Consistency Adjustment Strategy and Multiplicative DEA Cross-Efficiency for Group Decision-Making with Probabilistic Linguistic Preference Relations

Probabilistic linguistic preference relation (PLPR) is an effective tool for decision-makers (DMs) to express their preferences in the decision-making process. However, the preferences provided by DMs may be inconsistent, which may lead to unreasonable decision-making results. Therefore, this paper proposes a group decision-making (GDM) method with PLPRs based on a consistency improvement algorithm and an improved multiplicative data envelopment analysis (DEA) model. For a given inconsistent PLPR, we first propose an optimization model to obtain a complete consistent PLPR. And then we use the proposed consistency adjustment algorithm to get a PLPR with acceptable consistency. Subsequently, we develop a transformation function that can transform PLPRs into multiplicative preference relations (MPRs). Furthermore, we put forward an improved multiplicative DEA model to obtain the priority vector of MPR, and the reliable ranking order of all alternatives is determined. Finally, a numerical example of cold storage construction for storing fresh products is presented to show the effectiveness and applicability of the proposed GDM method.