Expected consistency-based model and multiplicative DEA cross-efficiency for group decision-making with incomplete distribution linguistic preference relations
Affiliations: [a] School of Business, Anhui University, Hefei, Anhui, China
| [b] Department of Industrial and Systems Engineering, North Carolina State University, Raleigh, USA
| [c] School of Mathematical Sciences, Anhui University, Hefei, Anhui, China
Abstract: Faced with complex decision problems, distribution linguistic preference relation (DLPR) is an effective way for decision-makers (DMs) to express preference information. However, due to the complexity of the decision-making environment, DMs may not be able to provide complete linguistic distribution for all linguistic terms in DLPRs, which results in incomplete DLPRs. Therefore, in order to solve group decision-making (GDM) with incomplete DLPRs, this paper proposes expected consistency-based model and multiplicative DEA cross-efficiency. For a given incomplete DLPRs, we first propose an optimization model to obtain complete DLPR. This optimization model can evaluate the missing linguistic distribution and ensure that the obtained DLPR has a high consistency level. And then, we develop a transformation function that can transform DLPRs into multiplicative preference relations (MPRs). Furthermore, we design an improved multiplicative DEA model to obtain the priority vector of MPR for ranking all alternatives. Finally, a numerical example is provided to show the rationality and applicability of the proposed GDM method.
Keywords: Group decision making, distribution linguistic preference relation, incomplete distribution linguistic preference relation, expected consistency, multiplicative DEA cross-efficiency
