Multi-criteria sorting decision making based on dominance and opposition relations with probabilistic linguistic information

The probabilistic linguistic term set (PLTS) is a powerful tool for describing linguistic evaluations derived from expert teams and has adequate capability to identify preferences among different evaluations. Due to the practicability of PLTSs, probabilistic linguistic decision making problems have been widely investigated in recent years. However, no study on probabilistic linguistic outranking relations has been conducted. This study aims to explore effective processing for the complex two-dimension structure of PLTSs and formulate probabilistic linguistic dominance and opposition relations for multi-criteria sorting decision making. Linguistic scale functions, which can generate different semantics for linguistic variables under different decision making environments, are introduced to deal with the linguistic terms in PLTSs. In this way, the probabilistic linguistic dominance degree, concordance and discordance indices are defined by systematically comparing the probabilities of PLTSs. Then, two kinds of outranking relations with dominance and opposition for PLTSs are formulated based on the defined outranking indices. Subsequently, an innovative sorting decision making framework is constructed by exploring the outranking relations between alternatives and characteristic actions under multiple criteria and implementing the outranking aggregation and exploitation. Finally, this framework is demonstrated using an illustrative example with result analyses and comparison discussions.