A parametric distance-based outranking method for probabilistic linguistic multi-criteria decision-making problems

Probabilistic linguistic term set (PLTS) is a useful tool to flexibly express uncertainty in experts' preferences and has attracted much attention. This paper aims to develop an outranking method with high generalization performance to solve the multi-criteria decision-making (MCDM) problems under a probabilistic linguistic environment. To simplify the computation, a novel standardization process based on the greatest common divisor is first put forward to preprocess PLTSs to have the same probabilities. On this basis, a parametric distance measure between PLTSs is proposed. Next, a new concept called the outranking degree of PLTSs is introduced to compare PLTSs and four kinds of binary relations for PLTSs are then defined by using this concept. Moreover, an outranking framework similar to ELECTRE I method is formulated to rank alternatives for MCDM problems with probabilistic linguistic information. Finally, a case study is provided to confirm the validity and effectiveness of the developed method, and the advantages of this study are further tested by some robustness and comparative analysis.