structure of PLTSs is complex, however, and many existing studies do not deal with probabilistic linguistic information appropriately. Hence, this study explores the simple and effective processing of PLTSs and develops an applicable multicriteria decisionmaking (MCDM) method to address realworld problems. First, PLTSs are characterised as probability distributions, and the corresponding cumulative distribution functions are presented. In this manner, the concordance and discordance indices of PLTSs are defined by the systematic comparison between different cumulative distribution functions. Subsequently, four kinds of novel binary relations for PLTSs are proposed. Then, an innovative multicriteria outranking method is developed by modelling pseudocriteria and implementing outranking aggregation and exploitation. Finally, an illustrative example concerning new energy selection is provided to elucidate the application of the developed method. The strengths of this method are verified further by some analyses and discussions.