2-Dimension linguistic PROMETHEE methods for multiple attribute decision making

In multiple attribute decision making (MADM) problems, 2-dimension linguistic term set (2DLTS) is useful for modelling both the linguistic evaluations on alternatives and the decision makers' self-assessments. This paper extends the preference ranking organization method for enrichment evaluations (PROMETHEE) methods to solve 2-dimension linguistic MADM problems. The extended PROMETHEE methods with 2DLTSs are mainly based on the improvement of the preference functions. For measuring two 2-dimension linguistic elements (2DLEs) in the improved preference functions, the possibility degree (PD) for 2DLEs is proposed to describe the PD of one 2DLE no less than another. It is shown that the PD for 2DLEs can measure the PD between two incomparable 2DLEs as well as two comparable 2DLEs. Furthermore, two examples are given to illustrate the effectiveness and flexibility of the proposed methods in solving the MADM problems evaluated by 2DLEs. (C) 2019 Elsevier Ltd. All rights reserved.