Multi-attribute group decision making methods with proportional 2-tuple linguistic assessments and weights

The proportional 2-tuple linguistic model provides a tool to deal with linguistic term sets that are not uniformly and symmetrically distributed. This study further develops multi-attribute group decision making methods with linguistic assessments and linguistic weights, based on the proportional 2-tuple linguistic model. Firstly, this study defines some new operations in proportional 2-tuple linguistic model, including weighted average aggregation operator with linguistic weights, ordered weighted average operator with linguistic weights and the distance between proportional linguistic 2-tuples. Then, four multi-attribute group decision making methods are presented. They are the method based on the proportional 2-tuple linguistic aggregation operator, technique for order preference by similarity to ideal solution (TOPSIS) with proportional 2-tuple linguistic information, elimination et choice translating reality (ELECTRE) with proportional 2-tuple linguistic information, preference ranking organization methods for enrichment evaluations (PROMETHEE) with proportional 2-tuple linguistic information. Finally, an example is given to illustrate the effectiveness of the proposed methods.