Multi-criteria outranking method based on probability distribution with probabilistic linguistic information

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 multi-criteria decision-making (MCDM) method to address real-world 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 multi-criteria outranking method is developed by modelling pseudo-criteria 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.